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My question is if I put you down somewhere in the Milky Way galaxy in any given period of time, is there a way for you to tell when and where you are based on stars or constellations? Or some known astronomical event like a supernova? How accurate would that be?

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    $\begingroup$ I believe I've seen pulsar mentioned as possible ways to navigate outside the solar system, but I'm doubtful we could do this for any time and any place (and I'm not sure what you'd use as a common temporal reference at two different locations in space-time). $\endgroup$ – StephenG Sep 26 '17 at 23:45
  • $\begingroup$ Overly simple answer for the when: measure the distance between the Sun and several nearby stars, especially those with high "proper motion". These set of distances are unique for a given time. Of course this assume: 1) you can find the sun, and 2) this is during the sun's lifespan. $\endgroup$ – user21 Sep 27 '17 at 14:24
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This question is someone open-ended since you don't provide many constraints, so I'll impose the following two conditions of my own to help me give an answer:

  1. I'll assume that after you're randomly placed in space and time, that you can make any observation one could make here on Earth - that is, you have whatever equipment is necessary to observe anything about the Universe we can currently observe.
  2. I'll assume that you have access to all current astronomical knowledge (in a digital library or some such thing) such as star catalogs, physics books, published papers, etc.

How do we know our location?

In determining location, because we exist in three dimensional space, we have to specify position with three coordinates. The simplest coordinate system in my mind, in terms of what we can measure, are the three coordinates below:

  1. our radial distance from the center of the galaxy,
  2. our height above or below the galactic plane,
  3. and our azimuthal angle from some reference point.

Yes I know these coordinates aren't orthogonal, but they relate well to measurements one could make and simple coordinate transformations could make them orthogonal.

The first one is pretty easy. We can currently measure the distance to Sag A*, the black hole at the center of the galaxy. It's not particularly easy and measurements have fluctuated over the years with respect to our position on Earth (see e.g., Eisenhauer et al. 2003 or Boehle et al. 2016), but it is a measurement which could allow you to define #1.

The second coordinate could be achieved by simply mapping the local star field. A survey akin to SDSS could accomplish this. This is precisely what was done in this Humphreys & Larson 1995. It would take time and a lot of work, but you could make this measurement pretty easily.

So far so good. Now we come to coordinate #3 and suddenly we hit a problem. We need to know our azimuthal position with respect to some reference point. That is, if you look down on the galaxy and consider our angle from some line, what would that line be and what would that angle be? Since the clear intent is to relate our new position to where the Earth is, the most logical reference line is the line connecting the Earth to the center of the galaxy. But how do we know where that line is with respect to our new position? I'm afraid I don't have a good answer here. Others suggested using pulsars but that isn't foolproof. First, you don't know when you're being deposited so it could be billions of years in the past or future when all current knowledge of pulsars is no longer relevant. Second, you might be on the other side of the milky way where we can't actually see anything currently and thus have no knowledge of pulsars over there.

Your best bet might be to map out the star distribution of as wide a swath of the galaxy as you can see to try and understand what the spiral arms look like near you. We've already done this for our current position in the galaxy. Galactic arms move and change slowly, taking hundreds of millions if not billions of years to change significantly. If you can recognize the general structure of the arms, that would give you a decent reference to your azimuthal position.

How do we know the time?

I'm going to break this down into two possible answers. The first assumes you've been placed in a time not too distant from our current time (think less than a million years) and you're still pretty near to our current position.

In the case above, pulsars are the way to go. Pulsars pulse with extreme regularity, so that they're great time keepers. But if your goal is to know how much time has passed, you need to look at the time rate of change of the pulses. As it turns out, the pulsars don't pulse with perfect regularity. The time between pulses decays very slowly over time due to the pulsars losing angular momentum very slowly. The general step to calculating a reasonably precise time is as follows.

  1. Find a pulsar that is currently known and has current measurements of the pulse rate and decay in pulse rate. To make sure you've identified a given pulsar as the correct one, you'll have to map its relation to other stars via a wide survey (the star fields will have changed, but if you're not too far away from our time you can predict with reasonable accuracy where most stars will be or have been in the past).
  2. Measure the pulse rate (and decay rate if you wish, but that may take years or even decades).
  3. Compare your currently measured pulse rate to the present day measured rate and decay rate and do some calculations. You should be able to figure out your current time with respect to the time now fairly precisely. I can't say how precise, but I wouldn't be surprised if you could get within a decade or so of the current time (depending on how accurate your pulsar models are).

The only caveat to the above approach is that pulsars can "glitch". Normally the pulse rate decays smoothly, but every once in a while a pulsar might just glitch and quickly change pulse rates. It is unclear exactly why these glitches occur and they're unpredictable so you have to make the assumption that your pulsar hasn't glitched between now and whatever time you're in. If it has, your time may be off wildly. To mitigate this, you should of course use as many pulsars as you can find. If one pulsar gives a different number than the rest, you can assume it glitched and throw it out.

The second case is more tricky. Now I'm going to assume you're in a time really distant from our own. Millions or possibly billions of years away from now. In that case, any hope in finding a precise time (or even a precise year) is wildly presumptuous. At best, you can figure out your general time within the universe by measuring the current age of the universe. We currently know the age to be $13.799\pm 0.021\ \mathrm{billion\ years}$ based on the latest and greatest measurements. You can see our uncertainty is down to 21 million years. If you make similar measurements of the Universe's age in your time, then the best you'll be able to do is define your time with respect ours with an accuracy of ~20 million years. But if you're a billion years in the future, that's a pretty good measurement in my opinion.

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    $\begingroup$ I like this and it could be extended in many ways. A simple way of estimating your cosmological age is just to measure the temperature of the CMB. $\endgroup$ – ProfRob Sep 27 '17 at 15:57
  • $\begingroup$ Brilliant answer, this is exactly what I was looking for! Thanks. $\endgroup$ – Darth Scitus Sep 28 '17 at 15:21
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Some of this might stray into WorldBuilding StackExchange territory, and 'when' will be tough to approximate as galactic rotation and stars going through different phases of their lives can make constellations and reference points obsolete with time.

As StephenG mentioned, pulsars, owing to their (usually) unchanging and detectable rotation periods, can be used as reference points. The plaques attached to Pioneer 10 and 11 provide the solar system's location relative to nearby pulsars. Pulsar coordinates were also added to the Voyager Golden Album too.

The alternative would be to adopt relatively fixed locations on your 'local' celestial sphere and determine your position relative to them, and therefore where your destination is. This assumes you know where your destination is relative to your reference points. The galactic core's location, the direction of galactic rotation, the Magellanic Clouds or other extra-galactic sources could be your reference points. They would hardly be accurate but if you are attempting a Voyager-esque journey through the Milky Way, it's a start.

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  • $\begingroup$ Pulsars will not work in general because the pulsar phenomenon lasts many orders of magnitude less than the age of the Galaxy. The Magellanic clouds cannot really be used as "reference points" since they orbit the Galaxy (and their orbits are not well defined); other nearby extragalactic sources are also in relative motion . $\endgroup$ – ProfRob Sep 27 '17 at 16:06
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    $\begingroup$ @RobJeffries I never emphasised these as being long-term solutions. As mentioned in my first paragraph; few reference points will remain useful in the long run. $\endgroup$ – user10106 Sep 27 '17 at 16:10
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The location part of the problem is mostly dealt with in Zephyr's answer. I completely concur, but the last part - the azimuth - is indeed tricky, but you also have to define what you mean by position in azimuth. If you are in the recent past or future then some definition would be possible based on the directions of a network of radio-loud, high-redshift quasars. Indeed, accurate measurements of their redshifts could then be combined with a cosmological model to tell you at what exact cosmic epoch your measurements were made at.

Similarly, a cosmological model could be combined with a precise measurement of the temperature of the cosmic microwave background to give you your cosmic age. This would work at any cosmic epoch (assuming we have got the cosmological model correct) and be far more precise than some alternatives you could think of, like measuring the current age of the Galaxy using the luminosity of the coolest white dwarfs or the ages of stars in the oldest globular clusters (maybe accurate to a billion years).

However, if you are billions of years into the future or past then defining the azimuthal location in any well-defined way becomes impossible. The Galaxy rotates with a not precisely known speed that varies with radius. Distant quasars come and go (or more precisely, turn on and off); local galaxies move with respect to our Galaxy with not precisely known (tangential) motions. Perhaps you could make a definition with respect to the cosmic ray dipole alignment, but this would change as the Galaxy's motion changes due to the influence of other galaxies in the local group and supercluster.

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