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A satellite mass $500\ kg$ is elevated from altitude $10000\ km$ to altitude $20000\ km$. Radius of earth is $6378\ km$. Mass of earth is $5.97 \cdot 10^{24}\ kg$. Gravity is given to be $9.81\ m/s $

My attempt is using final $mgh$ - initial $mgh$.

initial $mgh = 500 \cdot 9.8 \cdot (16378 \cdot 1000)$

final $mgh = 500 \cdot 9.8 \cdot (26378 \cdot 1000)$

Final - initial I get $4.9 \cdot 10^{10}$

The correct answer is $4.61 \cdot 10^9$

Were did I go wrong?

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Hint: You're far enough from the ground that the formula $mgh$, which is an approximation, doesn't really apply anymore. What is the true formula for gravitational potential energy?

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  • $\begingroup$ So you are saying I have to use -g(m1m2 / r)? Much thanks! I will be able to try this tomorrow. $\endgroup$
    – Sarabetorrius
    Commented Sep 22, 2014 at 13:52

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