# Angular separation of 2 stars

1. Jul 24, 2012

### TheSource007

Hi all.
I have been looking for a formula that gives me the angular separation of two stars.
So far I just found this one :http://www.skythisweek.info/angsep.pdf
but it uses the RA and DEC of the 2 stars, and I need to use the hour angle and DEC. Is it the same thing? Do I just replace HA by RA?

Also I need the equation that gives me the angular separation given the altitude and azimuth of two stars. Can I use the same equation by replacing RA by azimuth and so on?

My goals is to see if the angular distance between two stars given the RA, DEC is different from the angular distance given the ALT, AZ. I think it should be the same but I want to prove it. Also I want to know how that distance (given the ALT, AZ) changes over time. Does it stay the same or does it change?
I would appreciate answers but I really need the equations for a computer code.
Thank you

2. Jul 24, 2012

### Philosophaie

HA is Hour Angle. RA is Right Ascension. LMST is the Local Mean Sidereal Time. d is the time in days since Jan 1,2000.

HA = LMST - RA

where LMST = 24*( 18.697374558 + 24.0657098244191 * d - longitude / 15)
and d = (Julian Date - 2451545)

3. Jul 25, 2012

### Filip Larsen

Yes, you can use any pair of spherical coordinates in place of right ascension and declination, as long as the alpha coordinate in the equation you cite is the angle measured in the reference plane (equator) of the coordinate system and the delta coordinate is the angle measured from the reference plane and up, that is, delta is an elevation angle. As you can see, the alpha coordinates do only appear as an difference in angle and in addition in a way that makes the sign of the difference irrelevant, so the two alphas can be replaced by the angle subtended in the reference plane by the two objects.

You should very much end up with the same angular separation when you apply right ascension and declination as when you apply azimuth and elevation for the same two stars.

You can see a bit more about formulas for angular separation on [1]. Depending on what language you are using, it should be fairly straight forward to turn this into code. Note the comment on the wiki-page regarding the benefit of using the atan2 function to calculate inverse tangent [2].

[1] http://en.wikipedia.org/wiki/Great-circle_distance
[2] http://en.wikipedia.org/wiki/Atan2

Last edited: Jul 25, 2012
4. Jul 25, 2012

### TheSource007

Thanks a lot. I used the same formula for both coordinate systems and I got approximately the same result.