Calculate the change in gravitational potential energy

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SUMMARY

The discussion focuses on calculating the change in gravitational potential energy (GPE) for a satellite with a mass of 750 kg transitioning from an orbital radius of 7,000,000 m to a geostationary orbit at 42,000 km. The gravitational constant used is 6.67 x 10^-11, and Earth's mass is 6 x 10^24 kg. The correct calculation for the change in GPE results in a value of 3.7 x 10^8 J, indicating an error in the initial attempt which yielded 1.69 x 10^10 J.

PREREQUISITES
  • Understanding of gravitational potential energy calculations
  • Familiarity with the gravitational constant (6.67 x 10^-11 N m²/kg²)
  • Knowledge of Earth's mass (6 x 10^24 kg) and radius (6,380,000 m)
  • Ability to manipulate scientific notation in calculations
NEXT STEPS
  • Review the formula for gravitational potential energy: GPE = -GMm/r
  • Learn about geostationary orbits and their significance in satellite positioning
  • Study the impact of orbital radius on gravitational potential energy
  • Explore common errors in gravitational calculations and how to avoid them
USEFUL FOR

Students studying physics, particularly those focusing on gravitational forces and energy, as well as educators seeking to clarify concepts related to satellite motion and energy calculations.

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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