Having recently watched Timeline and ST:First Contact, I’m wondering how feasible it is to determine one’s space time coordinates through astronomy. If you were transported to an unknown location and time with only a laptop and some astronomy software, and perhaps a portable telescope, could you figure out when and where you were?
Could you determine the date and time?
Could you determine your location on Earth?
Could you determine your location and/or date in some random part of the solar system or beyond.
It is certainly feasible. If you are on Earth within about 10,000 years of the present, you should be able to figure out the date, time and your position after about 24 hours of observations. However, if you are further in the past or future, the constellations will start to look different and a lot more observation may be needed.
Locating Polaris gives you the north direction and your latitude. Time-laps photography can confirm the direction of Earth’s axis (it wobbles in 26000 year cycle). Position of planets and the Moon would give you date to within a few days. However, you may not see enough of them, giving you even dozens of possibilities. But seeing the direction where the Sun rises should rule out most of them. Once you are sure of the date, position of planets and the Moon will allow you to find your longitude. The Sun at its highest position will set the local noon, and knowing your position, calculating the UTC is dead simple.
The same applies to other places in the Solar system, the stars do not really change much and planets are of course the same. However, the movement of the body you are standing on is probably known will less precision than the Earth, so you may need to observe the sky for a couple of days.
Outside of the Solar system you are out of luck. If you can find the center of Milky Way (very difficult with visual observations) and compare it to objects outside of our galaxy (say Andromeda), you should be able to get a rough idea where you are in the galaxy - keeping in mind that the Galaxy rotates every 50 million years. Beyond that, trying to identify known stars would very very difficult.
Based on simple naked-eye observations that anyone can learn how to do, and with no books or tools, you can easily determine your latitude, the time of the year, and which way is north. Toss in an ephemeris (information on where the planets are in their orbits and when) and some means of doing the calculations (easiest with a computer, but could also be books and slide rules or scratch paper and pencils), and you could also determine the year, though it would be harder and require more precise observations if you didn’t already know it to within a century or three. With naked eye and straightforward but uncommon training, you could determine where you were in the 26,000 year precession cycle, which could be what it takes to get you close enough for the ephemeris to be useful. And comparing the drift of the stars in the constellations would probably be enough to tell you which precession cycle you’re in, but you’d definitely need books and very precise observations to do that part. In any event, longitude would be basically impossible unless you lucked out and got to observe a lunar eclipse, or you had a telescope to observe the moons of Jupiter, and either way you’d need a very good ephemeris and good observation skills to get even an approximate answer.
If you’re not on Earth, then you’d need a different set of landmarks: Bright stars, or globular clusters, or other galaxies, or if nothing else the cosmic microwave background radiation. All told, I estimate that from anywhere within a few dozen billion lightyears, you could (with computers and the appropriate databases) determine your position to within about 1% of your distance from Earth (thus, for instance, if you were 100 million lightyears away, you could determine your position to within about 1 million lightyears).