Question

Find the acceleration of our galaxy due to the nearest comparably sized galaxy.The approximate mass of each galaxy is
8 ×10^(11) solar masses and they are separated by 2 million light-years.
Each galaxy has a diameter of 100,000 light years.
(Assume 1 light year =10^(16)m Gravitational constant G =10^(-10)((Nm^(2))/(kg^(2))) and mass of sun =2×10^(30)Kg )
Ans 4×10^(-13)

Answer 1

According to Newton's second law,

$$a=F/m.$$

What is the force?

$$F=G\frac{m\cdot m}{r^2},$$

which gives us

$$a=\frac{Gm}{r^2}.$$

Substitute the following values:

$G=10^{-10}\text{ N}\cdot\text{m}^2/\text{kg}^2,\\ m=8×10^{11}\cdot2×10^{30}=16\cdot10^{41}\text{ kg},\\ r=2×10^6\cdot10^{16}=2\cdot10^{22}\text{ m}.$

$$a=\frac{10^{-10}\cdot16\cdot10^{41}}{(2\cdot10^{22})^2}=4\cdot10^{-13}\text{ m/s}^2.$$