The sun orbits the center of the galaxy in 225 million years at a distance of 26,000 lightyears. given that a^3 = (m1 +m2) x p^2, where a is the semimajor axis in au and p is the orbital period in years, what is the mass of the galaxy within the sun’s orbit?

According to Kepler third law the relation between orbital period and radio of matter in the Galaxy is given by

Where,

a = Radius of start orbit

p = Orbital Period

M = Total mass in a sphere of radius centered on galactic center

Our values are given as

Replacing we have,

Therefore the mass of the galaxy within the sun's orbit is 108Billion the mass of the sun.