# How to calculate a Galactocentric distance of another galaxy

So I have two parameters, I have the distance to a galaxy of 879 kpc and the sky distance in degrees (0.131501). How would I then use these two bits of information to calculate the Galactocentric distance in kpc?

N.B. for the two objects within M33, i.e., the centre of M33 and an undefined region of M33 are separated by 0.131501 degrees. Both objects can assume to have a distance from us of ~879 kpc.

So I want to convert the value for the distance between the two objects within M33 (0.131501 degrees) to kpc...

• Thanks for updating. It still seems like simple trig to me, but I'll defer to the experts. – called2voyage Aug 11 '16 at 17:54

## 1 Answer

Basic angle calculations: $\mathrm{arc\ length} = r\theta$ (angle measured in radians) and for small angles the arc length approximates the chord length.

The angle in radians is therefore $0.131501\pi/180=0.00223$, so the separation is $0.00223\times 879= 2.02 \mathrm{kpc}$

• Hi James, many thanks for this. Your answer is correct, but I gave the distance as 879 Mpc and this should have been 879 kpc! I apologise, hence the answer should be 2.02 kpc. My fault. – MichaelJRoberts Aug 11 '16 at 18:09
• The value is a lower bound for the distance. A more exact calculation could take into account the position of the object on the galactic plane and the inclination of the galactic disk (56°) mpifr-bonn.mpg.de/3254995/m33 – aventurin Aug 11 '16 at 20:17