Orbiting Satellite Energy Conservation

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The discussion centers on the conservation of energy and angular momentum in the context of an orbiting satellite after a collision. The user is grappling with an imaginary final answer in their calculations and questions whether energy is conserved before and after the explosion, given that no work is done on the satellite. They assert that angular momentum should remain constant due to the absence of torque. The conversation highlights the importance of considering both kinetic and potential energy in the analysis. Clarification is sought on the application of the work-energy theorem in this scenario.
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Homework Statement


I have uploaded the question. See attachment "question001"

Homework Equations


L=mvR for circular orbit

The Attempt at a Solution


See attachment "answer001". The problem is that my final answer seems to be imaginary, and I have tried to look for mistakes in my algebra which would lead me to this and haven't found any. Am I wrong in assuming that the Energy before the explosion is the same as the energy after the collision? I assumed that because no work was done on the orbiting mass, the energy was conserved. And there is no torque acting so angular momentum should be conserved.

I would be really grateful if someone could point out where I am going wrong :smile:
 

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The work-energy theorem refers to the change of kinetic energy. The KE of the satellite remains the same if no work was done on it. But what about the potential energy?

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