Question

Our galaxy, the Milky Way, contains approximately 4.0 x 1011 stars with anaverage mass of 2.0 X 1030 kg each. How far away is the Milky Way from ournearest neighbor, the Andromeda Galaxy, if Andromeda contains roughly thesame number of stars and attracts the Milky Way with a gravitational force of2.4 x 1030 N?

Answer 1

We will have the following:

First, we remember:

$F=\frac{Gm_1m_2}{r^2}$

Then, from the problem we will have that:

$2.4\ast10^{30}N=\frac{G(2.0\ast10^{30}kg)(2.0\ast10^{30}kg)}{r^2}$$\Rightarrow r^2=\frac{G(2.0\ast10^{30}kg)^2}{2.4\ast10^{30}N}\Rightarrow r\approx1.1116666667\ast10^{20}m$

So, the Andromeda galaxy is approximately 1.1*10^20 meters from the milky way.

The acceleration of the Andromeda galaxy towards the milky way is:

$2.4\ast10^{30}N=(2.0\ast10^{30}kg)a\Rightarrow a=1.2m/s^2$

So, the acceleration towards the milky ways is 1.2m/s^2.