# physics

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A 981-kg satellite orbits the Earth at a constant altitude of 103-km.
How much energy must be added to the system to move the satellite into a circular orbit with altitude 199 km?

• physics -

find the original PE+KE
find the new PE+KE

what is the difference?

• physics -

You need to do work against gravity to move it to a higher orbit, but you get some back because the kinetic energy will be less at the higher orbit. You have to consider the total energy required.

The total energy (kinetic + potential) for a circular orbit at radius R is
Etotal = (1/2) m V^2 - G M m/R

where G is the universal constant of gravity and M is the mass of the Earth. Since
V^2/R = GM/R^2,
Etotal = (1/2)m*GM/R -GmM/R
= -(1/2)GmM/R

Compute this quantity at R = 103 km and at R = 199 km and take the difference. The work required will be positive.

• physics -

ok sir is the formula
-(1/2)GmM/R

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