Two satellites of one metric ton and twelve metric tons masses are revolving around the Earth. The heights of these two satellites from the Earth are 1600 km and 25600 km, respectively. What is the ratio of their time periods and what is the ratio of the accelerations due to gravity at those heights?
(Radius of the Earth = 6400km)

Explanation

(i) Find the radius of the Earth from the given data.
Find the heights of the two satellites from the Earth.
What is Kepler's law of time periods ? Is `T^(2) prop r^(3)`?
Find the ratio of the time periods of the two satellites by the formula `(T_(1)^(2))/(T_(2)^(2))=(r_(1)^(3))/(r_(2)^(3))`
(ii) `T_(1) : T_(2) = 1 : 8`
`g_(1) : g_(2) = 16 : 1`