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Story starts out about 100 years from now.

While in orbit around Earth preparing for an interstellar mission, our spacecraft encounters some hand-wavey spacetime anomaly such that we're still in orbit around Earth, but approximately 20 million years into the future.

How would we be able to tell how far into the future we have traveled?

For the purposes of the story, H. sapiens has long since gone extinct on Earth (within a million years of the present day), and it's not obvious if they've left any descendants, or if they traveled to the stars. No other obviously intelligent or technologically advanced species has risen since then. The state of things is roughly the same as it was 20 million years before the present, way before the first humans showed up.

Some things that I've thought about:

  • Stellar motion (constellations won't look anything like they did before, and we should have a fairly accurate catalog for navigation purposes);
  • Continental drift (after 20 million years some motion should be evident, although since this meant to be an interstellar mission, we probably wouldn't have detailed maps of the Earth's surface to compare against);
  • Earth-Moon distance (Moon is receding at a rate of a few cm a year, should be measurable after 20 million years);

Since this ship was designed for interstellar travel, assume we have plenty of $\Delta{V}$ to tool around the solar system and landers to explore the surface.

What man-made structures (if any) would survive for 20 million years on Earth? If we find what used to be Yucca Mountain (or a similar site), could we somehow find and use the radioactive material that was stored there to estimate how long since it was buried?

What shape would the Apollo landing sites be in (or any other man-made structures on the Moon) after 20 million years?

What other things should I look at that would provide a somewhat reliable estimate?

Edit

To add some clarity and address some questions:

  1. For the purposes of the story, the estimate only has to be accurate to within a couple of million years - the exact number of years doesn't really matter. And they have to be able to determine they've moved into the future, rather than the past.

  2. The effect of the hand-wavey anomaly puts the ship in orbit around the Earth where the Earth will be 20-ish million years from now (magically preserving angular momentum), meaning they've travelled through space as well as time; however, from their perspective, they never really moved (although for some cheap initial drama, I may have it deposit them in a higher or lower orbit, or in a different inclination). And, for the purposes of the story, how they got there really doesn't matter.

  3. This was supposed to be an interstellar exploration mission using a hypothetical reaction drive with an insanely and likely impossibly high $I_{SP}$ allowing the ship to reach substantial fractions of $c$, such that the trip to the original target would have taken on the order of a decade within the ship's reference frame (centuries within the Earth's reference frame - the crew know what they're signing up for). Thus, they have plenty of $\Delta{V}$ to tool around the solar system (if they choose to do so), although high $I_{SP}$ usually correlates to low thrust, so it may take a while to get anywhere.

  4. While there are planetary scientists on board, the purpose of the trip is to analyze bodies in another star system, not Earth. They will have some Earth reference data, but not highly detailed maps of the surface.

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  • $\begingroup$ Would you edit the question to clarify the effect of the anomaly. Apparently your spacecraft (or the anomaly) does a few things and it's not entirely clear what they are. Does your spacecraft travel into the future and physically move to the new location where the Earth is, or does both your craft and the Earth move but only your craft travels through time, etc. - Also what accuracy do you want for knowing what time it is? - You say you have an accurate Constellation Map (20M years out of date?, or not), but no Map of the Earth. ... $\endgroup$ – user43711 Oct 14 '17 at 9:58
  • $\begingroup$ @Rob: The handwavy anomaly moves the ship through spacetime such that it’s in orbit where the Earth will be in the future. As for accuracy, within a couple of million years. So if they were shot exactly 21,374,521 years into the future, they’d be able to nail it down to between 19 and 23 million. $\endgroup$ – John Bode Oct 14 '17 at 12:43
  • $\begingroup$ Thanks for your reply. I've updated my answer to indicate the inaccuracies, danger and cost associated with launching one or more expeditions to mine enough samples for radiological dating and come up with an accurate, easy, cheap method; the Moon moves 22 mm away per year, so 440 km is 20 million years. $\endgroup$ – user43711 Oct 14 '17 at 16:16
  • $\begingroup$ Look at the stars. They drift known amounts. $\endgroup$ – Tony Ennis Oct 14 '17 at 22:04
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With proper excavation and radiometric dating, everything is possible.

Our current civilization is leaving a huge level of non-natural isotopes, some of these imbalances will be carried into hundreds of millions of years into the future. For example, the astronauts can use Uranium–lead dating:

The method relies on two separate decay chains, the uranium series from 238U to 206Pb, with a half-life of 4.47 billion years and the actinium series from 235U to 207Pb, with a half-life of 710 million years.

The real problem would be, as I see it, that your astronauts would have no idea what the "civilization baseline" level is, meaning, they would have no idea what isotopic composition was by the end of human civilization. It could be the same level as when they left, or 100 times higher because of a nuclear war or global contamination. Without knowledge of the baseline, accurate calculations would be very tough thing to do.

That means that they would have to perform excavation (or find exposed sedimentary rocks), just like geologists do today. They will inevitably come to a sediment layer that corresponds to human civilization, and from there they should be able to make more accurate estimate.

  • Earth-Moon distance that you have already mentioned should be another good timing method;
  • Individual stellar motion will be unpredictable for 20 million years into the future. But Sun's position with respect to the galaxy (and other galaxies) should be predictable.
  • Continental drift would be a good rough estimate, but it will lack any precision.
  • All human buildings will be buried at this point. Some will be preserved as they get buried. Your astronauts however will have to search for these buildings and do excavation.
  • Apollo landing sites will get degraded, but still going to be recognizable at close inspection.
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    $\begingroup$ Have some rep for the uranium-lead dating method. However, would 20M years of meteors and changing lunar geology (small and infrequent that it is, it's a lot over that time span) actualy leave the landing sites recognizable other than to find chunks of metal? I'm curious what you think. Even if they did, could you use them for any kind of time reference? $\endgroup$ – JBH Oct 13 '17 at 22:51
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    $\begingroup$ @JBH, in 20 million years it's going to be just debris. Earth is estimated to get 60 tons of cosmic dust falling on it every day. This translates to 1.76E-10 kg/(m2*day) or 0.858kg of material hitting 1 square meter of surface over 20 MY period. $\endgroup$ – Alexander Oct 13 '17 at 23:06
  • $\begingroup$ @JBH 20 million years produces a lot of dust, but ultimately its just that - dust - and 20 millon yers of weather will sweep most of it into rivers or the oceans. The radio dating techniques mentioned by Alexander will enable realtively accurate dating. Especially because there are around 40 different radioactive dating methods to use, each of which can be used to check the other (within certain time bands) so I don't think there would be any doubt. $\endgroup$ – Slarty Oct 13 '17 at 23:43
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    $\begingroup$ Manmade structures are not likely to last that long. Even the Rocky Mountains (80MM to 55MM years old) have changed enough by glaciation events in the past 20MM years that they would be barely recognizable to someone who saw them brand new. The great pyramid might have a chance since it's nothing but a honking big chunk pile of rocks, but by then it would be a smaller pile of rubble ... erm ... somewhere. I can't even say "in the desert", because that region has been at least savannah and desert within the past 20MM years. $\endgroup$ – pojo-guy Oct 14 '17 at 3:40
  • $\begingroup$ @pojo-guy - exposed structures definitely won't last that long. But once underground, rocks and fossilized remains can stay unchanged for as long as the whole tectonic plate is intact. $\endgroup$ – Alexander Oct 14 '17 at 5:55
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If you know, that you are in the solar system there might be another option you can reasonably construct. Your humanity did build an interstellar spaceship, so it is reasonable to assume that they also launched a load of other stuff into space in their time. Everything in a close to earth probably already decayed in orbit and is gone, but stuff sent further out might not be.

So I assume that in order to look for targets for interstellar travel, humanity build some space telescopes and in order to minimise interference from the sun and all the stuff in the inner solar system, they put them somewhere quiet, far out of the way, for example one might be in a really wide orbit around Pluto or something similar. Since solar power isn't good enough out there, they fitted it with an radioisotope thermoelectric generator (RTG). Since standardised parts are always good, your ship might also have the same model of RTG with identical fuel composition, maybe as an auxiliary power system. They might even have given you the tools to analyse the detailed composition of nuclear fuel, maybe for your main reactor.

Using this you should be able to get a rather precise time estimate, let's say $\pm 1 \%$ by comparing the composition of your RTG with the million years old one. The initial isotopes will probably be long gone, however some of the decay products will have half-lifes long enough to allow meaningful radiometric dating.

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    $\begingroup$ Indeed. If you're lucky enough to have an RTG based on Americium 241, its primary decay product is Neptunium 237 which has a half life of 2 million years, making the process particularly easy. You'd probably not even need one to compare with in that case. $\endgroup$ – Jules Oct 14 '17 at 9:50
  • $\begingroup$ @Jules You made me think maybe someone left a smoke detector on the moonbase, but of course the plastic would have deteriorated. $\endgroup$ – Spencer Oct 14 '17 at 23:36
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Alexander's answer is correct.

A different answer relies on the evolutionary clock. Despeciation is occurring at unprecedented rates at present time. We have begun the 6th mass extinction. This has the rather nice effect of setting the clock for the future.

Your explorers can look at the phylogenetic relatedness of life at 20 million years from now, and calculate (using the fidelity of DNA polymerase and reproductive rates) an estimate of time that has passed since H sapiens was busy killing everything.

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  • $\begingroup$ (1) Why would (even an interstellar) spaceship carry a DNA analyzer? (2) Why would it carry baseline information on every species of plant and animal? $\endgroup$ – RonJohn Oct 14 '17 at 3:57
  • $\begingroup$ @RonJohn - DNA sequencing could be performed relatively easily by any programmable device that is designed to visualize and analyse structures in the order of 0.1nm resolution. Today, such devices are extremely rare, but in future they may become more commonplace (particularly for a high-tech unit such as a spaceship that may want to be technologically self-sufficient, as such a device would be extremely useful in maintaining electronic equipment over the long term). (2) Why wouldn't you? But even if you don't, you can compare with anything your brought with you. $\endgroup$ – Jules Oct 14 '17 at 8:59
  • $\begingroup$ @Jules it all depends on the size and purpose of the interstellar ship, which wasn't mentioned by OP. $\endgroup$ – RonJohn Oct 14 '17 at 13:27
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    $\begingroup$ I don't know why they would carry a DNA analyzer, but it could be to do with medical diagnostic needs. Certainly all the starships in the federation use the technologies routinely. They don't need the baseline. They just need a decently complete series of sequences in the future. (think finches.) $\endgroup$ – DPT Oct 14 '17 at 13:45
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Based on your premise, I assume that astronauts are not well-prepared and willing time travellers.

In this case, the easiest way to determine time difference would be to compare current star positions with star maps in the spaceship navigation system. You should be able to calculate the time difference with at least 1000 years precision. Considering Bernard's Star moves very fast (relatively to other stars), you can get it down to a century if you spend a bit more time on charting the new sky.

Most likely, there will be no man-made structures on Earth if the humanity disappeared without reaching technological levels much higher than current. In 20 million years all surface structures will be completely destroyed by natural forces. Something (some glass and plastic) might survive by luck but it probably will be buried deep underground.

Moon will be your best bet for finding the remnants of human civilisation. The rubbish we've left there will likely survive for 100 million years more.

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    $\begingroup$ In 20 million years, Barnard's Star will be close to 10,000 light years away, and unidentifiable. In general, 20 million years is too far into the future to track the motion of nearby stars. $\endgroup$ – Mike Scott Oct 14 '17 at 9:24
  • $\begingroup$ @MikeScott, it is not a problem. We are talking about an interstellar spacecraft in the Earth orbit. We can safely assume that it has telescopes at least comparable to the Hubble, which can see stars billions of light years away. There is also no atmospheric interference, so we can see much clearer. $\endgroup$ – Olga Oct 14 '17 at 21:23
  • $\begingroup$ Star's trajectories are pretty much guaranteed to be non-linear on the scale of millions of years. $\endgroup$ – Alexander Oct 15 '17 at 1:14
  • $\begingroup$ @Alexander - Non-linear, yes, but not unpredictably so, at least on that sort of timescale. For stars in our vicinity, rotation period is about 240 million years. Simulations of galactic stability suggest that orbital trajectories of individual stars should be (approximately) stable over timeframes of 10s to 100s of orbital periods. Calculating the expected position of an individual star up to 20 million years from now is nontrivial but achievable, at least as long as we have good data about its starting state and nearby massive objects, which we should have for local stars. $\endgroup$ – Jules Oct 15 '17 at 2:04
  • $\begingroup$ @Jules For a star moving as fast relative to the Sun as Barnard’s Star, over 20 million years, “nearby massive objects” along its trajectory may be thousands of light years away at present. $\endgroup$ – Mike Scott Oct 15 '17 at 6:57
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First you need some degree of desired accuracy and a statement of the Units of Measurement, since you didn't say where you took off from and used the word approximately (and 20 million) in your question I will give approximation methods and the (currently) known accurate method.

Use of UT1 avoids considering where you launched from and an assumption that you wanted your answer in 'local time', continental drift caused by rotation of the core and crusts makes your starting location inaccurate after a long period of time.

For an approximate time @Alexander's answer is accurate to 1 or 2%, so 200K years. The precision and accuracy are fine, only affected by the accuracy, precision and duration of measurement available (which likely won't be very favorable). Simply bring a small rock with you and measure U vs. Pb then shield it and remeasure after your travel giving a base amount to compare with an expedition to the planets or Moon to obtain enough samples to make a plot. The answer should be accurate to a few decimal point, in Gyrs (billions of years). Use of other Elements and their decay ratios will improve the accuracy of the answer (assuming sufficiently accurate equipment and enough time to average your measurements).

Next method, measure the diameter and brightness of our Sun. Fairly easy, accurate and combined with the above method each makes the other better. Not particularly precise without accurate equipment. Combined with measurements of the sizes of other stars will improve the result.

The easiest and fastest approximation is to measure the distance from the Earth to the Moon (assuming no large meteor impacts changed the orbitb. The Moon moves away 22mm per year so 220 km per 10 million years; if it's 440 km further away then you're 20 million years in the future (this can be cross verified by doing the same calculations with other planets).

Before giving the 'accurate' method know that it relies on current science and mathematics - 20 million years from now we might have learned something new.

The "accurate" method is explained in many places including the book The Science of Time 2016: Time in Astronomy & Society, Past, Present and Future where the location of thousands of objects in space has been accurately determined and cataloged into the International Celestial Reference Frame (ICRF2) which is used to establish UT1 (Universal Time) based on their location (which varies little, in a calculatable manner, in a measly 20 million years).

Note: You're going to want a Doctorate in Mathematics and Astrophysics to read that book but there's Software available (See: https://www.iers.org/IERS/EN/Science/EarthRotation/EarthRotation.html) and plenty of information available by using Internet Search Engines.

For more information on the ICRF2 see: http://adsabs.harvard.edu/abs/2015AJ....150...58F .

I don't want to delve into Astrophysics and the associated Mathematics as I assume you don't want millisecond accuracy. In the interests of such precision I welcome edits that improve my answer as such would be greatly appreciated by our community.

I will come back and see if I can improve this answer.

From the way you've asked the question combined with your ability to pilot a spacecraft you could just look out the window, see the Sun, and guess somewhat accurately within a million years or so (if that's good enough).

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  • $\begingroup$ I'm confused about your example with the rock. If you bring the rock with you, it won't have aged 20 million years - it will have experienced the same amount of time you did. $\endgroup$ – HDE 226868 Oct 14 '17 at 1:44
  • $\begingroup$ True, you need to use it to compare with another rock retrieved from Earth (or the Moon). I was also going to add a point that simply changing your time doesn't change your location, but the question does specify that you'd still be in orbit around the Earth (so the Earth needs to move with you through time to maintain the same relative position - you orbiting). If only your time changed everything (including the Earth) would have moved and you could materialize within the Sun (which makes calculating the time out of the question). More editing coming. $\endgroup$ – user43711 Oct 14 '17 at 2:35
  • $\begingroup$ @Rob, comparing rocks is a good idea if they were extracted from the same location, which, for Earth, is going to be problematic. Lunar rocks, though, is a good idea. $\endgroup$ – Alexander Oct 14 '17 at 3:02
  • $\begingroup$ Pulsar spin-down. $\endgroup$ – Eric Towers Oct 14 '17 at 17:51
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If your story starts off 100 years from now, it's possible that by the time it begins, some more Voyager-like probes have been sent off into space, maybe some with transmitters a lot more powerful than Voyager / Voyager II.

Your protagonists pick up a weak signal from one of them, but the signal comes from where it will be in 20 million years!

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You wouldn't need detailed maps of the Earth to know that a long time had passed. Assuming current motion remains about the same as now, you'd see:

  1. The West Coast of North America looks different due to California west of the San Andreas sliding north. Vancouver Island has slammed into the mainland.
  2. The Mediterranean is much narrower, with Italy starting to jam into North Africa, and probably isolated from the Atlantic due to the closure of Gibraltar. Parts of it very likely dried out.
  3. The Red Sea has vanished as Africa and Arabia have re-joined.
  4. Australia has moved northward, collecting New Guinea and parts of Indonesia along the way and is sideswiping the Phillipines.
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    $\begingroup$ The OP asks specifically that it shall be possible to tell how far in the future the travel happened. What you state just show there was a travel in the future. $\endgroup$ – L.Dutch Oct 19 '17 at 7:30
  • $\begingroup$ At 50 million years the Med has completely closed and mountains are raising, and Australia is starting to slam into China. If you know that, and you know the rough layout of the continents now, you can get an estimate as to how much time has passed. $\endgroup$ – Keith Morrison Oct 20 '17 at 3:58
  • $\begingroup$ Your reasoning is not more different than answering to the question "How old is Bob?" with "look, Bob has beard. He must be older than 12". $\endgroup$ – L.Dutch Oct 20 '17 at 5:15
  • $\begingroup$ @L.Dutch - If one of the characters is knowledgeable about the pace of continental drift, s/he could make the appropriate deductions. $\endgroup$ – colmde Jan 4 at 9:41

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