A geostationary satellite is orbiting the earth at a height of 5R above the surface of the earth, R being the radius of the earth. Find the time period of another satellite at a height of 2R from the surface of the earth.

Explanation

From Kepler's III law, `T^(2) alpha r^(3)`
`T_(1)^(2) alpha r_(1)^(3) & T_(2)^(2) alpha r_(2)^(3)`
For F to be maximum `(dF)/(dm) = 0`
`(T_2^2)/(T_1^2) = (r_2^3)/(r_1^3) = ((3R)^(3))/((6R)^(3)) , (T_2)/(T_1) = 1/(2sqrt(2)) " " [ :' T_(1) = 12]`
`T_(2) = 12/(2sqrt2) = 6/(sqrt2)`.