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

Question

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.

Answer 1

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.

Answer 2

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

Answer 3

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.

Answer 4

There is a bit of confusion about my answer. I'm updating the answer with clarifications and additional information. The quotes are my original answer.

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.

Answer 5

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.

Answer 6

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.

Answer 7

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?

Answer 8

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.

6. 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.

Answer 9

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.

Answer 10

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.

Answer 11

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.

Answer 12

Shave Your Head

1. Shave your head
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.

Answer 13

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.

Answer 14

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.

Answer 15

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 bowl 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.

Answer 16

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

• Your finger nails grow about 3 millimeters per month

  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).

Answer 17

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.

Answer 18

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

Answer 19

Use your jetlag.

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.

Answer 20

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.

Answer 21

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!

Answer 22

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.

Answer 23

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.

Answer 24

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.

Answer

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.

Answer 25

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.

Answer 26

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.

Answer 27

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!

Answer 28

Do you have perfect pitch?

Sing an A and ask the natives what frequency it is in their units. Their second will be equal to 440/(frequency they say) of our seconds.

Answer 29

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.

Answer 30

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.