A satellite is revolving around the earth in an orbit of radius double that of the parking orbit and revolving in same sense. Find the periodic time duration between two instants when this satellite is closest to a geostationary satellite.

Explanation

We know that the time period of revolution of a satellite is given as
`T^(2) = (4pi^(2))/(GM_(e))r^(3)` [Kepler's III law]
For satellite given in problem and for a geostationary satellite we have
`(T_(1))/(T_(2))((r_(1))/(r_(2)))^(3)` or `T_(1) = ((r_(1))/(r_(2)))^(3) xx T_(2)`
`= (2)^(3) xx 24 = 192 hr`
If `Delta t` be the time between two sucessive instants when the satellite are closed then we must have
`Delta t = (theta)/(omega_(1)) = (2pi + theta)/(omega_(2)) = (2pi)/(omega_(2) - omega_(1))`
Where `omega_(1)` and `omega_(2)` are the angular speeds of the two planets