How do you compute the angular distance between two stars from their coordinates?

Let ra1 and d1 be the right ascension and declinations of star 1 in degrees.

Let ra2 and d2 be the right ascension and declination of star 2 in degrees,

he angular separation A, in degrees, between them is simply: 

cos(A) = sin(d1)sin(d2) + cos(d1)cos(d2)cos(ra1-ra2)

Example. Sirius is at 6h 41m and -16d 35' so ra1 = 6.68h = 100.2 degrees and dec = -16.58 so d1 = -16.58 degrees.

Betelgeuse is at 5h 50m and +7d 23' so ra2 = 87.5degrees and d2 = 7.38 degrees. Then 

cos(A) =  -0.285 x 0.128 + 0.958 x 0.9917 x cos(100.2 - 87.5)
       = -0.0364 + 0.9268
       =  0.890

so A = 27.1 degrees. You can check this by putting both stars at the same RA and getting their difference in declination as cos(a) = .9136 so a = 23.9 degrees which equals d2-d1= 16.58 + 7.38 = 23.9 degrees.

You can also use the calculator over at Celestial WOnders.

Return to Dr. Odenwald's FAQ page at the Astronomy Cafe Blog.