# Kepler's Third Law

I'm not good at this stuff, so I need some help from some smarter people... The speed of the Sun in its orbit about the Galactic center is 220 km/sec. Its distance from the center is 8500 pc. Assuming that the Sun's orbit is circular, calculate the mass of the Galaxy (in solar masses) interior to the Sun's orbit from Kepler's Third Law. Recall that the circumference of a circle is 2 pi r, where r is the radius. Remember that 1 pc is 206265 AU and 1 AU is 1.5x10^8 km.

Any help would be greatly appreciated!!!

## Answers and Replies

sridhar_n
...

Assuming that the mass of the galaxy is concentrated at its center, the force of the galaxy of mass M on the sun of mass m seperated by a distance r from the galaxy center is:

F = GMm/r^2. This force will be equal to the centrifugal force due the revolution of the sun around the galaxy.
Thus,

GMm/r^2 = mV^2/r, where, V is the velocity of sun around the galaxy.

From this u can calculate the value of M - the mass of the galaxy (Its, just mere substitution...)

Sridhar