Question

A satellite close to the earth is in orbit above the equator with a period of rotation of 1.5 hours. If it is above a point P on the equator at some time, it will be above P again after time 

(a) 1.5 hours 

(b) 1.6 hours if it is rotating from west to east 

(c) 24/17 hours if it is rotating from west to east 

(d) 24/17 hours if it is rotating from east to west

Answer 1

Correct Answer is: (b, d)

Let ω₀ = the angular velocity of the earth about its axis.

∴ 24 =2π/ω₀  or  ω₀ = 2π/24.

Let ω = the angular velocity of the satellite.

∴ 1.5 2π/ω or ω = 2π/1.5 .

For a satellite rotating from west to east (the same as the earth), the relative angular velocity, ω₁ = ω - ω₀.

Time period of rotation relative to the earth = 2π/ω₁ = 1.6 h.

For a satellite rotating from east to west (opposite to the earth), the relative angular velocity, ω₂ = ω + ω₀.

Time period of rotation relative to the earth = 2π/ω₂ = 24/17 h.