Question

A satellite is put in a circular orbit about Earth with a radius equal to 35% of 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

Answer:

0.21 lunar month

Explanation:

the radius of moon = r₁

time period of the moon = T₁ = 1 lunar month

The radius of the satellite = 0.35 r₁

Time period of satellite

The relation between time period and radius

              $T\ \alpha\ \sqrt{r^3}$

now,

              $\dfrac{T_2}{T_1}=\dfrac{\sqrt{r_2^3}}{\sqrt{r_1^3}}$

              $\dfrac{T_2}{T_1}=\dfrac{\sqrt{0.35^3r_1^3}}{\sqrt{r_1^3}}$

              $\dfrac{T_2}{1}=\sqrt{0.35^3}$

                              T₂ = 0.21 lunar month

hence, the time period of revolution of satellite is equal to 0.21 lunar month