Hello I read that Vega is getting closer to earth.
I would like to learn how to calculate its displacement and calculate the galactic coordinates that it will have next year or in 1000 years.
Knowing that it will not be accurate or true ^^
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Vega is moving towards the solar system at 14 km/s (and over the period of a thousand years, that value isn't going to change much)
So in 1000 years it will move 14 * "seconds in a year" * 1000 = 441000000000km. That is about 0.046 light years. That is less than the uncertainty in its distance now (0.07 light years) So to the limited accuracy that we know distance, it will still be 25 light years away in 1000 years.
"Galactic coordinates" (almost certainly) doesn't mean what you think it to mean. It is a system of describing the direct of a star from Earth, using the milky way as a reference line (galactic coordinates are not 3d coordinates within the galaxy). Galactic cartesian coordinates are 3D, but are also based on the Sun at the centre. But I suspect you want to find the coordinates in a system centred at the middle of the galaxy.
Vega also has proper motion (it isn't moving directly towards the sun) In 1000 years it could move about 300 arcseconds. For comparison, the moon is about 1800 arcseconds across. The proper motion is a consequence of its transverse velocity (and distance). Transverse velocity the components of velocity perpendicular to the ray from the sun to Vega.
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1$\begingroup$ thank you for your answer where did you find 14 km/s? this is its value Vr (t) Radial velocity = -13.9 km/s. I took my head trying to understand the difference between radial velocity, transverse velocity and proper motion. I thought I had to use all three to get the result I was looking for $\endgroup$ Commented Feb 18, 2023 at 22:13
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1$\begingroup$ The distance from Earth depends on the relative transverse motion too. However, in 1000 years, doesn't make much difference.Galactic 3D coordinates are written $X, Y, Z$ and can be defined centred on the Sun. $\endgroup$– ProfRobCommented Feb 18, 2023 at 22:15
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$\begingroup$ Yes 13.9 +-0.9 km/s ie between 13.0 and 14.8. I rounded. As Rob says, over 1000 years the transverse motion won't make much difference to the distance. So it is simple enough to approximate the radial motion as being constant over that time scale. If you were to ask the same question over 1000000 years, it would be different, and the maths would be more involved. However the answer to "where will Vega be in 1000 years" is "Where it is now (to within our ability to measure) $\endgroup$– James KCommented Feb 18, 2023 at 22:35
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$\begingroup$ Like the comparison with the size of the Moon in the sky as a reference. $\endgroup$ Commented Feb 19, 2023 at 9:10