Posted by Rachel on Friday, March 11, 2011 at 8:41pm.
find the original PE+KE
find the new PE+KE
what is the difference?
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.
ok sir is the formula
-(1/2)GmM/R
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