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I'm trying to imagine mystery setting when amateur astronomer stumbles upon a torrent which contains a 3D map of the Milky Way galaxy. The map contains all large objects: star systems, planets, nebulae, black holes.
Is there a way with our current knowledge to check is the map real or just an object of someone's imagination?
Just look at the sky1
Your protagonist is an astronomer (albeit an amateur one). He'll most certainly have access to a telescope or similar apparatus that allows him to start verifying the positions of certain stars or clusters relative to earth.
From there it is just a process of elimination, the more star locations they can verify using these methods, the higher the probability becomes that the map is *real.
On the other hand, anyone2 else will be able to do the same, so this method only allows you to garner a certain amount of proof.
Still, thanks to exact coordinates of stars, it becomes almost trivial to look out for certain electromagnetic-wave-patterns that would confirm3 the coordinates to be valid.
1you silly you...
2well not really anyone, but at least astronomers and people with lots of money/time yes, anyone - because star charts are a thing now(thanks to at @Zxyrra for that phantastic bit of information)
3well not really confirm, more like telling you that the chances of there being something like a star are higher than lightsecond to the relative left of that source
As of September, we have a fairly accurate map of our galaxy.
By measuring the parallaxes of distant objects, we know the relative locations of about 400 million stars.
The satellite which gathered this information, called Gaia, also found billions of other potential objects. Most if not all of the data recorded, including the map your character needs for comparison, is open to the public.
After some comparison, it should be clear that the file they found is or is not accurate.
Zxyrra's approach of comparing to a publicly-available, trusted map has a flaw: the person faking the map could have downloaded the same map you're comparing against, then added the planets by making that data up. All the data that exists on both maps would be the same. That'd be pretty obvious (different maps should not be exactly the same, there are surely mistakes in both). A more clever forger would of course introduce some errors, and move things a little within the error bars, etc. Of course, all of this will need to be done by computers—not like you can eyeball two maps of the galaxy and say if they're the same. So both the forger and especially the person checking need to be skilled.
Checking for forgery essentially will involve outsmarting the forger: find some signature left by the algorithm the forger used to generate the new data.
There is another, easier way that doesn't require outsmarting the forger: wait. Astronomers are, fairly routinely, announcing newly discovered planets. You can check new discoveries against your map—any that agree with your map and occurred after you downloaded the map are evidence the map is true; any the disagree with your map are evidence it isn't (or at least is incomplete).
Find an object on the map that is unknown but is within the detection capabilities of the best telescopes but no others. Point one at it.
Since the big scopes have good records as to where they have been pointed you can rule out prior human knowledge.
While this doesn't prove the map to be accurate it does prove it to be of alien origin.
The map can be falsified (proved false) if it describes something physically impossible or extremely improbable. However, a sufficiently motivated forger can avoid this by running physical simulations of the map and verifying that it is physically stable over the short-to-intermediate term (which is exactly what you would do to check for these physical impossibilities in the first place).
Otherwise, it's a matter of comparing the map to reality. The problem with that is twofold:
If you need to know whether the map is real based on the same set of information as the forger has, you are out of luck.
You could wait for more aspects of reality to become known (i.e. for more stars and exoplanets to be discovered), or perhaps use nonpublic information depending on who you work for (e.g. the military?), but the above dilemma continues to hold: Everything which is learned is now known, so the map can no longer provide new information about it. And that's assuming that science follows a straight line from unknown to truth without passing through falsehood, which is unrealistic. It would perhaps be more accurate to say that there is a continuum between (1) and (2), and it's often difficult to know exactly where you are on that continuum. It's possible that a genuine map might disagree even with supposed "known facts," if our understanding is badly incorrect.
Perhaps, after enough new stars and exoplanets have been discovered, and the map has agreed with these discoveries sufficiently often, you will conclude that the map is genuine, rejecting the possibility that a forger managed to guess all those discoveries by chance alone. But how often is "sufficiently often" and how many discoveries does this take?
To answer that, we (usually*) use statistical significance testing. Basically, you imagine (or simulate) numerous forgers creating numerous fake maps, and try to figure out what fraction of those fakes happen to look at least as realistic as the map you actually have. If this number (called the p-value) is very small, you can argue that it's unreasonable to continue believing the map is a forgery. Your definition of "very small" (the significance level) will depend on what (if anything) you plan to do with the map once you know it's genuine. If you're going to launch a generation ship at an exoplanet, you will probably be a lot more cautious than if you're going to point a space telescope at an interesting area of the sky for a few days. If you don't plan on doing anything in particular with the map, perhaps you should ask yourself why you care about its accuracy in the first place. That reason will inform your choice of significance level.
If all that is a bit hard to follow, here's the short version: You can wait for some more celestial bodies to be discovered by astronomers, compare the newly-discovered objects to those in the map, and use that to prove the map is (probably) real. But if you do that, you won't be able to use the map right away, and by the time you are able to use it, it will be partially redundant to the newly-discovered information.
* This link included for completeness; you can completely ignore it if it doesn't make sense to you.
Does the OP have any idea of hat a 3D map of our galaxy showing all the stars and planets would be like?
There are at least 100,000,000,000 stars in our galaxy and possibly a few times that many. And a large percentage of them have planets so there are billions of planets in the galaxy.
And how could you show everything to scale on a map? In our solar system the eight planets have average distances from the Sun of 57,909,000 to 4,500,000,000 kilometers - Neptune is 77.708 times as distant as Mercury. A light year is 9,460,700,000,000,000 kilometers. The nearest star is Alpha Centauri about 4.30 light years away, or 2,100.33 times as far as Neptune. The diameter of the galactic disc is about 100,000 to 120,000 light years, or about 23,255.813 to 27,906.9 times the distance to Alpha Centauri, or about 48,844,854 to 58,613,699 times the distance of Neptune.
So your map should be a gigantic computer database with all the information and the ability to display 3D maps of selected objects.
The way to check its accuracy would be to find out what astronomical projects are looking for objects in the galaxy and planning to do so in the near future. You will want to have a computer program to automatically record all announcements of discoveries of objects in our galaxy and automatically check against the data base.
If you want to prove to others that you have a accurate database you will want to search the data base for relatively small group of objects that are being currently searched for. For example there are only a few hundred star systems within a few tens of light years from Earth. Finding them all is important to getting a good unbiased sample of the stars in this part of the galaxy. So you can make a list of all star systems within 30 light years of Earth that have not yet been found to be that close and publish their distances and when astronomers check them and find you are correct that will convince many that you do have an accurate database.
