Black Hole War Part 2

Following on from Part 1, the Earthling's managed to escape the Andromedon's secret weapon thanks to your help and eventually managed to come to peace with the Andromedon's. The citizens of Earth wish to return to their home solar system and study the black hole to attempt to discover a method to revert their solar system back to normal.

To this aim, they wish to move the Earth back to the solar system, in the innermost stable circular orbit about the black hole with Schwarzschild radius equal to the solar radius. How much potential energy do they need to ensure the Earth has in a reference frame where the black hole with \(R_{Schwarzschild}=R_{Solar}\) is stationary? Give your answer in units of \(10^{39}\) Joules.

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