Question

A satellite is placed in a circular orbit with a radius equal to one-third the radius of the Moon's orbit. What is its period of revolution in lunar months? (A lunar month is the period of revolution of the Moon.)

Answer 1

0.19245 lunar months

Step-by-step explanation:

T = Orbital time

r = Radius

`r_2=(1)/(3)r_1`

1 denotes the moon

2 denotes the satellite

From Kepler's law we have

`T^2=(4\pi^2r^3)/(GM)`

So,

`\\\Rightarrow T\propto √(r^3)`

`(T_2)/(T_1)=\sqrt{(r_2^3)/(r_1^3)}\\\Rightarrow (T_2)/(T_1)=\sqrt{(\left((1)/(3)r_1\right)^3)/(r_1^3)}\\\Rightarrow (T_2)/(T_1)=0.19245\\\Rightarrow T_2=0.19245T_1`

The period of revolution of the satellite is 0.19245 lunar months