Posted by **Rachel** on Friday, March 11, 2011 at 8:41pm.

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?

I need answer in MJ

please tell me what formula

- physics -
**bobpursley**, Friday, March 11, 2011 at 9:19pm
find the original PE+KE

find the new PE+KE

what is the difference?

- physics -
**drwls**, Friday, March 11, 2011 at 9:19pm
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 -
**Rachel**, Friday, March 11, 2011 at 10:00pm
ok sir is the formula

-(1/2)GmM/R

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