# How to convert ra&dec between different epoches?

For example, how to convert B1950.0 into J2000.0?

Do we need to know the proper motion of the star and the time it was observed?

• As @Rob_Jeffries notes, you have to make two separate transforms: one for precession and the other for proper motion. Any good astronomical library will do the precession part, and some astronomical libraries may do the proper motion part as well, but I'm not sure about that part.
– user21
Oct 14, 2016 at 13:56

The difference between B1950.0 AND J2000.0 is not really concerned with proper motion., they refer to the definition of the coordinate system. Thus a star with zero proper motion would still have different B1950 and J2000 coordinates.

Usually (but not always), if you quote a position as equinox 1950 you are implicitly assuming that this is epoch 1950 (unless otherwise stated). And similarly for J2000, the implicit assumption is that the coordinates refer to epoch 2000 unless you specify otherwise.

Thus there are two things you needs to do. One is to apply a correction for (roughly$^{*}$) 50 years of proper motion (if indeed you only have the epoch 1950 position; or maybe 66 years if you want the coordinates of the star now). Second is to apply (roughly) 50 years of precession to the coordinates to put them in the J2000 system.

This description seems reasonable.

$^{*}$ There is some detail about B= Besselian years and J = Julian years which you can read about here.

• "...is not really concerned with proper motion." "apply a correction for (roughly) 50 years of proper motion" These two statements seem to conflict. Could you clarify more precisely what you mean? Oct 14, 2016 at 13:37
• @rob For a quasar, the difference between B1950 and J2000 is just because of the precession of our earth, right? This correction is basically rotating the frame of B1950？ Oct 14, 2016 at 13:39
• @questionhang I think that is correct. Note that the ICRS reference frame does not distinguish epoch/equinox - so an ICRS coordinate is just at a given epoch, with the reference frame precessed to that epoch. Oct 14, 2016 at 13:42
• @rob Since the positions are relative, why do we insist on rotating the frame? We can still use B1950. Oct 14, 2016 at 14:06
• @questionhang Sounds like different question - you asked how to convert. For objects without proper motion, the difference between a B1950 and J2000 position is just precession. Oct 14, 2016 at 15:36