Question

The galaxy that contains our solar system, the milky way, is approximately a uniform disc of mass 10^12Msun and diameter 175×10^3 light years. Assuming that the center of mass of the galaxy is at rest, estimate the time that it takes the sun to complete one orbit around the galaxy center. A few useful numbers: the mass of the sun Msun = 2 × 10^30kg, 1 light year = 9.46 × 10^15m, and the distance between the sun and the galaxy center d = 26.4 × 10^3 light years.

Use the viral relation PE = -2 KE, and estimate the period using, t=2pir/v

Answer 1

Given:-

Mass of the Sun

The mass of the galaxy

One light year

Diameter of the galaxy light years

Distance between the Sun and center of the galaxy is light years

The Viral Theorem:-

For stable, self gravitating orbiting masses

Here,

M is the mass of the galaxy

m is the mass of the sun

R is the distance between objects

G is the gravitational constant

v is the velocity of the sun

From the Viral theorem

Rearranging above equation for velocity

Plugging the values in above equation

Using relation to estimate the period

Thus the time taken by the sun to complete one orbit about center of the galaxy is earth years.