# How to calculate the heliocentric velocity of an object?

My task is to calculate the heliocentric velocity of an object to correct for wavelength in a spectrum. I have the RA, Dec and observation date, and I know that the NED velocity correction calculator(https://ned.ipac.caltech.edu/forms/vel_correction.html) will do the job, and I found out the equation here (https://ned.ipac.caltech.edu/help/velc_help.html#notes), but honestly I don't have a clue where these parameters come from. Could some one give me some hints on the reasoning behind it? Thanks!

• This sounds like a homework question, which is generally considered a poor question for Astronomy Stack Exchange. It may be closed. Could you at least show what you've tried so far? – HDE 226868 Sep 27 '15 at 21:56
• What is the NED velocity correction calculator? – barrycarter Sep 29 '15 at 13:31
• I have updated the question and included the links to the calculator and the equation. – RaynDrop Nov 2 '15 at 7:36
• @HDE 226868: I assure you this is not a homework related question and I have the equation now but I just want to know how to get it. Would you mind giving some hints? Thanks. – RaynDrop Nov 2 '15 at 7:37

The heliocentric velocity $V_\mathrm{H}$ of an object is its velocity wrt. the Sun. When you measure an object's velocity, you measure it in the reference frame of Earth, which revolves around the Sun with ~30 km/s (varying a bit from aphelion to perihelion), so convert to $V_\mathrm{H}$ you need to know the time of the year of the observation (unless the line of sight toward your object is exactly perpendicular to the ecliptic plane), as well as the angle between the line of sight, and the line of sight toward the Sun. This involves a number of sines and cosines that you can find in e.g. Barbieri (2006).
If you further want to convert from $V_\mathrm{H}$ to the reference frame in which the Milky Way's center is at rest, the Local Group is at rest, or the Cosmic Microwave Background is isotropic (the "cosmic" frame), then you use the formula you link to, adding a similar term as described above, but instead using the velocity (i.e. speed and direction) of the Sun wrt. to the given frame.