Obtain the expression for total energy of a circularly orbiting satellite.

Explanation

We know that potential energy at a height 'r' away from the centre of the earth
` P.E = - (GM m )/( r)`
where M = Mass of the earth
m = Mass of the satellite
For circular orbit, kinetic energy
` K.E = 1/2 mV_0^2`
where ` V_0` = orbital velocity
but ` V_0 = sqrt((GM)/(r))`
` therefore K.E = 1/2 .m. (GM)/(r)`

i.e., ` K.E = 1/2 (GM m)/(r)`
but total energy E = P.E + K.E
i.e., ` E = (GMm)/(r) ( - 1 + 1/2 )`
i.e., ` E = - (GMm)/(2r)`