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A satellite moves in a circular orbit around the Earth with total energy E = -2 x 10⁵ J. It is transferred to a different circular orbit in which its potential energy becomes U = -2 x 10⁵ J. Find the amount of energy that must be supplied to the satellite for this transfer.

1. 1 x 10⁵ J
2. 2 x 10⁵ J
3. 3 x 10⁵ J
4. 4 x 10⁵ J

Correct answer: 1 x 10⁵ J

Solution

For a circular orbit, the total energy equals half the potential energy: E = U/2. Initial total energy E_i = -2e5 J. In the final orbit U_f = -2e5 J, so total energy E_f = U_f/2 = -1e5 J. Energy to be supplied = E_f - E_i = (-1e5) - (-2e5) = +1e5 J = 1 x 10⁵ J.

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