Calculate the change in gravitational potential energy

AI Thread Summary
To calculate the change in gravitational potential energy (GPE) for a satellite moving from an orbital radius of 7,000,000 m to a geostationary orbit at 42,000 km, the formula used is the difference between final and initial GPE. The initial GPE is calculated using the radius from the Earth's center, which is the sum of Earth's radius (6,380,000 m) and the satellite's orbital radius. The user initially calculated the change in GPE as 1.69 x 10^10 but noted that the correct answer should be 3.7 x 10^8. The confusion arises from the correct calculation of the new radius for the geostationary orbit, which must be accurately determined to solve the problem correctly.
ASidd
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Homework Statement


A satellite of mass 750kg is changed from an orbital radius of 7000000m to a geostationary orbit of 4.2*10^4. Calculate the change in its gravitational potential energy

Mass= 750
Earths radius= 6380000m
Gravitational constant= 6.67*10^-11
Earths mass=6*10^24

Homework Equations



So I am guessing I have to use this equation
Final Gpe- initial Gpe
(-GMm/r)-(-GMm/r)

The Attempt at a Solution


(-6.67*10^-11*750*6*10^24/(7000000+6380000))-(-6.67*10^-11*750*6*10^24/(4.2*10^4*10^3)
= 1.69 *10^10

The answer is 3.7*10^8
I don't know where I went wrong?
 
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