What is the Mass of the Milky Way and How is it Calculated?

[anyaxo]

M = Mass of the galaxy = ?
r = Distance of sun from galactic centre = 10kpc= 3.09 x 1017 km (3 sf)
G = Gravitational constant = 6.67 x 10-11 Nm2kg-2
v = Radial velocity of the sun = 220,000 ms-2

Since the Sun’s orbit around the galactic centre is nearly circular, it undergoes circular motion and experiences a centripetal force:

〖mv〗^2/r = - GMm/r^2

v^2 = GM/r
M= ((220,000)^2 (3.09 ×〖10〗^17))/(6.67 ×〖10〗^(-11) )
=2.24 × 〖10〗^38 kg (3 sf)

However the mass of the Milky Way is said to be around 2 x 10^42 kg? help?

 

[granpa]

for one you mixed km with m