CBSE Class 9 Answered

Let an artificial satellite revolves around earth in a circular orbit of radius r . Cenre of orbit is centre of earth.

Then by Newton's law of gravitation , we get

Where LHS is the gravitational force between earth and satellite and RHS is the centripetal force .

Where G is universal gravitational constant , M is mass of earth , m is mass of satellite and v is velocity of satellite in orbit

Let T be period of orbital motion of satellite. Then we have

v = ( 2π r ) / T  .................(2)

By substituting v from eqn.(2) , we rewrite eqn.(1) for the period T after simplification as

Hence , time period T of satellite is proportional to square root of cube of radius  r .

Let T be the time period of satellite that revolves around the earth at a height of 2R above earth surface , where R is radius of earth.

Let τ be the time period of geo-synchronous satellite that revolves around the earth at a height of 5R above earth surface .