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How might it be possible to determine (via some specific online empemeris or via some well-understood algorithm) the observed position of some distant celestial body (e.g. Betelgeuse)?

To be concrete: suppose I wished to do what any number of mobile phone applications do, i.e. computationally model the observed position of stars and project them onto the screen using GPS coordinates and compass direction, so that an `overlay' of the night sky is produced. Then:

a) Where could I source the relevant data from?

b) What coordinate system would it be best to use?

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  • $\begingroup$ What information would already be available? $\endgroup$
    – HDE 226868
    Aug 29 '15 at 16:30
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    $\begingroup$ Latitude and longitude. $\endgroup$ Aug 29 '15 at 17:11
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    $\begingroup$ Do you mean "current position" as distance from us and angle on the sky that you can see it at, or "current" as meaning where it physically is at this very moment, which will be different due to the time taken for the light to travel to us? Please clarify the question. $\endgroup$
    – FJC
    Aug 29 '15 at 18:55
  • $\begingroup$ What do you mean by "latitude and longitude" in the comment? Are you asking where in the night sky you need to look / point your telescope to see some specific star? As FJC commented, please clarify this question. Don't do it in a comment. Edit your question so the clarification is part of the question. $\endgroup$ Aug 31 '15 at 9:27
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A fine place for reliable information on the location of the vast majority of cataloged stars is the Simbad Astronomical Database. For example, here is the data for Betelgeuse. As you will see, the first line after "other object types" is the position given in the ICRS coordinate system (the first set of numbers is Right Ascension, in degrees minutes seconds and the second set of number is Declination in degrees minutes seconds). For all but the highest level research-grade astrometry or proper-motion purposes, this position will be more than sufficient.

Now, given you have the 'global' position of the star, you can calculate its relative position as seen from wherever you are on Earth. Doing so is a function of your latitude, longitude and current time. There are online calculators that can do this such as this one, or you can make a program to crunch through the math yourself (it's not exactly trivial, but if there are lots of stars you want to do it for, or you want to do it on the fly, this is a better bet). If you really want to be clever about it and you have lots of stars, you only have to do the calculation once, since all the stars are essentially fixed relative to one another. When all is said and done, the most intuitive local coordinate system to use for your projecting would be altitude & azimuth.

If you are concerned about also including the relative motions of stars over time, I would say don't be. Nearly all stars have proper motions of less than 1 arcsecond a year, which means it would be half a century before most stars have moved in even the most remotely perceptible way to the naked eye (the human eye has an angular resolution of roughly one arcminute). Other apparent motions, such as parallax, are also negligibly small for objects outside of our solar system (again, unless you are doing research-grade work).

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The most robust, but generally not computationally feasible way would be a full N-body simulation of all the relevant interacting neighbours of the object in question.

On a more crude note, one could observe the eigen motion of the object (its velocity vector), its distance to us, and from that information (assuming the eigen motion is constant over the period between now and when the light was emitted from the object) one may infer the current position.

You can of course make a hybrid of the above methods: use the observed motion of the object, and use simulations to include the interaction with other objects.

Note that 'current position' is not unambiguously defined. Astronomers would often consider the observed position to be its current position, even though we are looking back in time. And, needless to say, on cosmological scales these concepts pose more problems.

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