(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A satellite of mass M is in a circular orbit of radius R around the earth.

(a) what is its total mechanical energy (where Ugrav is considered zero as R approaches infinity)?

(b) How much work wouldbe required to move the satellite into a new orbit, with radius 2R?

2. Relevant equations

(a)

mv²/R=GMm/R² →→ mv²=GMm/R →→ K=1/2mv²=GMm/(2R),

therefore, E=K+U=GMm/(2R)+(-GMm/R)=-GMm/(2R)

(b)

Here's where I got stuck :

This is the correct answer on the book:

From the equation Ki+Ui+W=Kf+Uf,

W=(Kf+Uf)-(Ki+Ui)

=Ef-Ei

=-GMm/(2(2R))-(-GMm/(2R))

=GMm/(4R)

Here's what I did, instead of using the equation above, Ki+Ui+W=Kf+Uf, I used the WORK-ENERGY THEOREM. But it came out the different answer.

W=Kf-Ki=GMm/(4R)-GMm/(2R)=-GMm/(4R) , the same magnitude but different sign.

What's wrong with using WORK-ENERGY THEOREM?

3. The attempt at a solution

As above.

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# Homework Help: Gravitional potential energy

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