Satellite Orbiting Earth Energy

AI Thread Summary
A 962kg satellite currently orbits Earth at 99km and needs to be moved to a circular orbit at 195km. The energy change required for this transition is calculated using the equation ΔE = Ef - Ei, where Ei and Ef represent the initial and final energy states, respectively. Initial calculations yielded an incorrect energy value of 858MJ, prompting further discussion on the method used. Participants confirmed that the difference between the 1/r terms was crucial and noted the importance of dividing by two in the final calculation. The conversation highlights the collaborative effort to resolve the energy calculation for the satellite's orbital transition.
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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