# Radial Velocity of the Sun around Galactic Centre

#### anyaxo

I need to calculate the radial velocity of the sun. Every time I try using Newton's Laws of Gravitation, I end up getting a value of 0.733 m/s. Apparently the actual value is 220000 m/s.

Mass of Sun = 1.99 x 10^30 kg (3sf)
G = 6.67 x 10^-11 Nm^2kg^-2
r = distance of Sun from galactic centre = 8.0 kpc = 2.47 x 10^20 m

mv^2/r = -GMm/r^2
v^2 = GM/r

v^2 = (6.67 x 10^-11 (1.99 x 10^30))/(2.47 x 10^20)
= 0.537...
v = 0.733 m/s (3sf)

What am I doing wrong?! This is driving me insane.

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#### issacnewton

since sun is rotating around the center of the galaxy, m would be the mass of the sun.
it gets cancelled here. so M is actually mass of the galaxy and not the sun.

"Radial Velocity of the Sun around Galactic Centre"

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