Calculate the kinetic energy , potential energy and total energy of a geostationary satellite of mass 100 tonne. The radius of the earth is 6400 km and the radius of the orbit of the satellite is 42400 km.

Explanation

100 tone =`100 xx10^3 kg =10^5 kg.` Radius of the earth =6400 km `=6.4x10^6m` and the distance of the geostationary satellite from the centre of the earth,
`r=4200 km 4.24 xx10^7 m.`
Hence , kinetic energy
`=(GMm)/(2r) =1/2 m(GM)/(R^2)*(R^2)/r`
`=(mgR^2)/(2r) =(10^5xx9.8xx(6.4xx10^6)^2)/(2xx4.24xx10^7)`
`=4.73xx10^(11)J`
potential energy `=-(GMm)/r =-2xx(GMm)/(2r)`
`=-2xx(10^5xx9.8xx(6.4xx10^6)^2)/(2xx4.24xx10^7) =-9.47xx10^(11)J`
Total energy `=-(GMm)/(2r)=-4.73xx10^(11)J`.