Satellite Orbiting Earth Energy

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SUMMARY

The discussion centers on calculating the energy required to move a 962kg satellite from a circular orbit at 99km altitude to a higher circular orbit at 195km. The relevant equations used include the gravitational potential energy formula E = (-GMm)/2r and the change in energy formula ΔE = Ef - Ei. Participants identified errors in their calculations, specifically in the application of the 1/r terms and the division factor. The correct energy requirement, after adjustments, is confirmed to be approximately 858MJ.

PREREQUISITES
  • Understanding of gravitational potential energy equations
  • Familiarity with orbital mechanics concepts
  • Knowledge of the gravitational constant (G) and mass of the Earth (M)
  • Basic algebra for manipulating equations
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  • Review the derivation of gravitational potential energy equations
  • Study the principles of orbital mechanics and energy transfer
  • Learn about the implications of altitude changes on satellite energy requirements
  • Explore numerical methods for solving energy calculations in orbital dynamics
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Aerospace engineers, physics students, and anyone involved in satellite design and orbital mechanics will benefit from this discussion.

blackheart
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1. A 962kg satellite orbits the Earth at a constant altitude of 99km. How much energy must be added to the system to move the satellite into a circular orbit with altitude 195km?

2. Homework Equations :

E = (-GMm)/2r
\Delta E = Ef - Ei

3. My work (which produced the wrong answer)...

Ei = (-GMEms)/(2(rE + 99000m))

Ef = (-GMEms)/(2r(E + 195000m))

\Delta E = ((-GMEms)/2)((1/rf)-(1/ri)

The answer needs to be in MJ. I got 858MJ which is incorrect.
 
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Hi blackheart. The method looks good. I got about half your answer.
Did you get 2.26 x 10^-9 for the difference between the 1/r terms?
 
Oh! I didn't divide by two... I have it now. Thanks a bunch.
 
Most welcome.
 

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