a satellite of mass 1000 kg moves in a circular orbit of radius 7000 km round the earth , calculate the total energy required to place the satellite in orbit from earths surface. assuming it is initially at rest.
please answer quickly !!!!!!!!
Mass of the satellite, m = 1000 kg
Radius of orbit, r = 7000 km = 7000000 m
At the orbit, centripetal force = gravitational force
=> mv2/r = GMm/r2
[M is the mass of the earth]
=> mv2 = GMm/r
Let the energy provided to launch the satellite from ground be E,
E + Potential energy at the ground = Potential energy at the orbit + kinetic energy at the orbit
=> E - GMm/R = -GMm/r + ½ mv2
=> E = GMm/R - GMm/r + GMm/(2r)
=> E = GMm/R - GMm/(2r)
=> E = GMm(1/R – 1/2r)
=> E = 6.67 × 10-11 × 5.9 × 1024 ×1000{1/6400000 – 1/(2 × 7000000)}
[M = 5.9 × 1024 kg, R = 6400000 m]
So, E = 3.35 × 1010 J