How can my accidental time travelers determine the year using star/stars?

Question

Time travel on movies and tv always say they were able to tell the year by looking at the stars. But how?

For example Voyager goes back in 1996 and Ensign Kim says astrometrics puts them in the year 1996. In the movie Timeline they said they sent probes and pointed it's cameras at the night sky and determined the date.

http://www.chakoteya.net/voyager/304.htm

Star Trek Voyager

JANEWAY: The question isn't where we are, it's when we are. Mister Kim.

KIM: According to astrometric readings the year is 1996

http://www.script-o-rama.com/movie_scripts/t/timeline-script-transcript-michael-crichton.html

Timeline movie

That's when Mr. Doniger made the brilliant decision to point the camera straight up. So once we cross-referenced star charts to the horizon, we realized that the camera was not only in the wrong place,- but it was in the wrong time.

My problem is my accidental time travelers are amateur astronomers/stargazers (they also have Stellarium software or equivalent and laptops), and I want them to at least be able to isolate the year or decade they time-jumped to.

I was planning to use Barnard's Star as the easiest reference. Am I wrong? Is there an easier way?

https://oneminuteastronomer.com/8869/barnards-star/

Barnard Star’s main claim to fame is its large proper motion, the angular change of its position across the sky. It moves about 10.4” per year, more than any other star, which is a result of its true motion through the galaxy and its proximity to our solar system. Over an average human lifespan, the star moves about a quarter of a degree or about half the diameter of the full Moon. In astronomical terms, that’s mighty fast. - See more at: https://oneminuteastronomer.com/8869/barnards-star/#sthash.xGxKkwnN.dpuf

This is what Ensign Kim (Star trek Voyager) should see in 1996 if using Barnard's Star. Sorry about the zoom factor I wanted to show the Ophiuchus constellation.

Kapteyn's Star is second highest then Groombridge 1830 third highest proper motion are also possible choices.

Answer 1

The technique should work. I can't really say much besides that.

There are other things they could do, too. They might not be easier than tracking the proper motion of a star, but they'll work:

• Use variable stars. Most variables stars have regular periods hat can (and have been, in many cases) determined. They can also be used to figure out the exact date. Here's how:

  Take a star - $A$ - that has a period of $P_A$. It has a light curve that remains constant over time. Here's an example: the light curve of Delta Cephei:

  

  During each cycle, the star reaches a given brightness twice (unless the brightness is he maximum or minimum brightness), unless it is an eclipsing binary. So you can figure out that at a given brightness, it is at one of two points in its cycle. Observations a short while later can confirm the exact point by seeing how the curve changes.

  After taking these measurements, you know at what point in the cycle you're in. If you know the point in the cycle the star was at when you left, you know the star has been though $a+n_A$ cycles, where $a<1$ and is the amount of cycles the star would have gone through if $n=0$. You can figure out $a$; now you need to find $n_A$.

  Take a second star, $B$. It has a period of $P_B$, and another light curve. You can figure out, as before, that it has been through $b+n_B$ cycles. These two stars should have different periods; this configuration only arises within a given amount of time that is longer than $P_A$ or $P_B$.

  Continue this with more stars, and you can better figure out what $n_A$ and $n_B$ are. Given that variable stars can have extremely long and extremely short periods, this can help refined your other measurements to high accuracy.

As far as I can tell, there aren't any other methods involving stars that your spacefarers could use. They need to observe things that predictably change with time. On a larger scale, they could use thee expansion of the universe and the recessional velocity of galaxies, as dictated by the Hubble parameter, which changes with time. But it's extremely hard to measure to any usable accuracy.

Answer 2

It depends on how far they've traveled, and if they've got a rough idea of when they are.

• Days: If you know when you are to within a month or so, the Galilean moons of Jupiter can tell you when you are to a precision of hours or less if you've got a good pair of binoculars.

• Months to years: If you know which century you're in, you can pin down the date to within a month or so by observing which planets are visible at night, and what constellations they're in.

• Centuries to millennia: Over longer time periods, Earth's orbit shifts and the constellations themselves change. Where is Barnard's Star? Which star is closest to the North Pole? Is SN 1006 a star or a nebula? What shape is Ursa Major?

• Longer periods: Beyond a hundred million years or so, there's no good way to figure out the time. The Solar System has a Lyapunov time of around 200 million years: it is effectively impossible to predict positions that far out from current conditions. Many of the bright stars have lifespans shorter than this. The longer-lasting stars are dim enough that they move out of amateur observational range over this timescale. Your best bet is geologic rather than astronomical: radioisotope dating of rocks, or measuring the U-235/U-238 ratio of uranium ore.