Answer:
mass of the galaxy = 1.05 * 10^11 solar masses
Explanation:
According to Kepler’s third law, A^3 =P^2
Where A = Average distance of a planet from the sun, in AU
And P = The time taken by the planet to orbit the sun, in years.
Newton’s modification to Kepler’s third law applies to any two objects orbiting a common mass
According to Newton, M1+ M2 = (A^3) / (P^2)
Where M1 and M2 are the masses of the two objects in Solar mass
From the question,
Let M1 = the mass of the sun
and M2= the mass of the milky way galaxy
Distance, A = 28,000 light years
1 light year = 63241.1 AU
A = 28000 * 63241.1
A = 1,770,750,800 AU
Time taken for the orbit, P = 230,000,000 years
M1= 1 solar mass
M2 = ?
Using M1+ M2 = (A^3) / (P^2)
1 + M2 = (1770750800^3)/ (230,000,000^2)
1 + M2 = 1.05 * 10^11
M2 =( 1.05 * 10^11) – 1
M2 = 1.05 * 10^11 solar masses