Question

A satellite is put in a circular orbit about Earth with a radiusequal to one-half the radius of the Moon’s orbit. What is its periodof revolution in lunar months? (A lunar month is the period of revolution of the Moon)

Short answer

Period of revolution of satellite in lunar is$0.35lunarmonths$

Step-by-step solution

Step 1: Given

Satellite in a circular orbit about the Earth with a radius is equal to one-half the radius of the Moon’s orbit.

Determining the concept

Using Kepler’s third law, find theperiod of revolution of satellite in lunar months from the given radius and the ratio of Earth’s radius to Moon’s radius. According to Kepler’s third law, the squares of the orbital periods of the planets are directly proportional to the cubes of the semi major axes of their orbits.

Formula is as follow:

${\left(\frac{T_s}{T_M}\right)}^2={\left(\frac{R_s}{R_M}\right)}^3$

where, T is corresponding period and R is corresponding radius.

Determining the period of revolution of satellite in lunar

Now,

${\left(\frac{T_s}{T_M}\right)}^2={\left(\frac{R_s}{R_M}\right)}^3$

As,

$\frac{R_s}{R_M}=\left(\frac{1}{2}\right)$

Putting given values in formula,

${\left(\frac{T_s}{1lunarmonth}\right)}^2={\left(\frac{1}{2}\right)}^3$

$T_s=0.35lunarmonth$

Hence, the period of revolution of satellite in lunar is $0.35lunarmonths$

Therefore,using Kepler’s third law of gravitation or law of period, the time period of the satellite can be found.