I'm stranded on an alien planet. How do I measure an earth year without a clock?

I just got shoved through a stargate onto a planet I don't know. I was told the gate would open again in exactly one Earth year.

I wasn't carrying anything; I don't even have my watch. How do I know what day I can return home?

I can count days, but first, I need to determine the absolute length of this planet's day. How can I do that?

I can't just count off seconds - way too inaccurate over a period of hours.

I could make a pendulum to use as a clock, but that's useless unless I know the value of gravity here.

I don't know the air pressure or % oxygen, just that I'm able to breathe.

The scenario should be recognized as contrived and not picked over. I recognize that it probably wouldn't be worthwhile to actually try to measure time in this situation. The point is, how accurately can you measure time without a reference?

I asked this because I was wondering if there was any physical process (other than nuclear decay) with a rate that was independent of (or at least highly insensitive to) gravity and pressure, and not requiring an accurate measure of mass.

• Someone already posted a really good answer to this. You could use stars or other astrological landmarks to keep track of time. Sep 22, 2015 at 13:57
• Based on how modern clocks work today, I'm wondering why there has been little mention of measuring quartz vibrations and atomic vibration. Here's a great video from EngineerGuy describing how quartz clocks work compared to pendulums: youtube.com/watch?v=1pM6uD8nePo The basic idea is that you need a physical material that vibrates at a consistent frequency when struck. By continuing to strike it, you can accurately measure time from the consistent vibrations. Sep 22, 2015 at 19:52
• I'm surprised that this question has attracted more immediate attention than worldbuilding.stackexchange.com/questions/13364/… which I would have thought of more worldbuilding importance. Sep 23, 2015 at 14:59
• This seems perfectly on topic to me... Feb 10, 2016 at 15:42
• You need to know the gravity to compensate for the affects of general relativity, right? Mar 9, 2016 at 20:59

Use a stick to create a sundial. Now start counting your heartbeats. Very roughly you can expect ~5,000 per hour (80 BPM). Make marks where the shadows lie every ~2500 beats or so. Make sure you're in a resting state when you take the measurements.

Do this over and over on several days and you should be able to start making a good estimate of the planet's day length and seasonal cycles, with a value defined by your resting heart rate.

Now you need to estimate what your heart rate is compared to earth time. Don't go for an exact value, like 83 or 65. Instead try for a range. Maybe you're pretty sure your heart rate is between 74 and 89 BPM. Take your day data, combine it with your estimates, and that will give you a lower and upper bound on the number of days before the portal will re-appear.

Now use the time before your lower bound to prepare - gather food and water, create shelter, see if you can set up some sort of alarm, etc. Then wait and hope.

• +1 for try for a range--this is the most important part of any plan you choose. Sep 22, 2015 at 1:12
• Unfortunately Dan, you don't know the value of gravity. In a low gravity environment, the heart does not need to work nearly as hard.
– Aron
Sep 22, 2015 at 5:39
• Unless you know your own resting pulse rate, then any calculation based on an overall average is likely to fail. Mine is around 55bpm, so if I didn't know that and followed your plan, I would over-estimate the length of an hour by over 50%, and be six months late for the stargate. Sep 22, 2015 at 5:54
• @Aron: I'm assuming you could tell if the gravity was significantly different, and maybe adjust. But really anything you can do without technology is going to be a guess wrapped in a hypothesis wrapped in an estimate in this scenario, I think. Sep 22, 2015 at 6:07
• is time not relative? so even if you could calculate, your calculations wont be relative to earth anyway, for all you know, one second on this new planet, could be 1 year on earth due to the gravity of the planet, galaxy, etc. even if you was to count, or measure, this would still be relative counting. I.E from earth it might look like you are speaking really, really, really slow. earth mite look like it is spinning like crazy. however, light, is supposed to have a constant speed, if you can find a way to measure it Sep 22, 2015 at 14:05

Are you female? And if so, how regular is your period? A healthy female in prime child-bearing years will cycle on 29.5 days. Even women that cycle longer or shorter will usually cycle a set number of days. So, that could get you at least to a range of days to hang around the stargate.

Now, that said, stress and diet (starvation) will affect the cycle -- it can shut it off; which, knowing that can add some nice tension to the story. So you could also use your cycle early on to calibrate how long a local day is.

And there's the potential worry that light affects the female cycle. The moon also cycles 29.5 days, and a woman's cycle (potentially) synchronizes to it (maybe). It's not very well understood at this point. But, I'm sure that'll haunt you out there on that planet... :D :D :D

• I call this "(almost) 50% of an answer". Sep 21, 2015 at 20:45
• This is a really good point - if you can get just one unstressful cycle, you can at least set that as the precedent, even if your future cycles get set off. And +1 for an excellent storyline addition. True, just a 50% answer, but still. Sep 21, 2015 at 21:35
• According to wikipedia it's normal to be off by $\pm$ 4 days from average, and unlikely to be off by less than $\pm$ 2 days. Also, the average is 28 days, not 29.5, and is unlikely to have any correlation to month lengths. Even if a girl started her period the day she went through the gate, her next period would have a margin of error of several days, if it came at all. Sep 21, 2015 at 23:23
• I suspect that the Menstrual cycle is affected by the Circadian Rhythm. Hence the length of a sol there would largely affect your "clock".
– Aron
Sep 22, 2015 at 5:41
• I think, that menstrual circle is affected by the value of gravity. Women in micro-g environments have very unusual menstrual cycle. Even moon gravity affects their period, and planet gravity would affect it very much. Sep 22, 2015 at 10:55

Use John Philip Sousa... (I like "Stars & Stripes Forever" personally, but do ignore the rallentando going into the third repeat of the first strain!)

If you've any exposure to him you can probably hit 120 beats per minute to within +/- 10; if you've any musical training that's closer to +/-2 bpm. Let's assume +/- 6bpm, because I don't know you. That's an error of one part in twenty.

...to calibrate a pendulum's length...

Holding the top with one hand, occasionally giving it a kick at the bottom of its swing to keep it going—pushing it at the bottom will perturb its timing the least. Once you've got the length marked out of a 120bpm pendulum, go ahead and rest your arms a moment while gathering material for the next part. This solves your problem of not knowing the local acceleration due to gravity. (Which we hope is constant to better than 5% over a span of hours. If not, you've got bigger problems.)

...to calibrate a sundial.

Quadruple the length of your pendulum—doubling its period—and hang it from some improvised frame. Within seated arm's reach of your new grandfather clock erect your gnomon, mark your starting point, and start your grandfather clock. (Remember to give it its kick at the bottom—not like pushing kids on the swing.) Make a tick somewhere every 60 (or 100, if you're ambitious) ~seconds~ and after 60 (or 36) ticks mark the end of the hour at the shadow's tip. And do it again. And again. (Counting this many beats is do-able, but it takes discipline. Again, you'll be in good shape if you've some musical training. Particularly if you've been a brass player in an orchestra--plenty of hundred-plus measure rests in that repertoire!1)

Now build yourself a bevel gauge:

mark out eight times your three-hour count. There's your Earth-day. Now in 346 of those go to your gate location prepared for, at most, a nineteen-day wait. (That is, assume your one-part-in-twenty error was in the direction of counting too slow: you want to show up 1/20 *365 days "early" so that even your slowest count gets you there a good half-day before your gate opens.)

This won't work if...

• Local gravity varies by more than a few percent over a few-hour span. By itself, I don't think that would wreak too much havoc on you, biologically. I'm guessing you could survive elevator-like levels of gravitational variance2 for a year. But I'd be seriously worried about whatever's causing that level of variation. Nearby orbiting attractor? Probably no atmosphere, then. Your system orbits an infalling pair of black holes? Good luck surviving the irradiation. &c.

• There's not enough light to use a sundial. For long periods. If it's overcast for a few presumed-days before you can do this work, not a problem: pad the wait-window by those few days. But if we're talking many many weeks of no appreciable visible light, then will this biome support your food needs for a year?

• The planet rotates slowly enough that you can't perceive the shadow's motion in mere hours. In this case you've got temperature differentials on the light and dark sides of the planet that are going to cause killer (literally!) weather. Not just a problem for you but, again, for your support biome. I don't doubt things could live in perpetual 200 mph winds, I just doubt you could digest them!

It's better than the non-answer "it can't be done" because now you're not tied to an area within (gate open-time)$\times$(running speed) of the gate location.

It's better than heartrate because that can be soooo variable. As a runner I know that my resting rate may be as low as the 40s, but on a stressful (Earth) day my resting rate might be nearing 60. +/- one part in five is no good. Even at the bad end of the tempo-range you'd be hitting one part in twelve.

It's better than sleep cycles because we're actually diphasic sleepers: in darkness we can easily sleep three or four hours then come wide awake, feeling refreshed as after a full night's sleep, only to re-tire an hour or two later. That's in our preferred environment, when well-fed. Throw hunger, stress, and unnatural stimuli into it and I don't think you're going to get one part in twenty accuracy.

1 - Much rarer, but better-equipped for this particular exercise, are change ringers. They'll stand upright for nigh-four hours one morning, pulling rhythmically and counting their way through the 5040 permutations of their band's bells; have lunch; and do it all again in a different order in the afternoon!

2 - I know gravity's variance isn't what you're feeling in an elevator. But I'm hard-pressed to find any other description of what it'd feel like living in an area where local acceleration due to gravity varies by a few percent within hours. Suggestions welcome.

• Actually gravity does vary in an elevator, since your distance to the center of mass changes. Sep 22, 2015 at 5:21
• I'd use youtube.com/watch?v=uu9W4ln_Pyo that's ~100 bpm Sep 22, 2015 at 5:29
• This still has a lot of problems. For a start, you drastically overestimate how much like you the general population are. Not everyone has such good rythm. I'd be doing good, even here on earth with ideal circs, to hit 120bpm +-20. While watching a pendulum that's not already right at 120, it'll be even worse, as my brain will subconsciously try to cheat off the pendulum. That's on earth. In this scenario, add in that unfamiliar atmosphere and gravity intensity, and the stress of getting tossed through a stargate with no gear, and your perception of time is likely distorted... and on and on. Sep 22, 2015 at 8:41
• How about determining gravity using free fall? Drop a dense object from a known height and count how long it falls. For height you could use your body (e.g. I know that I’m 180cm±1cm tall) to build a ruler. The main inaccuracy still comes from counting seconds though. And I can’t think of a better method without a known gravity. Sep 22, 2015 at 9:10
• While this is another creative approach to the problem, it still isn't particularly accurate. I highly doubt any but a tiny minority of people know the BPM of any particular musical piece, and most people aren't going to maintain very good timing while multitasking to build a pendulum (which adds more inaccuracy because of the method). And of course all the same problems stemming from an alien world compound the errors. You still need to be within running distance of the gate for a span of a couple months to be remotely sure you'll get there. Sep 23, 2015 at 2:37

The only measurable thing you have with you is your body, but you won't want to rely on it.

Certain bodily functions happen at a generally dependable rate, at least over the course of a year. Hair growth is one, though accurate measurement may prove difficult. Your pulse is another stand-out candidate, particularly because it is discretely countable. This isn’t going to always be accurate, however, since the gravity and atmospheric makeup of your new planet may not be equal to Earth and could feasibly affect your resting heart rate.

With a significant portion of your concentration you might be able to track your pulse, but as soon as you become heavily active it will become a less stable timepiece. You will also lose track of large swaths of time when you fall asleep. You may be inclined to simply assume it was an 8 hours (or your equivalent back-of-the-envelope heartbeat conversion) rest, but the stress of your situation and the differing solar cycle are almost guaranteed to cause a wide array of fluctuations that lead to multiple hours of error a day.

Constructing a physical timepiece is a necessity, but it suffers from the same core problem as manual tracking: your base units of measurement can’t be guaranteed to be constant or accurate. Even if your timekeeping was only off by thirty minutes a day, your estimation of when the gate reopens would be off by more than a week.

I strongly recommend you build base camp at the foot of that gate and never let it leave your line of sight.

• This is all great reasoning (and honestly I wouldnt leave that base camp the moment I got everything I needed to it.) But it really doesn't answer the question other than saying : 'you can't' Sep 21, 2015 at 20:40
• @Spacemonkey Yes, that's more or less true. Though you could argue that the option of sitting at the gate is itself an answer to the question: the only accurate way to measure time is in one year increments, specifically determined by the reopening of the gate. Sep 21, 2015 at 20:44
• I agree with this. There are so many variables that it's literally impossible to tell when an Earth year has passed. The only consistent, surefire way to know when a year is up is that apparently there will be a portal, at which point you'll know. Sep 21, 2015 at 21:13
• @spacemonkey That's because "you can't" is all the answer this question legitimately has. The question as stated simply doesn't allow for access to anything capable of calibrating to earth societies' arbitrary temporal unit designations. Sep 22, 2015 at 8:32
• The problem with this answer is this: "Even if your timekeeping was only off by thirty minutes a day, your estimation of when the gate reopens would be off by more than a week." - This is easily resolvable, arrive at the gate 2 weeks early, making sure you have supplies to survive without leaving the gate for 4 weeks. Worst case would mean that you where tied to the gate for 21 earth days. This is far better than being tied to the gate for a full year. Sep 24, 2015 at 12:57

TL;DR

I think the best answer is: you can't.

You can't realistically get close to 24-hour accuracy with any method mentioned. The only methods that close require atypical knowledge and very specific circumstances. More realistically, you're probably looking at an error window of 30-60 days.

Try to stock up and stay as close to the gate as possible for those last couple months.

Assumptions

The question specifically asks how a person could know what day to return. My assumption is this is an Earth day, and I'm going to be generous and assume $\pm$24 hours is acceptable. Said another way, we're looking for accurate enough timing that you could walk away from the stargate for 364 days, then come back and be confident that you're not late, and no more than 24 hours early.

(Note the question was edited so it's no longer so specific. The revised information tries to calculate the realistic accuracy and why this was my answer to begin with.)

We know the planet has breathable air, but nothing else. For all we know, you're literally the only living thing on the planet. But since there's a presumption that survival is possible, I'm going to assume this planet is fairly Earth-like, is populated by plants and animals similar to Earth-life (particularly, they're made of proteins, vitamins, etc. that are digestible by humans), and that the environment near the stargate is similar to some environment here on Earth.

The question asks about a "stargate", so I'm going with a Stargate approach: a few million years ago, some ancient almost-humans explored the galaxy, constructed stargates on thousands of planets, and terraformed quite a few of them. In that time, other aliens have moved in, invaded, crash-landed, etc., and natural evolution has occurred as well. The planet is similar to Earth, but may have marked differences from Earth.

The question specifies that "I" got stuck on the alien planet. I don't know much of anything about the writer, so I'm going with a statistical approach. The writer obviously has access to a computer and the internet, so I'm assuming we're looking at a statistically-normal first-world citizen who is probably reasonably smart, understands at least the basics of core subjects at about a high school level, and to make the answer interesting, I'm assuming this person has a strong desire to live.

Clearly, some of the suggestions below would fail if the planet were less Earth-like. For example, if it's tidally locked to the local star and the star is too bright to see any other celestial objects, sundials and the like wouldn't work. That just makes my answer more right, so it's not really important here.

Most of the suggestions here would get you in the ballpark, but none of them would be highly accurate. Circadian rhythms, menstrual cycles, resting heart-rates, etc., are all based on many factors. First, none of those are the same from person to person, so you'd have to know your own. Second, they're all affected by stress, metabolic rates, nutrition, and so forth, so the instant you hit the new planet they change. Third, none of them are going to be the same from day to day or month to month with extreme accuracy even in a modern, normal, predictable life, much less on an alien planet.

Before we begin, note that there are two separate parts to this answer. The first part is counting time on the new planet. The second part is determining the ratio of local time to Earth time.

Local Time Keeping

Very few people would have the knowledge or skillset to build a pendulum clock or anything more complex, so you'd basically be restricted to sticks and shadows, which would be accurate to a few minutes, but not much more. And unless the planet is in a perfectly circular orbit with zero axial tilt, the scale of your clock will change every day. So you'd need a local year or two to really calibrate the clock.

First, let's look at suggestions for determining local time. It's pretty easy by comparison.

1. Count the Days. The easiest counting method is alien days. You've got a giant alien clock right under your feet. Just tick off how many days have passed, apply a conversion factor, and voila! You could also use a readily-identifiable constellation, a moon, whatever. (Technically, distant stars are best, because highly-eccentric orbits don't affect that measurement.)

2. Use a Sundial. But you need to correlate alien days to Earth days. It's unlikely you can maintain any particular counting method for the entire day (moreso to do so without errors), so you'll want a shorter interval. A sundial will give you a good way to track time in hour-ish increments, and possibly as good as minute-ish increments. Sundials are extremely easy to implement, so that's good. Use one of the Earth-time methods below to see how long 5 alien minutes, or one alien hour, etc. are.

The bad part of a sundial is that the ratio (probably) changes from day to day, so you'll have to take that into account. It's best if you can get the timing of an entire day/night cycle, so you'll want a "stardial" of some type. Using a raised, flat rock with sand on top, you can put a pointy rock near the edge, then sight along it from below and beside the flat rock. Put a mark in the sand directly between your eye and the rock, while "aiming" the end of the rock at some notable star as it comes off the horizon, then another mark every so often (every thousand heartbeats, or every tenth time you finish Mary Had a Little Lamb, whatever). Make another mark when the star goes behind the horizon. By comparing the arc length of several smaller intervals to the arc length of the full night, you can estimate the length of the night.

Unfortunately, neither of these is going to be terribly accurate. You either need to build a really big sun/stardial (this is possible, and probably a good idea), or make very precise, very tiny marks each time. Otherwise each mark will span minutes, perhaps tens of minutes.

3. Build a Pendulum. A really nice way to tell shorter time periods is some type of periodic motion. Like a pendulum. Unfortunately, keeping the pendulum swinging is a rather large feat of engineering unless you want to push it manually, in which case you'll introduce more error. Still, this is probably a pretty decent approximation given your options. But you need to make sure to use a thin, light string of some sort, or get some really slick goop to "oil" the contact if you slide, e.g., a stick onto another stick with a hole. Otherwise the stiffness or friction is going to introduce errors that will be hard to account for later.

For most people, the pendulum will be adequate for measuring time over several hours to more accurately calibrate the day, but it's unlikely many people could construct an actual clock any time soon.

4. A Water Clock. This requires you to be capable of moving water in sufficient quantities to fill at least one bucket, and preferably several, and is a pretty decent way to estimate the length of a day. You wouldn't want to keep it running constantly, but you don't really need to so that's fine.

5. Find a Local Clock. It's possible there is an existing civilization who has existing clocks. This makes your job trivial, but isn't remotely guaranteed. Plus, they aren't guaranteed to be friendly if they do exist.

I think there are probably some other methods I missed which would work decently. All of them will have some margin of error, but it's plausible they would be good enough.

The worst problem here is that you don't have very long to build an accurate device. If you spend 6 months constructing an elaborate grandfather clock, any physiological processes you might have used to calibrate the clock will have long since changed.

Relating Local Time to Earth Time

If you could engineer stuff, and you happened to have an object of known mass, one of known length, and one with a known spring rate, you could use all of that to determine the local gravity and make a clock from there. But you'd have to remember of bunch of physics equations off the top of your head and be able to apply them with rudimentary technology. All while not getting eaten by a Grue.

There are probably ways to make chemical clocks, but I doubt a layperson could do it at all, and even a chemist would have trouble without a lab on the planet. The speed of sound and electricity are variable depending on the medium, so wouldn't work very well. The speed of light is pretty constant through air, but you'd really need to know either time or distance for it to help. And good luck building a device to measure any of the above out of sticks and stones.

So now we need to get the Earth duration of some unit of alien time. This is where it gets extremely difficult. I'm going to cover the major ideas presented on the page so far, and why none of them are particularly great. I'll also try to give reasonable estimates of how accurate they are. Naturally, these don't cover every single variation of answer, but the same premises will apply to similar answers.

1. Count Your Heartbeats. My resting heart-rate, as measured by professional nurses with actual medical equipment, while I'm as calm and rested as I can get, has ranged from ~70 to ~110 BPM. It tends to be in the 80-90 range. I don't know what a typical deviation is for a single person, but it's probably at least $\pm$5 bpm.

So 85 $\pm$ 5 is an error of $\pm$ 5.9%. After a year (I'm using 365.2422 days, although I doubt the extra precision matters here), that 's a $\pm$ 21.5 day deviation.

That assumes the person going through knows their own average resting heart-rate. It also doesn't take into account the incredibly significant effects of stress (you just got tossed through a stargate and have to survive here for a year), the alien environment (different gravity, oxygen levels, air pressure, etc. will have an effect on your biology), or, as days and weeks pass, the different nutrition you'll be getting, your physical condition, etc.

Realistically, most people probably won't be able to be certain of an error margin of anywhere near the $\pm$ 5 BPM range, driving the deviation even higher.

2. Measure Your Period. It's quite typical in normal, everyday Earth life for a woman's period to be off from average by $\pm$ 2 days or more. Average period length is around 28 days, which gives an error range of $\pm$ 7.1% or $\pm$ 26.1 days. Wikipedia puts $\pm$ 4 days as more typical, which is an error range of $\pm$ 14.3% or 52.2 days. The highest typical period length is around 45 days for adolescents, or 31 days for adults. 45 days $\pm$ 2 days gives an error of $\pm$ 4.4% or $\pm$ 16.2 days, while 31 days $\pm$ 2 days is $\pm$ 6.5% or 23.6 days.

Like heart-rate, period length will be greatly affected by stress, diet, etc. It's actually a bigger issue here, because the next period will be days to weeks away, meaning your body will have a lot of time to adjust to the new conditions, while the heart-rate measurement could be taken within minutes of arrival.

And, period length is usuable to less than half the population. About 50% of the planet is male, and while I didn't bother looking up numbers, young girls and older women don't menstruate, so actual numbers will be less than 50%.

Another issue my room-mate mentioned is birth control. Anyone currently taking birth control will have substantial hormonal changes going on once they hit the new planet and have no more pills.

3. Use Your Favorite Music. Obviously, not everyone has heard of John Philip Sousa, let alone memorized any of his songs, but most people know a decent number of songs. Great! But does that help? Not really.

I highly doubt the average person can tell you the BPM or running length of any particular song they own. I can guarantee that only a (relative) handful of people are capable of singing through an entire song without missing a beat. Then they have to get the exact right tempo.

Certainly there are plenty of musical professionals who could do a pretty decent job. But even then I doubt they'd hit the 24-hour mark. That answer says 120 BPM $\pm$ 2-10 is reasonable for someone with moderate to little musical training. That's an error margin of $\pm$ 1.7% to 8.3%, or 6.1 to 30.4 days. Even the tight end of that scale misses the mark by quite a bit, but is looking good compared to other answers.

I'm not a musical expert by any means, and had no luck looking up statistics relevant to this, so I can't comment on how accurate that $\pm$ 2 BPM estimate is. But something tells me that's after sitting in front of a metronome or similar device, and most people probably program that timing with a musical instrument. The lack of any such tools would probably throw the estimate off by more.

Again, stress and local factors could have a huge impact on the perception of time and the ability to maintain a consistent rhythm, even for the pros.

4. Measure Hair or Nail Growth. To add to the idea, when I went through basic training the new toe nails were much thinner than my old nails, and I could visually see the time passing.

Hair grows around 6 inches per year, while nails grow around 1.44 inches per year. It's probably a lot easier to measure hair than nails in this case, but it's easier to cut into nails to keep them marked in more precise intervals. And there's a big difference between the length of neatly-brushed hair and caveman hair.

However, as Wikipedia points out, actual growth time can depend on many factors, such as the stress, etc. on our alien planet. More importantly, I highly doubt many people could tell you their personal growth rates right now with any significant accuracy.

It's hard to put an estimate on the accuracy here, but it's probably at least $\pm$ 10%. Hair on different parts of your head doesn't grow at the exact same rate, so you'll have to average it out a bit. Not everyone will have just gotten a haircut when they got pushed through, so the unevenness will be even higher. Plus the biological factors.

5. From freshman astronomy, you remember that the period of Delta Cephei (a cepheid variable) is 5.36 days, doubling its brightness at maximum. This is a pretty good trick, but that requires the person to have learned this fact (or one like it) at some point, still remember it to an exact enough value, and be able to find the star in question. Given that stargates could dump you all over the galaxy (or even other galaxies), this is a very niche technique.

If you can use the trick, the $\pm$ 0.01 day accuracy is good to about 2.4 seconds at the end of the year, although you'd likely be off by at least a few hours in trying to determine the center of the maxima and guessing at how long it had been between arrival and the first maximum. But certainly a very good technique.

But if you can't use the trick, it's worthless, and the odds of the trick working are very slim.

6. Practice a Speech or Clapping Your Hands. This sounds like a neat idea on its surface, although I doubt it's terribly accurate. Remember that alien worlds could easily affect your speech and muscles by a considerable margin.

But the worst problem is it requires preparation. If I was going to prepare, I would bring something with me that was far more accurate, like a watch. Even simple things like calibrated springs, weights and rulers would do a better job. If preparation is allowed, it becomes trivial to calculate time. But that's not what the question asked.

7. Dial a Random Gate for 38 minutes. I thought of this one, and it's not a bad idea. There are still problems. First, this narrows the assumption from "Stargate-like" to "this is the Stargate universe", which is probably too narrow. Second, most people probably never knew about the 38 minute limitation, let alone remember it.

But more importantly, it took trained professionals (in-universe, which we need to consider meaningful if we're using the 38-minute rule) decades to get one correct address. The odds of successfully dialing out in the entire year you're there are vanishingly small.

However, if it worked and you happened to get a gate open, $\pm$ 1 minute translates to about $\pm$ 2.6% accuracy or $\pm$ 9.6 days. So we've still missed our window, but it's not a bad estimate.

8. Calculate the Period of a Pendulum. For starters, your height is probably much less variable, and a longer length translates to better accuracy in the long run. So I'd use that rather than an erection.

But can we actually do it? Not really. The formula for the pendulum makes several assumptions already, so we need to be careful. But let's pretend we can meet those assumptions using weeds and sticks and so forth.

We still need to find both L and local g. L is easy enough with something like your own height. Pretty much everyone knows their own height, which is a huge plus, but it's not ridiculously accurate. Best case measuring accuracy is around half an inch, and most people are probably between 5' and 6.5' (60-78") tall. That gives us an error margin of $\pm$ 0.8% to 0.6%, which is quite good, leading to a $\pm$ 3.0 to 2.3 day total error.

But we still need to be able to replicate that height on the alien planet, which is probably going to double our error margin to around $\pm$ 6.0 to 4.7 days. But we're not finished. We still haven't found local g.

The proposed method won't work once you're on planet. It requires you to know the initial velocity of an object, which requires you to measure distance over time, and time is the things we're searching for. Two unknowns, one equation.

If we happened to know how far and how fast we could throw a particular object on Earth (as suggested), it could work. But there are several variables to consider. According to this random site, MLB pitchers (they're literally pros at throwing things) throw a baseball about 92.15 mph, $\pm$ 2.6 mph. That's $\pm$ 2.8% or 10.3 days of error. Then remember that most people aren't pros. And we're throwing random rocks or sticks that won't be the exact same mass and shape.

Then there's throwing distance. I can't find any good references, but we're adding at least a few percent here.

Finally, there's throwing angle. According to Wikipedia, MLB pitchers had an easy time hitting a strike zone between a batter's shoulders and knees. Let's call that a 4 foot height, which is at a distance of 60.5 feet from the pitcher. That's an angle of $\pm$ 1.9°.

Using the $d = \frac{v \cos \theta}{g} \left( v \sin \theta + \sqrt{v^2 \sin^2 \theta + 2gy_0} \right)$ given, with a velocity of 70 mph (we're not all MLB pitchers), $y_0$ of 6 ft, Earth gravity, and a horizontal throw, we get distances between 52.8 and 74 feet. That's 63.4 $\pm$ 10.6 feet, giving an error margin of $\pm$ 16.7% or 61.1 days.

Now, the errors given so far have been per measurement. We need to add them all together to get the final measurement. With a tall person (6.5'), that's a total error of $\pm$ 20.8% or 76.1 days. And, yet again, local factors will cause more deviation.

(Of note, adding them together means you get a more condensed curve, so it's actually a little better when accounting for whatever arbitrary probability cutoff we're using. $\pm$ 15% or 54.8 days might be a better estimate.)

9. Drop an Object Off a Cliff.

10. Measure Echo Distance. These suffer the same problem that they require a precise, working clock to make your measurements, which negates the purpose of the experiment.

11. Measure Time to Run a Distance. The problem here is it assumes people can accurately determine a half-mile distance and know how fast they run it. But both of these assumptions are flawed. First, normal people don't do that much running to begin with, and can probably guess their half-mile speed to $\pm$ a minute or something. But anything substantially better than that isn't likely. Second, I've met many people who couldn't judge 100 yards within 20%, let alone 1700. This second problem can be somewhat overcome with time (use your height to measure a length of wood, then use that to measure half a mile to decent accuracy -- probably $\pm$ 2-5%).

Additionally, even professional runners are unlikely to maintain close to their normal pace when you put them on a random alien planet on rough terrain. Even if they can easily tell they're slower than normal, they won't have any particularly reasonable way to determine how much slower they are. You're still going to be off by at least several percent, and probably 10-20% depending on just how rough the terrain is.

This is another place where it's pretty hard to make any estimates, but probably a minimum of $\pm$ 10% or 36.5 days.

12. Find an Atomic Clock on the Planet. This would certainly be an excellent method of telling time, because it's the same frequency anywhere in the universe.

However, you'd have to remember off the top of your head that Cesium oscillates at around 9.19 billion cycles per second, and hope the aliens are using Cesium, and that you know enough chemistry to verify that they're using Cesium (they aren't likely to call it Cesium).

And there's no guarantee there are people on the planet, let alone an advanced civilization. Using my "Stargate-like" assumptions, we know that most of the gates lead to extremely primitive planets, if the planet is even habitable.

So this is another case where the timing is more than sufficient if everything lines up, and worthless if it doesn't.

13. Use the Dimensions of a Dollar Bill. Assuming you have any such items on you, this is certainly an excellent suggestion. But you have to know the length, weight, etc. of such items for them to be useful (I have no more idea of the length of a dollar bill than my own finger). And you have to have these components on you as you get shoved through.

This isn't an answer so much as a "how to help with other answers" suggestion. It's certainly good advice, but the question doesn't specify we have these kinds of tools so we can't presume we do.

How To Maximize Survival Odds

Consider that your daily activities are going to be hunting, gathering, fishing, etc, just to stay alive, and possibly running and hiding from alien predators. Your first few weeks on the planet will be one hellish blur, and by the time you get into a normal routine (assuming you even survive, which, let's be fair, you probably won't), any connection between Earth time and alien time will be long gone.

One of the comments suggests that survival is trivial. It might be. You could land in the literal Garden of Eden that was taken from us and placed on this planet thousands of years ago.

But it's probably not. You have no way of knowing what's edible, what's poisonous, what's edible but totally worthless, etc. You can certainly just eat a bunch of everything, then use binary search methods to figure out what made you sick. But if you're throwing up all your food you might not survive the process.

There will be alien bacteria your body isn't used to fighting. You won't have immediate access to distillation methods, and most people probably wouldn't figure out anything better than boiling the water for treatment at all. That super-clear river water will probably make you very sick at first.

You could land in the middle of a desert. Or the arctic. Or anything in between. There could be extremely dangerous predators on the planet, or human-sized carnivorous plants. Or RouS's.

Another comment mentions that "it's the only ticket back" and assumes that means people will automatically find a way. Unfortunately, that only works in the movies. While perseverance and the will to live certainly help, they can't magically turn a person into a chemist or engineer or teach them advanced physics or math skills. Nor can they generate a fire out of solid ice, or food out of famine.

Your best bet is to stockpile food and water in an area near the stargate, then camp out right next to the gate for the last several months. But that assumes you have the materials and knowledge to keep food fresh for a couple months. Depending on the local season, you might be able to harvest fruit from trees that grow near the stargate.

Various sources I've read say that it takes between 1 and 10 square miles of land to support one person doing hunter/gatherer survival methods, so you could be very far from the stargate when it opened if you were out hunting. You would really want to transplant as many fruit and vegetable plants as possible to an area right next to the stargate, and keep it protected from the local fauna. You could set up traps and lures to hopefully get meat with spears or a bow and arrow, but you wouldn't want to leave the immediate area once you were close to the jump window.

A commenter suggests 10 mi² is a circle of radius 2 miles. However, it doesn't really work that way. First, the wildlife isn't going to happen to congregate in a perfectly-symmetrical circle around the stargate so you can slaughter them. They're more likely to be concentrated near lakes, rivers, and valleys in a more linear arrangement. Second, the nearest concentration of wildlife might be many miles from the stargate. Third, animals tend to migrate with the seasons, and random events, and the fact that you're murdering them, so you'll have to keep up, which could lead you hundreds of miles away.

The same comment also suggests you could always run 2 miles in 30 minutes. There's no guarantee the gate will be open 5 minutes, let alone 30, so you don't want to rely on that. But there's also no guarantee you happen to be in an area with relatively flat ground between you and the gate. If there are a few cliffs in the way, it could take hours to go 2 miles. And there's always the possibility of a major strain or break.

Also, there's the issue of season. It might be great near the stargate when you arrive, but the middle of the worst winter ever when the gate reopens. You'd really want some kind of greenhouse going near the stargate for this, although it could be nearly impossible to pull off.

Depending on the planet, and where the stargate is located, it might be impossible to survive very long near the stargate. In this case, you'd best hope you can run from your camp to the stargate before it shuts down again. And practice that run so you can do it as fast as possible when the time comes.

As an addendum, it's always possible the nearest reasonably-habitable zone is dozens to hundreds of miles from the stargate. A comment somewhere on the page suggests Earth might send someone through to re-open the gate from your side. In this case, it would be advisable to leave messages around the stargate explaining where you were so they could signal you or come get you since you probably won't happen to check the gate just as it opens.

• I downvoted you because "you can't", is an oft repeated cry throughout history and has mostly been proved wrong. In any case, I've given an answer that I believe proves you incorrect. Sep 22, 2015 at 10:17
• not really. You can measure gravity and then use a pendulum. Most people might not have the skillset or knowledge, but thats why we use trained astronauts and don't simply grab people off the street. Chances are someone exploring a stargate will have basic science skills. Sep 22, 2015 at 20:08
• Just because "you can't" is eventually followed by a success doesn't mean it's been proven wrong. If I told you that you can't land on Mars, I would be wrong once out billions of times. The question isn't about finding that one specific person who has just the right skills, knowledge, and luck. Certainly it's possible. But the vast majority of people would be utterly incapable of measuring time very accurately at all. Hence why "you can't" is the best answer. Sep 23, 2015 at 2:28
• This answer is wrong. I can get an time estimate of accurate to about one part in two by subvocalising a seconds count. That gives me fully 6 months of freedom to explore before I need to return to the gate. Sep 24, 2015 at 13:05
• Take each measurement, take the 95% error range, calculate the maximum and minimum day length. Ideally, you end up with a lot of overlap. Eliminate anything that isn't within every error range you calculated. Hypothetically, there's a very good chance the correct number is in that intersection. But a 95% chance of $\pm$ 100 days isn't really going to help you much. And you could get multiple ranges that don't intersect, which wouldn't help much, except to tell you there's a problem. Sep 26, 2015 at 7:47

From freshman astronomy, you remember that the period of Delta Cephei (a cepheid variable) is 5.36 days, doubling its brightness at maximum. You can observe this by eye if you can find Delta Cephei. Unfortunately, finding a known star is going to be hard if you're too far away from Earth, since the constellations will be distorted.

• Or not visible with the naked eye at all Sep 22, 2015 at 9:39
• (As luck would have it, the stargate took you to a planet orbiting Delta Cephei.)
– wjl
Sep 23, 2015 at 3:25
• @wjl hm. I don’t know, if “luck” is the appropriate word: A twin star system, where the large sun changes its surface temperature by 1000 degrees every 5.36 days, might perhaps not be a sufficient base for a pleasurable environment... Sep 24, 2015 at 12:55
• @Boldewyn : The good thing: this question will no longer be important after you arrived! Sep 24, 2015 at 15:37
• @Boldewyn: wjl didn't say good luck. :-) Sep 26, 2015 at 10:48

Unfortunately no, there is no way to measure an Earth year on an alien world due to possible time dilation (which affects everything, including atomic clocks).

As we all know from the movie Interstellar (or a layman's knowledge of general relativity), 10 minutes on a world near a black hole can be several years in Earth time.

And, special relativity notes that a galaxy moving at a significant fraction of the speed of light would also provide plenty of time dilation for our traveler.

So both speed and gravity can affect the passage of time. Unless you know the difference between the alien world's and Earth's time frames there is no way to predict the opening of the stargate.

Remember, even spacecraft orbiting Earth are affected by this phenomenon so another world would almost assuredly be different - the only question is, how much of a difference would there be?

• This is a very important observation, but this should be posted as a comment instead of an answer. Sep 24, 2015 at 17:04
• @VictorStafusa, my answer was no, you cannot measure an earth year without a clock - or even with a clock for that matter - for the reason I stated. Why is that not appropriate as an answer? Sep 24, 2015 at 17:13
• It was not clear for me that you were answering that, it looked like a critique about the question that forgot about left time dilation. Your last paragraph tells it, but I missed it anyway, sorry for that, my fault. However, this part of your last comment "you cannot measure an earth year without a clock - or even with a clock for that matter" is perfect, so I recommend you to edit the answer and add it there. Sep 24, 2015 at 17:54
• The only device that might work is one yet to be invented - some sort of quantum syncing mechanism, where one half is on Earth, and the other half is with you on that planet Because quantum physics. Sep 29, 2015 at 8:00
• Relativistic effects on a habitable planet can easily be ignored. Lorentz factor starts to grow very late. For instance if your planet spins 100 times faster than earth, you will get error rate about 0.5%. The effect is much smaller for gravity. If it doesn't rip you apart, it wont have affect on time. Mar 22, 2017 at 19:34

Talk fast (literally)

If there's a stargate, there is a good chance that there is a civilisation also. An Earth year gives you time to explore before you return and set up camp next to the stargate.

Find the locals and make friends with them. Any civilisation will have its own means of time keeping so your priority is to synchronise your time with theirs. Then perform the necessary conversion and allow a good margin for error.

As others have pointed out, you have only your body to rely on and most bodily functions are variable in periodicity. Therefore you need to know a constant.

Solution

You need to prepare before your travels but that's only sensible for any gate traveller.

1. Learn a long piece of poetry or a passage of Shakespeare. You must learn it perfectly and be able to recite it without stumbles.

2. Practice it many times getting faster and faster. Keep a graph of your progress. When your speed of recitation has peaked, measure the overall time that it takes.

3. Fine tune the length of the text to last a time period you choose, for example an hour. You don't have to do this but it just makes later calculations easier.

4. You now have a constant that depends only on the physical constraints of your vocal apparatus. Maintain speed by practicing every day at full speed and time yourself.

5. Work out the mean error. People who go for world record speaking contests get down to a remarkably constant rate so the error is likely to be 'small'. (Note: I say this from memory from an interview I heard a few years back. It would need research to back it up but I'm pretty certain it's true. The same applies for athletes, they tend to peak at a fairly constant level.)

Now and only now are you ready to journey to other places.

1. If you are alone on the planet, you have a PGTC (pretty good time constant). You must synchronise with local astronomical or other regular events. If there is a friendly civilisation, you can synchronise with their time system and from then on rely on their time-keeping. Allow a generous amount of time for error and then spend the intervening time building relationships and supplies to prepare you for the time you decided to encamp next to the gate.

Update

If you don't have the time or patience or ability to learn long portions of verse, there is another way. Hand-clapping has a maximum speed for each individual (there are world records for this as well!). Practise your hand-clapping before the trip and measure your maximum rate over a few minutes. Again this removes the uncertainty of autonomous biological processes. This gives a very quick estimate of time over a relatively short period but it can be extremely accurate and it is better than relying on natural biological clocks or mechanisms.

• So you need to be a world record speed speaker in addition to being an astronaut. Seems reasonable. Sep 22, 2015 at 14:51
• @corsiKa - Not at all. Think about your reasoning! I mentioned world-records because usually only such people actually bother to time themselves. I used the fact that athletes and record-holders reach a personal maximum. The important point is that everyone has their own personal maximum. It may be far from world-record standard but it is consistent for that person. Therefore it provides a personal time-constant - even for a person who is very slow. Sep 22, 2015 at 16:31
• If you had time to do all of this preparation, you would have the time and sense to ... bring a watch. I can think of thousands of ways to learn all kinds of things about an alien planet, but the question asked about just being shoved through. Sep 23, 2015 at 2:23
• (c) The person knows they have been left on another planet and that the means was a time-gate (all derivable from the question). It is highly unlikely that some random person off the street who got into a fight and knocked through, would understand what had happened to them. I suggest that this must be someone in the business of gate travelling. Such a person is likely trained to cope with all sorts of emergencies. (d) You cannot exclude the possibility that this is someone who happens to have timed some repetitive muscular action. There is a finite probability that they have. Sep 23, 2015 at 9:35
• Unfortunately, time dilation precludes this (and any other method) from working. Even an atomic clock is subject to our current understanding of relative time frames throughout the universe. If you updated the answer to include an assumption of time frames that are within the error bounds of your estimation then it could suffice as an answer. Sep 28, 2015 at 18:38

Assuming that the stress of your unusual situation has elevated your pulse rate by an unknown amount, desynced your period (if you are female), or any other natural time measurement.

We can calculate the period of a pendulum as 2 pi SQRT(L/g).

So if we know L and g, we have our clock.

And fortunately, we can calculate g if we have a ruler.

Gentlemen, lets admit, we've all measured 'it' and know exactly how long 'it' is. Don't forget that self measurements typically overestimate by an inch or so.

Ladies, (to continue my theme of being sexist), probably know your measurements as appropriate to fit clothing, find some string-like material that you can wrap round your waist for a calibrated ruler. In fact, just use that string as the pendulum.

Now, we need to calculate g.

The best bet will be some sort of projectile motion. Jumping, spitting, peeing (yes, this post went rapidly downhill), throwing a rock could all be used to determine a total distance travelled by a projectile thrown horizontally using:

$d = \frac{v \cos \theta}{g} \left( v \sin \theta + \sqrt{v^2 \sin^2 \theta + 2gy_0} \right)$

Of course, you will have to know the distance that one of these projectiles traveled on Earth in order to calculated launch velocity (and then use that launch velocity and the distance on the new world to calculate g), so I hope you know how far you can throw/excrete something.

Plug in our calculated L and g into the pendulum formula and we have a working pendulum. From there, it's some simply gears to get us a clock and calendar.

This avoids us needing to directly measure/assume anything to do with speed or time, because those are hard.

• right, because throwing a object perfectly horizontally is easy. Sep 22, 2015 at 5:23
• What percentage of the population can calculate square roots of fractions or trigonometric functions in their heads? Sep 22, 2015 at 5:46
• Given a stick, some dirt to write in, and a high school education and a lot of time, I would assume everyone. Just remember SOH-CAH-TOA, draw a triangle and you can easily work out Sin(0) =0, cos(0)=1. For the square roots, just to trial and error. square root of 87 is going to be somewhere in between 9 (sqrt 81) and 10 (sqrt 100) Sep 22, 2015 at 5:57
• SOH-CAH-TOA what is that? Sep 22, 2015 at 7:44
• It would be far more sensible to use your height as the ruler. You probably know that much more accurately than the other things you mention, no sexism required. Sep 22, 2015 at 15:14

Since there is no way to know the relative distances and velocities of Earth and the planet you're on, Special Relativity tells us that we can make no assumptions about simultaneity. Even if you can somehow manage to bash some bits of rock together and make a Caesium clock, there is no guarantee that someone measuring out 31557600 seconds (which is one year) on Earth will take 31557600 seconds to do it from your point of view. All that is guaranteed is the ordering of events, not the intervals between them. From your point of view, you could be waiting 10 centuries or 10 minutes.

Or you could just take greater care when passing by open stargates.

• Time is relative. Full stop. +1 Sep 25, 2015 at 0:42

Can you dial the gate? Ether with the DHD(Dial-Home-Device, or the round thing with the many buttons with constellations on them next to the gate), or if thats deactivated/missing and you're in the Milky Way Galaxy you can manually dial the gate (Pegasus Gates don't have that feature) by turning the ring by hand (but be aware that you have to General O'Neil a power source).

If yes, you already have a pretty reliable way of measuring time, because a stargate will stay activated for 38 Minutes (see SGA Episode "38 Minutes" for details) if nothing passes trough.

So you dial the gate to a random address(could take some time to find a working one though), make a sundial(see nitsua60s answer) with that measurement. And viola, you have a (rough) way to measure time on this planet.

• Or peek through the gate and ask if anyone there can sell you a watch... Sep 22, 2015 at 9:40
• That would mean you know the address of another inhabitat planet that just gives watches to people without money. And then you can just get of that planet and live your life somewhere else, where people dont get shoved trough stargates and left alone. Sep 22, 2015 at 9:43
• Well, if you are able to dial random addresses, then in a year you have enough time to find both, a planet with watches, or a planet which you want to go.. Sep 22, 2015 at 9:44
• There is the possibility of space gates, which would kill you, gates with an damaged DHD, which would leave you stranded on another planet with no hope of return, inhabitable planets, and, of course, planets with Goauld/Replicators/Ori/Wraith/Other unpleasant species and people on them, which would make randomly dialing addresses a very high risk. If you have no idea where you are going, or an adress ready, staying on that planet is your best chance. And dont forget, If you find someone nice/not trying to kill you, you have nether money nor valuables, which would make survival harder. Sep 22, 2015 at 9:50
• ITS O'NEILL!! WITH TWO Ls. Sep 30, 2015 at 9:44

I just though of another way to find duration from distance: echo. (Here again, you need first a proper distance measurement, and a relative time measurement (other answers cover that))

Find a place that has significant echo, measure the time of roundtrip of the sound, measure the distance to the other side of the cave/cliff/thing.

Sound travels at ~340m/s, depending on the pressure and temperature (which you can estimate)

Another one, which requires a bit of luck. Build a big lightning conductor on top of a hill (if you can find some metal, it will be easier (and not entirely impossible, a tribe of inuits is known to have used metal cutlery without access to mining - from a meteorite)). Go far, but make sure you can see when the lightning falls on your device. Measure the time of sound propagation. (again, need a device to measure relative time). (You need a planet with thunder, of course).

Works also with explosions, or rock falling from a cliff, as long as you can measure the time between the visible and the audible.

• This would only allow you to calibrate if you have some sort of local clock accurate to the second, but still is interesting. Sep 24, 2015 at 17:17
• "...depending on the pressure and temperature (which you can estimate)". That's a pretty big detail to gloss over. Sep 24, 2015 at 20:55
• @chepner everything depends on a lot of factors. Pressure and temperature (and athmosphere composition) influence the speed of sound. However, you probably can tell the temperature to 10C. And pressure is not the biggest influence. Sep 24, 2015 at 21:35
• I agree with chepner that atmospheric composition will probably mess this up. Still the idea is pretty good, because apart from chemical composition, the biggest influence on sound speed is indeed temperature, and temperature is probably the quantity you can measure most precisely without any device. (You can clearly distinguish 17° C and 27° C, i.e. 290 K from 300 K – error less than 5%.) Sep 25, 2015 at 0:26
• If you run the calcs through, speed of sound in air depends only on temperature, and gas makeup. en.wikipedia.org/wiki/Speed_of_sound#Equations There is a pressure term in the equation, but it's balanced out by a density term. You could be messed up if your atmosphere has a high percentage of argon, but if it's breathable air and a reasonable temperature, the echo effect may give you a reasonable answer. Oct 24, 2018 at 14:19

Overall, you always need 2 of the three following:

• Gravity
• Time
• Distance

Distance is easy to estimate. Your belt and pants, your feet length, your height, your finger span, you usually know a few measurements.

Relative time can be estimated too, using various mechanisms. A pendulum, counting your heart beats, singing in rythm (those 2 can also imprecisely estimate the absolute time).

Absolute time requires something more, and can be obtained by knowing the gravity.

Not very precise, and very time consuming, but you can estimate the mass of the planet (and therefore its gravity) using the method Eratosthenes used and assuming that the density of the planet is somewhere between Mars (4g.cm^-3) and Earth (5,5g.cm^-3) (not very precise, like I said).

Gravity gives you the duration of a free fall (find a cliff of some sort, measure its height).

You will need a precise timepiece at some point to measure the duration of the fall and extrapolate to a day. A pendulum could work, or may be just your heart, as long as it stays globally regular for a good period of time.

2. Use the inseam of your pants to cut a 6-in strip of cloth
3. Survive
4. Come back when your hair is 5.5 inches

365 days is a long time to survive and the first couple days will be crucial (you'll be at your peak). Depending on the environment, hygiene and safety might necessitate a buzz anyway. Keep it simple. Since the hair on a human scalp grows about 6"/yr, come back when your hair is 5.5" and chill for a month.

Sidebar

National parks in the US have an overall mortality rate of 0.26 deaths per 100,000 visits. If we are generous and assume 'visit' is an 'all-day visit' and assume that 365 consecutive 'all-day visits' won't increase this rate, then we would expect 94.9 deaths per 100,000 or about 1/1,000. Now instead of a planned, year-long visit to a national park in the US, you are on an unplanned, year-long exile to the wilderness of an alien planet. Figuring out when you are going to be rescued is inconsequential to figuring out how you're going to survive.

• A 2005 study mentioned in this article { livescience.com/42868-how-fast-does-hair-grow.html} gives slightly over 5 inches for male and female Caucasians, so to be safe, the person should come to the gate at 5 inches and sooner if of African descent. In other words, you could still be at the gate for over a month using this method, which is similar or greater than other methods. Apr 29, 2018 at 23:53
• I love the simplicity of this answer, though. Apr 29, 2018 at 23:55

I'm going to assume that you have access to water. If not, I don't think you'll make it a year anyway. If you do, you can build a water clock:

Make a bowl out of clay, metal or wood with some extra weight (you have a whole planet at your disposal, I'm sure you can find something) and poke a hole in the bottom. Do a few runs, counting mississippis to see how long the bow takes to become submerged. This is your smallest unit of time, which you can convert to seconds. Just spend a couple of days watching the bowl and emptying it each time it becomes submerged, and you can figure out how long a day is.

• "This is your smallest unit of time, which you can convert to seconds." How? Sep 24, 2015 at 13:38
• @mattdm Counting: one-mississippi, two-mississippi, etc. The OP clearly stated that counting for a full day was two laborious, but counting until the bowl becomes submerged should be fine. He can do the experiment many times and average the results, to increase his accuracy.
– PTm
Sep 24, 2015 at 17:48
• Lets suppose that it took 5 minutes to fill the bowl and the planet has a 36-hour long day. Being around the bowl for a couple of days emptying it every five minutes to measure the day length will be hard to do at least, because you can't sleep nor get distracted. Further, doing a so boring, repetitive and uninteresting observation work, will make you either fall asleep or get distracted with something else very soon. Sep 24, 2015 at 18:29
• This could also be used to calibrate a sundial, so he doesn't have to do it all in one day.
– PTm
Sep 25, 2015 at 4:13
• You could use multiple bowls for better long-term counting. Have a five-minute bowl you count with whatever method you think is best, then have a 5-hour bowl you measure by counting the number of 5-minute bowls you filled. Then as long as you fill the 5-hour bowl every 5 hours, you can keep long-term time without being constantly attentive. Sep 25, 2015 at 6:47

You can only go forward through a stargate, so you should hide and camp near it. When you hear noise, either Earth is dialing you to send someone that dials back, or the stargate is programmed to dial Earth automatically within a year.

In the mean time, you'd eat, protect yourself (probably underground), farm and gather resources.

You should stop any activity that requires you to move away when you realize your hair has grown about one of your finger's length, given it should grow about 15 centimeters per year (so pick your finger wisely). By then, you'd wait for the stargate to open, consuming what you have gathered.

You don't have any reliable way to measure the passage of time, but you have many rough ones based on distance. Measuring distance is tangible, or at least a much less rough estimate than time alone.

For instance, rhythm or internal clock is very susceptible to failure, you can't really count the time it takes for a rock to fall of a multiple of your height, heartbeat depends on effort, stress and tiredness, etc.

Here are somethings you can measure the length of to determine the passage of time:

• Your hair grows about 15 centimeters or 6 inches per year

If you have grown finger nails, you can bite your finger nails up until the white part is gone, and roughly estimate the length of the regrown white part

• If you're a man and you've shaved your beard recently, you should know about how many days it takes to grow e.g. a 1 finger girth of beard

Likewise if you're a woman, but replace the 1 finger of beard with e.g. 1 or 2 millimeters of leg hair, or visually, whatever you usually let grow

• If you somehow know how much time you take to relieve a full bladder, you can drink all the local water you can and go for it

It's equally good to know how much time it takes until you feel the need to relieve your bladder since you filled an empty stomach with water

If you can't find potable water, measuring the passage of time is the least of your worries

In case you can think of other things that take a few minutes and at most one hour with relatively good reliability, you could also build a big hourglass: a base and a funnel made of tree cork, or leaves and sticks, or a cone-rolled sheet of malleable plastic or metal, filled with sand or dust.

Once the timed task is done, you'd remove the rest of the sand, and perhaps a handful more (see last paragraph).

You can then build a weight scale with relatively regular sticks standing on a middle point, and measure just as much sand, and join all the sand together.

Do this until you get something above 8 hours worth of sand; remember, you'll always double the sand, so be careful not to overweight. You'll have to rotate or refill the hourglass all the time, so you better sleep well right after a rotation.

Otherwise, stick to the longer term estimates.

As a final hint, always make your estimates below, because you'd rather be early than late for the stargate opening. And keep calm, as that will allow your body to function with less inhibitions, thus making your early time estimates more accurate (yes, because the Earth year doesn't wait for you to find a good estimate, you must take into account the time you spend from the first moment the stargate is closed).

Get some help from the locals to learn c

This is a little bit of a stretch, but can you find some friendly advanced aliens who can measure the speed of light to at least the same level as we could in 1878? And do you remember the speed of light to an accuracy of at least 3e+8m/s?

Communicate with the aliens until you learn the speed of light in their units, and then you know one very useful constant. Remember during this time to carefully count the number of local days which have passed, knowing this is critical.

Use your body to calculate 1m

Next problem, can you find how long a meter is? I hope you didn't come out of the stargate buck naked, but if you did you'll just have to use your own height in meters. If you aren't naked perhaps you have a handy tape measure or ruler on your person, otherwise probably best to stick with your height. This wont be perfect, I'll give an estimate of inaccuracies later.

Calculate the ratio of Earth to Alien days

With the length of a meter and the speed of light in human units, you now know how long 1s is (or at least you can calculate it - hint it is the time light takes to travel 3e+8m). You'll need to reconcile these units and numbers with the alien units and the alien speed of light and the number of alien seconds in an alien day, but if you passed high school calculus it shouldn't be any difficulty at all. The harder part will be learning the alien language. If you are a dunce in maths but a genius in languages, get the aliens to calculate it for you! All you need to know is the ratio of earth days to alien days, then you will know that 365 earth days is 217 or 461 alien days or whatever.

Count down the alien days

Once you know the ratio of an alien day to an earth day, continue to count down the alien days until that special day arrives.

Margins of error

How accurate will this be? The main problem is the margin of error in your height, assuming you (correctly) remember your height as 200cm but with a margin of error of 0.5cm, then your numbers could be out by as much as 0.25% (it's worse for short people), over a period of 365 days, this could be +/- 0.91 days (22 hours), this incidentally is a much higher margin of error than the error which comes from approximating the speed of light as 3e+8. If you were lucky enough to arrive with a tape measure, you could enjoy significantly higher accuracy.

Camp at the gate

Even in this fabulously fortunate case, of having helpful aliens who know the speed of light and help you to calculate the ratio of earth days to alien days, you still only get an accuracy of about +/- 1 earth day. So it would be advisable to arrive a day early and camp out at the stargate.

Water will be an essential ingredient, i just assume there is plenty of it, otherwise you are screwed anyway.

Preparation
But we get to it later, the most important thing is to start measuring time right away in some way. Before you go to sleep you should hack together some "clock" that can run unattended for at least the duration of your sleep. A sundial. How fast will water drain from a bamboo trunk with a tiny hole in it? How fast will water evaporate from a hollow rock? How fast will an ant-like insect colony consume an apple-like fruit? Dont worry about the details, you can calibrate those methods once you found a more exact timekeeping device, you have one year to do so. And dont rely on a single method, run them all in parallel it will reduce the error margin and a sudden rainstorm wont wipe out your progress.

Now, after you spent 3 hollow rocks = 7 apples = 34 bamboo buckets worth of time on gathering supplies and making some tools, its time to do science.

First, stand next to a tree and mark your height, you should know it up to $\pm 1cm$, thats better than 1% precision.
Next we will be using heat transfer $\frac{dE}{dt} = -kA\frac{\Delta T}{\Delta x}$ to measure time
Wait, what? All we can measure so far are lenghts but here we also need energy and temperature, how the hell is that gonna help?
Thats where water comes into play, its very easy to manipulate and its properties barely change under most circumstances.

• Freezing point at 0°C, this is affected by impurities like salt, but those are easy to get rid of by distilling the water.
• Boiling point at 100°C, this barely changes with atmospheric pressure, only by 5°C if the pressure changes by 20% and at most by $\pm 20°C$ in survivable range. Fortunately we can measure that too (more on it later). Impurities dont affect it that much, a saturated salt solution has its boiling point raised by only about 8°C
• density $\rho_{water} = 1\frac{g}{cm^3}$ and $\rho_{ice} =0.917\frac{g}{cm^3}$. Solids and liquids are pretty much incompressible so even at tenfold gravity the values will be the same for practical purposes.
• thermal conductivity $k_{water}=0.609\frac{W}{mK}$ and $k_{ice}=2.22\frac{W}{mK}$
• Latent heat of ice $334 \frac{J}{g}$

Process
Now we are good to go. First make a few ice spheres, use a string to make sure they are spherical and same size, dip them in water to make it even more spherical, store just below 0°C.
Next make a fire and boil a big bucket/bison skin/giant snail shell full of water, you dont want it to cool too much from the ice.
Finally, start a pendulum, throw in an ice sphere and stir it like your life depends on it, because it does. Count the pendulum swings until it fully melts. Done.

Evaluation
Simply putting ice in hot water melts the outer layer and cools the surrounding water, it is circulated away by convection but very slowly. By stirring we make sure that the water in contact with the ice is always at its boiling temperature and makes the calculations much easier.

did some math here but i messed up, might expand on it later, for now a summary
The total flux of energy into the ice sphere of radius $r$ is $\frac{dE}{dt} = h_{eff}\cdot 4\pi r^2 \cdot \frac{T_{boil}-T_{ice}}{\Delta x} = \alpha r^2$
The total energy required to melt an ice sphere of radius $r$ is $E = \frac{4}{3}\pi r^3 \cdot \rho_{ice} \cdot 334 \frac{J}{g} = \beta r^3$
expand the differential: $\frac{dE}{dt} = \frac{dE}{dr}\cdot\frac{dr}{dt}$ and plug in previous equations: $\alpha r^2 = \frac{\beta}{3} r^2 \cdot \frac{dr}{dt}$
and we get $\frac{dr}{dt}=3\frac{\alpha}{\beta}$ that is, the radius of the ice sphere shrinks at a constant rate. According to an experiment performed in a teacup it is around $1\frac{mm}{s}$

Heat transfer by thermal radiation might play a non-negligible role here and makes the computations more difficult therefore its better to determine the coefficients $\alpha$ (depends on atmospheric pressure) and $\beta$ before the journey

As mentioned before, if the atmospheric pressure is within $\pm20\%$ of earth pressure, the error will be at most 5% and you will be able to calculate the date with up to 3 weeks precision

This is not nearly accurate, but can get you to a magnitude of order at least.

With different rotation, revolution around the 'sun,' and all other seasonal variations, you cannot rely on anything cosmological at first.

Your initial sleep cycle will be hopefully a healthy 8 hours. If not, you will have to average out your days. You KNOW when you've only had a nap, vs. a four hour nap, vs. a full 'nights' sleep. Take that measurement and align it with the daily passage of time. If it appears to equate 8 hours with three days (fast rotation), calculate that out, and so on.

It's not nearly accurate, and I know you were looking for something more accurate, but without anything from Earth, it will let you know with greater accuracy a range of when you should be back to your gate. Or you could just hang out there.

• If the local day length was say 26 hours (earth time), I'd think your body would adapt to that fairly quickly. Given the stress of the alien setting you probably wouldn't notice the slight extra length. With that day length, after 365 alien days had passed that would mean that 395 days would have passed on earth. You'd be a month late. Sep 21, 2015 at 20:22
• @KillingTime - The first day or two time is of the essence. When I travel to a very different time zone, I know I got more-or-less xyz hours of sleep. It's a terrible way to tell time, but on this alien planet (different sunsets and sunrises, different plants, whatever), you have to use the only time-keeping device you have: your intuition. And apply a contingency, even if that means it's a months' contingency. Sep 21, 2015 at 21:31
• You can't get sufficient accuracy here. A four-minute error in your estimate of the day length produces a one-day error in figuring out when the gate opens.
– Mark
Sep 21, 2015 at 21:35
• @Mark - but you can calculate a range. I suggest I should be at the gate within 1.2 months of my range of possible error (for example). Sep 21, 2015 at 21:37

Use your body's internal clock. Go to sleep 365 times and you'll be in generally the right place. This approach requires lots of darkness so that you're circadian rhythm doesn't adapt too much to the new planet's night and day. Even in periods of extended sunlight, human bodies default to a 24 hour cycle.

Keeping time is as simple as scratching off marks on a wall every time you wake up. This should also help you get a handle on the local day length.

A few people will desync from the 24 hour cycle and other people will find that they have a >24 hour cycle.

• You don't think that the stress of being in a survival situation in a totally alien environment might affect your sleep cycles? Sep 21, 2015 at 20:25
• My body's internal clock attempts to get me to go to bed later and later, and therefore get up later and later. Sep 21, 2015 at 20:26
• @DoubleDouble I found this in a paper from NIH: "A few people desynchronize from the 24-h day (free-run) and show their intrinsic circadian period, usually >24 h." This leads me to believe that most people keep a 24 hour day cycle regardless of the length of nighttime or daylight. Sep 21, 2015 at 20:38
• Most people can adapt to a day-night cycle of 22 to 26 hours; if the planet's day is within that range, you can't count on your internal clock. For example, if you wound up on Mars, waiting 365 sleep cycles would put you at the gate a little over a week late. (The article you link is about how people don't adapt to a 8766-hour day.)
– Mark
Sep 21, 2015 at 21:28
• Had no problem doing 6 28-hour days each week for a few straight years in grad school. It got me to the mid-day collaboration meeting each week, but still allowed me to take four overnight shifts each week at my experiment. Nine down, nineteen up with a half-hour nap somewhere in there, and that was against the driving stimulus of the 24-hour natural light cycle. Don't trust in a "natural" 24-hour cycle that you'll maintain alone. Sep 22, 2015 at 1:18

Use statistics!

You can't count to 60 and expect it to be a minute. You cant sleep one night and think you got a perfect 8 hours.

But you do have a year, and you can start building datasets. You know the relation between all your Earth time measurements. Now start forming approximate connections - a sundial will tell you about the Alien day, and its hours, and its minutes. Does it take 60x60 seconds to cross a twelfth of the dial? Does this change in the morning or evening versus midday?

Exploit relations:

After a week you wont have a conversion chart, but you'll know if a day is longer here or not. You'll also be able to guess by about much, since that 'hour' happened too fast, or the nights lasts too long. The drift on your circadean rhythm will also help. If each morning comes too soon or not soon enough, or each evening, these are hints. If there are moons, track how long each one takes to drift across the sky, relatively. Do they make it from Alien-east to Alien west, or vice versa, before the ngiht ends? Do they make multiple passes?

Have the terrain tell you:

Observe the animals and plants and whatever else lives on this world. Draw relations between them and known creatures of Earth. Are they larger? Smaller? Do trees have leaves all the way around, or do they favor a side. Which way to birds fly more often? There is an unending amount of data to be collected from the environment, ever living things adapted to life here, and can tell you how to survive given the natural time.

Put it all together.

You can count Alien days, hours, minutes. You can draw the relations. From there, you can guess about how many Aliens days equal 365 Earth days. Depending on how much skew you think you have, you can pad yourself which 5% or 10% earliness, or simply try to underestimate time so that you are guaranteed to arrive back early.

Example:

Counting off rough minutes, coupled with a 12-hour sundial shows that each hour is about a third longer than you think it should be. You observe a moonrise and moonset every night, which at least 30-60 minutes to spare on either side. That would lead to two or three tide cycles in a day, and you can chart that on any body of water. If its truly periodic, you can find out roughly what time of day it is that way too. Both together and you can guess that a day is about 30-32 hours; you have about 273-292 Alien-days to wait. If either method contradicts the other, observe more and take more data, averaging the two.

Go Explore!

Now that you have a general timetable, go enjoy the local scenery and try not to get detained or captured. Also, they might be able to sharpen your time-conversion, or at least provide some paper so you can write all this down. Good Luck!

• If you end in Mars, which has a day just 37 minutes longer than Earth's day, you will unable to tell if it is longer or shorter than Earth's day. Also the circadean rhythm might just adapt to that. Further, how does the observations on moons and terrain tell me anything useful? And the most important part, "From there, you can guess about how many Aliens days equal 365 Earth days" you didn't explain how can I heck guess that, which was exactly the purpose of the question. Sep 24, 2015 at 16:48
• By the relation. Maybe I could clarify, but basically if its longer and shorter, and by how much. If you land on Mars then you are in luck, because everything lines up, and so being 5% or 10% early (18 and 36 respectively) early will account for the 37 minutes, or 9.3 days of drift. If the day feels longer or shorter, and by how much, you can do the same math and get the same rough "I should be X amount early" numbers. Sep 24, 2015 at 16:53
• The difference in length between the lunar "day" and the solar day won't really help you. If the lunar day is 30 hours and the solar day is 32 hours, and your attempt to count Earth hours is off by 10%, you'll measure the lunar day at 33 hours, the solar day at 35.2 hours, and each local month will be 16 local days. Everything will reconcile, but you're still off by +10%. And I really don't see how the local plants and animals can give you any information about Earth time. Sep 26, 2015 at 6:53

Action VS Time

With any luck, you have vast open terrain at hand. AND either way, you won't be staying sitting at the portal's location for a full year. (You lazy )@(#* )

So start moving those feet. Now if you're used to walking a lot, you know what speed you travel at. And anyone with a bit of practice can be able to accurately judge distances up to a kilometer. So if I know it should take me about an hour to walk say 6-7 kms at a normal pace, I can judge a km of land, and walk back and forth along it to total what SHOULD be about 2-3 hours. (You dont want to walk too long otherwise fatigue starts having a bigger effect etc...)

The back and forth is for a reason. You can use shadows to apply that 2-3 'earth' hours to this new planet's day cycle.

(maybe it equaled what seems like 1/5th of a day, maybe 1/40th 'yikes' )

repeat this activity for a couple of days, and keep track of shadows regularly. Eventually you'll have a very good grasp/guess as to the ratio of earth days versus this new place days. 'Ok 1 new day = .75 earth day so I have to be back in 275 days or so, I'll say 250 to be safe.'

EDIT
A lot of people keep bringing back : 'But you might be totally exhausted etc.. so your answer is invalid'

I feel like you are confusing 2 things. Physical state, and ability to judge time doing something you know well. If you know it takes you 10 minutes to walk all the way to your bus stop. You'll know if you walked it in 10, or a bit more or less. Regardless of if you are completely out of breath and tired, or perfectly fine.
This isn't much different then @chasly from UK's answer where he uses speech to measure time. You could also argue that if he's exhausted by simply being there, it will also affect his speech (try reciting something very fast when out of breath.) And that the difference will have a greater impact since the time measure is smaller (and has to be repeated more in order to obtain any useful time-frame)

Both our answers state doing something you can easily judge time against through habit. This is not something thrown completely out of whack by sudden physical exhaustion. SURE you might be slightly off, but that holds true without the planetary differences. I guess I could've explained better right off the start (I changed the header to reflect this). But in my case, I'm good at guessing elapsed time against anything I do physically, especially walking/trekking. If that doesn't work for you because it's not something you are used to doing - use an activity you are very used to.

• As noted in the question, the planet's relative oxygen level is unknown so endurance and physical performance may be affected. So your earth based guestimates might not be all that accurate on the new planet. Sep 21, 2015 at 20:35
• I disagree. If I,d be running 10 miles, sure. (but youd also KNOW you either ran it faster or slower than normal). I might be more tired but I will not be walking slower unless the gravity or oxygen level is significantly different, in which case, again, I'll know. But at those levels, that would also affect your entire body at rest, so none of the other answers would work either. Sep 21, 2015 at 20:38
• Your energy expenditure depends a lot on gravity, and you don't know the local gravity. If it's more than 10-20% different from Earth, you'd notice, but you wouldn't be able to estimate it very well. Sep 22, 2015 at 2:33
• Moved to 8000 feet above sea level, tried to quickly catch a bus a half-block away on the first weekend, couldn't catch my breath for fifteen minutes. It didn't take much of a change in atmospheric composition to completely tank my ability to go at a pace I know as well as this needs. Sep 22, 2015 at 3:28

Atomic Clock

I think that a highly likely possibility has been missed. There is a very good chance that you will land on a planet with a high level of technology. If there is a working timegate then this is almost certain.

Any technologically advanced society will know the speed of light and have atomic clocks. These will work at the same rate anywhere in the universe. Provided the traveller knows the speed of light then everything else can be translated into local time units. Even if the technology is only at 19th century Earth level, our traveller can talk to their scientists and pass on the necessary information to make a measurement of a suitable constant. They will be grateful that their science has been boosted and will be predisposed to help him return.

EDIT

People seem to be shooting first and asking questions afterwards. Or rather, in this case, they are raising an objection but down-voting before waiting for an answer. The assumption seems to be, "I know better therefore there can be no valid answer to my objection." When I have a minute I'll do some actual maths and show how the calculation would be done and the amount of error that can be expected.

• This is a valid as "just look to the big digital tower clock that aliens, that were just waiting for you, built in the front of the stargate showing the precise UTC date and time and then add a year to it", which is a stupid invalid answer. Sep 24, 2015 at 16:38
• Your suggestion may be stupid. I'll leave it to you and others to judge. My point is about using a universal constant. It seems perfectly sensible to me. I notice you don't have any useful ideas of your own. Sep 24, 2015 at 16:46
• You need to add in a way to account for time dilation due to gravity or velocity and add that as a factor to what you estimate Earth's time dilation factor is. An atomic clock in a gravity well or moving at high speed is wrong compared to 'Earth time' (as noted from GPS satellites, the space shuttle, etc.) Sep 24, 2015 at 17:29
• "Provided the traveller knows the speed of light then everything else can be translated into local time units." How? Say, they manage to communicate you that speed of light is 6.7×10^8 alien-distance-units per alien-time-unit. How do you get time units from this?
– user8808
Sep 24, 2015 at 18:08
• Also, how exactly do you propose to "ask" the locals anything? Are you assuming the OP to be fluent in all the languages of all the technologically capable people in the universe? Even on this one planet, that's more languages than any one person knows, and those are all languages that some humans have at some point in their lives had the opportunity to be exposed to. Or are you assuming the aliens all speak English? Unlikely, but even if they do, that doesn't mean they'll be polite enough to actually do so; just try visiting Paris with midwestern American English as your only language. Sep 28, 2015 at 18:59

First thing first: put a stick in the ground and mark where the shade falls. That way you will know exactly when you arrived. Then...

Go to the loo

Seriously, if you usually go to the loo at regular times you can compare the length of the alien's day to your.

Obviously the new environment will affect your functions but you should have a couple of days of "normality" until your body gets used to the planet.

Use a sundial to measure the alien's day, divide the day in equal parts and then mark at what alien-time you need the loo. Then it should be easy enough to do the conversion.

• Would the downvoters please stand-up (unless you are "sitting")? Sep 28, 2015 at 8:17
• So, using your "period" (which happens only to women and only once a month) is ok, going to the loo (much more common and frequent) no... Sep 28, 2015 at 13:12
• I haven't down voted, but seeing your self in a different planet might wreck havoc on your systems. You might be peeing before being able to manage to mark your height. Mar 22, 2017 at 19:48

Admitedly, this is not a great answer, but was not covered by anyone else. I am just adding on top of other answers.

If you find some fine sand and is able to carefully melt it, with some days of work you may be able to produce glass, and eventually an hourglass. Ideally, you could produce a big hourglass that takes somewhere from 20 minutes to an hour to empty its upper half.

The hourglass, per se will not tell anything about the relation with Earth's time, but you could use it to refine the measurements and reduce the error margin from other methods, like sundials, water clocks, counting heartbeats, counting mississipis, singing your preferred song, etc. Further, you could create many different hourglasses with different periods and then choose the best ones and also crosscheck them.

However, this would probably require that you already have that skill when you arrive. Although it is possible, you will unlikely to be able to learn this yourself on the planet in say, 6 months.

Edit: Although an hourglass indeed needs a non-zero gravity to work, you don't need to measure it or even care about it's value. You could just measure the time needed by the sand to empty the upper half by counting heartbeats, counting mississipis or singing your preferred song while watching the sand falling to relate the hourglass time to seconds, regardless of what is the gravity value. Then, if it takes, lets say 10 minutes, you could use something like "flip the hourglass 6 times" to measure an hour in order to place a mark in a sundial or do something else which requires time intervals too large to mentally compute.

• That's not a bad idea. And you don't need glass to do that. You could use hollow plants like bamboo or sugar cane. Sep 28, 2015 at 8:23
• This wouldn't work because an hourglass depends on g which you don't know (see above answers on pendulums for that). g is different in every single celestial body.
– user13477
Sep 28, 2015 at 16:04
• @user1512321 I edited the answer just to respond to you. You don't need to know g. Sep 28, 2015 at 23:10

Other answers have gone over details, including math, of building a clock or whatnot provided you have some calibration standards for our unit system, not for time but for other kinds of units, like the length of a pendulum. I'll elaborate on finding these known units (and other junk that might further the plot).

You really have nothing?

In Have Spacesuit, will Travel the teenage boy finds himself captive. He has among other items in his pocket a dollar bill. He knows the dimensions of such standardized objects, and uses that to measure his cell. The feasibility of his escape requires considering a volume of water, and rather than just invoke cartoon physics, the author elaborates on figuring this out.

Although not wearing a watch and the smartphone and any all electronics are fried, he might have other items on his person, of known size or mass. Perhaps a pocket multi-tool is marked with a ruler along one edge and happens to be stamped with its mass for use with some more typical use.

Perhaps a neck chain piece of jewelry happens to have specs that he knows. Coins might have a known mass as a matter of course, even if it's not simple; e.g. 32g of (valuable metal) with the composition being 0.87 (value-metal) of the coin.

Take a careful inventory. Consider everything, even things that would normally be unnoticed: the lint in your pocket might just save your life.

Maybe you'll remember buying "24-inch" shoelaces. You might know the length of your belt counting up to the noch where you normally hitch it. What you don't? Well, the label in your underwear will tell you.

• The OP clearly states that he doesn't have any of those things. Sep 22, 2015 at 8:48
• Even if he had those (and he clearly says he doesnt) what use would they be? Sep 22, 2015 at 9:41
• He didn't say he went through naked; just that he wasn't prepared to go out. In a good story he might discover that "nothing" was not strictly true if, like innthe story I cited, he did a careful inventory of his clothing. Do I recall, perhaps buying "24-inch" shoe laces? Or the label in my underware stating the length of the circumference of the waistband? A folded dollar bill that came off the money clip... as for what to do, other answers have gone ocer details. My point is that "nothing" may not be the case and he carries calibration standards upon careful inspection. Sep 22, 2015 at 20:13
• He might still have pants. Pants in America at least have their measurements on the tag in inches. Those pants could be used to form other rulers of native objects (e.g. My fat ass has a 42" waist, half that is 21", half that is 10.5"; Now I have a ruler of an approx foot. ) Shoes, shirts, recently cut hair, fingernails, and other parts of the body all have dimensions, and at least a few of my parts I know the exact length of. Sep 24, 2015 at 15:45
• Note to self: memorize the dimensions and mass of my "Towel". If I'm sent to an alien planet without pants I at least hope I took my Towel. (H2G2 reference) Sep 24, 2015 at 20:23

The most important thing to figuring this out is how long is a local day. It is pretty easy to keep track of days, I won't bother telling you how to do that, but the key is figuring out how long a single day is.

The best way to do this would be to use some sort of a pendulum to estimate how long a second is, and use that to figure out the other relevant information. I'm going to assume that you don't have a mastery of physics, but do have some knowledge of principals. I know most grandfather clocks I see have a pendulum of about a meter. I know there is some relationship to gravity, but I don't really know what that is. Depending on the length of the local day, I could stay up to count the entire cycle (If short), or else figure out the number of swings over some period of time, perhaps by marking the position of the sun between elements, and using that.

As for the gravity, I'm going to assume that I would know at the very least what direction the change in gravity was. I could try jumping, and see how high I jump. I don't know really well how high that is, but I would guess a couple of inches. If I could barely jump, I know gravity is higher, if I jump really high, I know it's lower. I would use the reciprocal of the difference to estimate the gravity difference, as a guess.

I'm not sure how the pendulum differs with gravity, but I would guess it would be a linear factor, because distance is directly proportional with acceleration in such systems, and that gives a time estimate.

How would I measure the meter? I know my waist size pretty accurately, and that is close enough to a meter that I could fudge it to get one meter almost exactly. The exactness wouldn't really matter all that much, however, because I'm not quite sure of all of this.

I could further calibrate the pendulum clock I built based on my heart rate. I'm not really sure how accurate that would be, but it would take into account some of the stuff that I'm missing.

I also am a runner, and I know both my walking speed, and my jogging speed. These vary by around 15 seconds per mile, but is reasonably accurate. I could take my distance of measurement, and use this to chart out a course. That course would give me a reasonable estimate of time.

Okay, so I did the above without reference to any outside materials, to give me an idea of what it would take. How accurate was I?

First of all, a pendulum would be 2 seconds period, not one second. The distance is rather close, however, 99.4 cm. Assuming my extra sensing could tell a difference of a factor of two, and I could build within one inch, that would give me a precision of 5%, give or take.

As for the gravity measurement, that would potentially be very rough. In addition, my sense of physics was off, the period is proportional to the inverse of the square root of gravity. Woops. Still, this would actually likely work in my favor, as any changes in gravity would have a smaller effect.

My resting heart rate fluctuates by at least 10%, so that wouldn't be really useful.

Bottom line is, I think in a completely stranded situation, I could probably only estimate the time to within maybe 10%, assuming I can correct some mistakes in my knowledge.. With some accurate technology, I might be able to be a bit more accurate, especially if I had proper physics resources. In particular, with my pretty accurate meter estimation, and knowledge of light speed, I could probably be very accurate, to within a couple of percent.

• Your walking speed and your jogging speed would depend on gravity and atmosphere pressure and composition, so those two won't work, and they will likely compromise the time took to walk a mile. Also, measuring a mile or any large distance might be cumbersome (but is doable anyway), specially if the place is (unlucky) something swampy, full of obstacles (like trees, big rocks and high grass) or montainous, which is something that will also affect whatever is your walking speed. Sep 24, 2015 at 18:06
• Fair point on the variable gravity... That really does make things difficult... Sep 24, 2015 at 18:18

If your resting heartrate is a known quantity (say you're a runner) that might be a good source to calibrate a pendulum or waterclock or hourglass from (if inexact). If you happen to have a pacemaker, you could definitely calibrate from your heartrate. You might be able to calibrate for gravity in other kinds of calculations if you know your exact height (to use as a base unit for measuring height), and the mass of whatever you're going to drop (maybe yourself) or its weight on earth (since you can use that to figure out the mass if you happen to know G). From the force (perhaps measured by displacement, or an impression left in clay) you can derive the acceleration, and from the acceleration figure out the gravity. Its not gonna be precise. If you're much better at science than I am, you might know some way to put together a quartz or salt crystal based resonator of some kind. I don't happen to know in detail how that would work.

If you are an amazingly talented drummer the problem might not exist.

Some drummers are able to recognise the speed of different beats by ear to an insane degree of precision as well as being able to reproduce it at will. Not all speed might be known very precisely, but some which are very common and often played will be. One that is commonly recognized is of course.. 60bpm!