A geostationary satellite orbits the Earth at a radial distance R_G from the Earth's centre. Another artificial satellite orbits the Earth in a circular orbit of radius R_G 4 . What is the time period of this second satellite?

Step-by-step solution

The time period of a geostationary satellite is T₁ = 24 hours . According to Kepler's Third Law, the square of the time period is proportional to the cube of the orbital radius, i.e., T^2 r^3 . For the two satellites, we can write: ( T₂ T₁ )^2 = ( r₂ r₁ )^3 Taking the square root on both sides: T₂ T₁ = ( r₂ r₁ )^ 3/2 Given r₁ = R_G and r₂ = R_G 4 : T₂ 24 = ( R_G / 4 R_G )^ 3/2 = ( 1 4 )^ 3/2 = 1 8 T₂ = 24 8 = 3 hours . Answer: 3 hours