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Assume that you have a Rogue Planet hurtling through deep space.

Somehow, an alien civilization from, say, 1,000 ly away acquires astronomical data from this planet. This data is in the form of high resolution photographs of the sky above said Rogue Planet (presumably no clouds on an ice planet). This data is collected repeatedly, so the planet's motion may also be calculated.

I imagine this will largely depend on the precise resolution of these photographs, but would it be broadly realistic for - say - a civilization 1,000 ly away to pinpoint the location of this Rogue Planet at any one point in time (say, within the area of the Moon's current rotation around the Earth)? How would precision change with the photos' resolution and the aliens' distance from the Rogue Planet?

Bonus question: How would the accuracy of this method compare with the Earth straight up beaming radio signals at the aliens? (Or, at what resolution would sky photos become competitive with it).

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  • $\begingroup$ What is the meaning of the word "resolution" in this question? Hint: when was the first time that the annual parallax of a star was measured? How did they do it? How do we measure star parallaxes today? (And what on Earth is "night time" supposed to be on a rogue planet?) $\endgroup$
    – AlexP
    Nov 3, 2019 at 20:35
  • $\begingroup$ Let's clarify the task - we have some night sky photographs (in visible light). We don't know where they were taken, and don't know the direction of transmission, but do know it's approximately 1000 light years range. We do know that those photographs are fresh, in the sense that they were transmitted to us immediately or almost immediately after they were taken. $\endgroup$
    – Alexander
    Nov 4, 2019 at 18:34

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I’ll help you understand what it means to be 1,000 ly away. First, it won’t be possible, in any way, to beam a radio signal to the planet, or to see it:

  • the planet is rogue, that means you don’t know where it is. And that means you don’t know where to aim your radio beam. Also, even if you were able to see where it is, you are seeing where it was 1,000 years ago. It’s not there anymore - it has moved. If you aim the radio at the spot you see the planet, you will definitely miss. But even if you hit the planet by luck, or maybe it wasn’t moving at all, you would have to wait 2,000 years before you knew. At that point, your location information is 2,000 years outdated.

  • The planet is 1,000 light years away. There is no telescope which could ever see a planet that far away. First, it has no sun, so it isn’t lit up. There’s nothing at all to see. But if it did have some sunlight on it somehow, there wouldn’t be enough light reaching us to make a picture at all. Even if it did have some light on it, it would be too small to see by any telescope we have or could even build.

  • The astronomical observations you received will be much older than 1,000 years because they got to you somehow traveling through space, or they were transmitted to you by that other civilization. Anything the planet passed by in 1,000 years may have changed its course and you would never know. Even though you are getting “repeated” updates, those updates are 1,000 years old. And even then, you did not specify how old the data was. We’re the astronomical pictures being sent in real time or were they historical pictures? In this century, Earth could not match those pictures to our star charts from 1,000 years ago to within the radius of the moon, as you say.

For example, our Hubble space telescope can see objects with a resolution of 0.04 arc seconds.

Let’s assume your rogue planet was a huge gas giant, 142,984 km diameter, like Jupiter. And assume it was fully lit up by something (no idea what). From 1,000 ly away it would be so small, it would occupy only 0.00000000865935221 arc seconds of your vision. This means a telescope 4.6 million times more powerful than Hubble could barely see it as a single spec. But the problem again is, it would see the speck of light coming from where the huge glowing planet was 1,000 years ago.

The only way to detect this planet would be if you were lucky enough to have a star or galaxy somewhere DIRECTLY behind it, then you need a telescope millions of times more powerful than anything we have, and several years of observations, to try to calculate the planet’s approximate location by gravitational lensing. Even after you do this, your position will still be 1,000 years old.

The accuracy of these methods in determining where the planet is today will be the same. No accuracy.

Bonus

Since you asked about changing the distance, that makes all the difference. If you get within 10 ly of Earth our data would be recent enough to match with theirs and you could possibly triangulate a location within slightly larger an area than the orbit of Mars. You will never get any location resolution within the size of the orbit of the moon because our own star charts don’t have that kind of resolution - even if their charts were perfect, our charts would be the weakest link. The closest star to Earth has the very best resolution - this is Proxima Centauri. Using our very best parallax measurement method, we estimate it’s distance at 268,770 Astronomical Units, within an error of +/- 5 AU. Everything else in the sky has a much larger error, so no computer is going to accurately pinpoint this planet to the resolution you want.

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In order for this to work you'd need something more than 'photographs'.

The problem you're describing is basically the same 'solve for x' trig problem that we all did ad nauseam in school. Position relative to another object is always measured in three values, and if you know any two of them you can solve for the third.

In this case, the two values that you could 'know' based on observations from the surface of the Rogue planet is it's distance from visible stars, and where exactly those other stars are.

In order to do that, your civilization would have to be able to identify stars visible from the Rogue planet that are ALSO visible from their own planet, and that they know the relative positions of. Identifying stars in this way requires a spectroscopic analysis to measure the entire spectrum of electromagnetic radiation coming off the star.

If you had this level of detail in the data gathered from the rogue planet, then you could go through a process of comparing the spectral profiles of stars visible from the Rogue planet against stars visible from your own planet until you find at least three exact matches.

At that point you can take two different points in time from the Rogue planet and compare them and you'd be able to figure out the Rogue planet's relative position, velocity, and vector relative to those three stars and, by extension, your own planet.

HOWEVER.

In order to know where the Rogue planet actually is now (relative to your alien civilization, you would also have to know exactly when both images were taken.

This is a non-trivial problem as there isn't a universal time ruler that you can check your images against somehow. You would have to get lucky and have the images from the Rogue planet include something you can match against observations from your own planet that has a very specific time frame. Supernovae are ideal for this because they are very bright, very unique, and only last for a short time. However, there's no guarantee that there's going to be a visible supernova at any given time for you to use.

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Assuming that the photographs include the entire sky of the alien planet and includes magnified telescopic images, the civilization that receives the photographs may be able to pinpoint the location that the photographs were taken at. Thus the alien civilization might receive thousands of separate photographs to cover the entire sky of the mystery planet.

If the Milky Way is visible in the sky of the alien planet, the alien planet must be within the disc of the galaxy. The disc of our Milky Way galaxy is about 100,000 light years in diameter and about 1,000 light years, or a few thousand light years, in thickness "up" or "down".

If the apparent diameter of the central bulge of the galaxy is measurable from the photographs it can be compared with the actual diameter of the central bulge to deduce how far the mystery planet is from the center of the galaxy.

If some of the photographs and "photographs" covering the center of the galaxy are made in the proper wavelengths of electromagnetic radiation, it may be possible to calculate the precise direction to the super giant black hole at the center of the Milky Way Galaxy.

The central points of the Andromeda Galaxy, M31, and M32, an elliptical satellite of M31, should be easy to locate from most parts of the Milky Way Galaxy. And the central point of galaxy M87 in the center of the Virgo Cluster should be easy to locate.

So by comparing the angles between those three or four directions it should be a simple trig problem to plot the approximate location of the mystery planet.

The directions to a few globular star clusters in the Milky Way Galaxy should help narrow down the position of the mystery planet. Some globular star clusters are bright enough to be visible to the naked eye at distances of over 10,000 light years, so if the photographs of the sky are telescopic some globular clusters should be detectable and identifiable. That shoud pin down the position of the rogue planet more precisely.

If the civilization that receives the photographs is as advanced in astronomy as early 21st century Earth it should have some data on the directions,distances, and absolute magnitudes of many of the stars within a few hundred light years of the rouge planet's position. So once the position of the rogue planet is narrowed down to a vaolume of space several light years on a side that is 1,000 light years away, the directions to the brightest stars in the sky of the rogue planet and their apparent magnitudes compared to other astronomical data available to the civilization receiving the photographs should be enough to calculate a much more precise position for the rogue planet.

And the civilization could use infrared sensing telescopes to try to directly see the infrared radiation emitted by the rogue planet at its temperature, and thus directly locate the rogue planet.

So the civilization that receives the photographs should be able to narrow down the position of where the mystery planet was when the photographs were taken. How long did it take for the photographs or the information needed to digitally construct them, take to reach the alien civilization 1,000 light years away?

Were physical photographs dropped off by a slower than light ship that took 100,000 years to make the journey, or dropped off by a faster than light ship that took only a single year to make the journey? Was the data to reconstruct the photographs transmitted by radio at the speed of light taking 1,000 years, or by a faster than light "hyperwave" transmitter, or by an instantaneous Dirac transmitter?

Assuming for the moment that the information took 1,000 years to arrive, the rogue planet should have an orbital velocity differing from that of the investigating civilization by approximately 10 to 1,000 kilometers per second. There are 60 seconds in a minute, 3,600 seconds in an hour, 86,400 seconds in a day, and 31,557,600 seconds in a Julian calendar year.

So there would be 31,557,600,000 seconds in 1,000 Julian calendar years. At a speed of about 10 to 1,000 kilometers per second, the rogue planet would travel about 315,576,000,000 to 31,557,600,000,000 kilometers in 1,000 years.

A light year is defined as 9,460,730,472,580,800 meters, or 9,460,730,472,580.8 kilometers.

According to my rough calculations, in 1,000 years the rogue planet will probably move about 0.033356409 to 3.335640952 light years from its previous position. Its new position should be somewhere within a cube 0.0667 to 6.671 light years on each side, centered on its old position. Of course it is possible that the civilization receiving the photographs can deduce something about the speed and direction the rogue planet is traveling and can narrow down its current position more precisely than that.

And similar calculations can be made with other assumptions about the situation.

Suppose that the photographs don't come from a rogue planet but from a planet that orbits a star. In that case a similar process should be able to narrow down the approximate position of the planet. Once that is done, any information about the spectral type or the precise spectrum of the star it orbits should help the receiving civilization to identify that star by comparison with astronomical data about stars in that region of space.

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I think it is possible. Just simple maths and very big computers and databases.

Start by identifying a couple of stellar objects on these pictures. Then calculate at which time and place the objects would be in the relative positions on each image. A series of images would give the flightpath of the planet.

  • It would be easier if there was data on very distant pulsars.
  • Failing that, it would help to have spectral data.
  • On each individual picture, it would be difficult to tell dim, close stars from bright, distant ones.

But all those can be overcome by the mass of data.

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  • $\begingroup$ The question specifically says "photographs". How do you get spectral data from a photograph? (Other than the spectra of the pigments / dyes / phosphors which make up the image.) How do you identify pulsars on a photograph? $\endgroup$
    – AlexP
    Nov 4, 2019 at 15:46
  • $\begingroup$ @AlexP, my answer is that it would be trivial with spectra or pulsars, and that sufficient data can overcome that problem. Compare the various pictures to find distant stars which move little from image to image. Compare those with your galactic database. Repeat until there is a match. $\endgroup$
    – o.m.
    Nov 4, 2019 at 16:33
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You can do that if you have a database with the exact location and brightness of stars over time. If you have this you can look at the problem backwards. From the database you can compute what the sky would look like from a particular point in space and time. From this point you have the distance to any visible star and its absolute brightness, so you compute how bright it would look as seen from that point.

Now you just need a match between the picture you got and something computed from your data base. To get a unique match your picture should have a lot of stars on them and enough resolution to sort out different levels of brightness. What a human being can see on earth under ideal conditions should be good enough.

If you have multiple pictures and know how much time has passed between them being taken, you can also find the movement of the planet and compute where it will be in the future.

PS: in Liu Cixin's 'The three body problem' series this method of identifying a point in space from the stars visible is used.

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Star Clusters

As a few people have mentioned, a photograph, even a very high resolution one, isn't going to give the sort of detailed spectrographic or astronomic data that would be needed to definitively identify any singular star in the image. This makes it difficult to fix points to begin triangulating from.

However, if there was a star cluster visible, like the Pleiades in the Earth's sky, that would be a group of stars that could be readily identified and easily positioned in relation to one another, which could be used as a reference to determine a bearing and approximate distance to the rogue planet at the time the images were taken.

You definitely wouldn't get "orbit of the moon" resolution, though. Think of how little the night sky changes to our eyes over the course of the year. Yes, with good telescopes and detailed instruments you can start measuring parallax between stars, but that's across a 2AU baseline. Even a high-resolution wide-view photo isn't going to show that sort of motion. So with really well-defined and comprehensive star charts, you could might get a location within a few light years.

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I understand the proposition is that we detect some alien signal without knowing anything about which direction it originates from and it appears to be picture of night skies.

If the time frame is very long (hundreds of years) we can compare supernova sightings and triangulate their location from.

For shorter time frames (years) there are light curves of luminous variable stars. They can be deduced from photographs if they're detailed enough. For example Betelgeuse is estimated to be 500 light years away, so if it is somewhere in the middle, we can match the dataset. There have to be such stars visible for both parties. Also the time frame must roughly match, if they see them hundreds of years before/after us, then it can't be matched as we don't have hundreds of years of observations.

However, now we do have accurate 3D map of most stars in 1000 light year radius and beyond, thanks to GAIA mission. So it's easy problem for a computer, as stars don't move so much in 1000 years.

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