# How strong is the force between the Sun and the centre of the Milky Way?

I know the Sun is orbiting around the Milky Way, but how strong is the attractive force between them (e.g. what is the order of magnitude in terms of newtons)?

Nevertheless, the Sun's orbit is roughly circular, so we can use kinematics to get some idea of the forces involved: For circular motion $a=\frac{v^2}{r}$. The velocity of the sun is about 225000 m/s, and we are at a radius of about 2.5e20 m from the centre. The formula above gives a very small centripetal acceleration of 2e-10 m/s²
However the sun is quite massive, 2e30 kg, so using $F=ma$, the force on the sun is of the order 4e20 N. This is about 0.01 of the force acting on the Earth by the Sun. (3.6e22 N)
• Just out of interest, if we model the galaxy as a disc with uniform density at a given radius (but varying with radius), does the mass distribution inside the sun's orbit, applied to $\frac{gMm}{r^2}$ come close to the estimate in your formulation? – Carl Witthoft Oct 26 '16 at 12:49