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

  • 9

mgh = 1000*10*7000= 7 * 10^7 J

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