Question

A 1000 kg satellite orbits the earth at a constant altitude of 100km. How much energy must be added to the system to move thesatellite into a circular orbit with altitude 200 km?

Answer 1

We know that at this altitude the only change in energy is the change in Potential energy, P = mgh

Now at surface we know that g = 9.81 m/s²,

and the earth's radius = 6371km

We know that g is inversely proportional to the square of radius.

Hence at altitude of 100 km, total r= 6371+100=6471 km

Therefore,

g₂/g₁ = 6371²/6471²

=> g₂ = 9.81 x 6371²/6471²

=> g₂ = 9.5 m/s²

Hence potential energy at 100 km

= P₂ = mg₂h₂ = 1000x9.5x100

= 950000

Similarly g at 200 km,

g₃/g₁ = 9371²/9571²

=> g₃ = 9.4

Hence potential energy at this point,

P₃ = mg₃h₃ = 1000x 9.4x200

= 1880000

Hence the difference in both the energy

E = P₃-P₂ = 1880000-950000

= 930000J

Which is the required amount of energy to be added to the system.