Calculate (i) kinetic energy (ii) potential energy and (iii) total energy of a satellite of mass `200 kg` orbiting around the earth in an orbit of height `100 km` from the surface of earth. Given, mass of earth `= 10^(25) kg`,radius of earth `= 6.4 xx 10^(6) m, G = 6.67 xx 10^(-11) Nm^(2) kg^(-2)`.

Explanation

Here, `m = 200 kg , M = 10^(25) kg`,
`R = 6.4 xx 10^(6) m`
`h = 100 km = 0.1 xx 10^(6) m`
Orbital velocity of satellite is `upsilon_(0) = sqrt((GM)/(R + h))`
(i) `KE` of satellite, `K = (1)/(2) m upsilon_(0)^(2) = (1)/(2) m (GM)/(R + h)`
`= (1)/(2) xx (200 xx(6.67 xx 10^(-11)) xx 10^(25))/((6.4 xx 10^(6) + 0.1 xx 10^(6))`
`= 10 xx 10^(9) J = 10^(10) J`
(ii) `PE` of satllite, `U = - (GM m)/(R + h) = - 2 xx K`
`= - 2 xx 10^(10) J`
(iii) Total energy of satllite `= K + U`
`= 10^(10) + (-2 xx 10^(10))`
`= - 10^(10) J`