# Linear motion in the equatorial frame

I would like to calculate how the RA/Dec changes when an object has an apparent linear motionin the equatorial sphere. For example, more or less what an artificial satellite would do in a circular orbit.

In particular, what I'm looking for is as follows:

I have the RA/dec of the object at two times, t1, and t2. Assuming it has a linear motion at constant speed, what RA/dec will it have a t3? So it will have an angular separation proportional to the one it had between t1 and t2, and the three points will form a straight line.

• This appears to be a simple spherical coordinates math problem. Am I missing something? – user21 Jul 28 '15 at 15:16
• @barrycarter no, you are not missing anything. I did not know how to search for the formula in the internet even assuming that it looked like a very simple problem. I later found the formula (for Earth surface motion using lat/long but it is the same problem). Thank you, – siritinga Jul 30 '15 at 5:52
• @siritinga If you solved your problem, you can post an answer to your own question, in case someone else with the same problem finds this post in the future. – usernumber May 13 '20 at 13:36