Calculating Work with Kinetic Energy in Orbit

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To calculate the work done by an external force on a satellite moving from a higher orbit to a lower orbit, both gravitational potential energy (GPE) and kinetic energy (KE) must be considered. The initial and final GPE can be calculated using the formula GPE = -GMm/r, while the KE is determined by the satellite's velocity in each orbit. The correct approach involves setting up the equation GPEfinal + KEfinal = GPEinitial + KEinitial + Work of external force. The initial calculations provided were incorrect as they did not account for the increased velocity and corresponding kinetic energy at the lower orbit. Properly integrating these factors will yield the correct work done by the external force.
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Homework Statement


A 62kg satellite orbits the Earth with a radius of 3.3*10^7 m. A net external force acts on the satellite to an orbit of 7.7*10^6 m, what work must the external force do?


Homework Equations


W = integral of F with respect to d


The Attempt at a Solution



Integrate F which in this case is GMm/r^2 which becomes -GMm/r, then plug in the radii. However, the answer that I got was -2.46*10^9, which is incorrect.
 
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You need to include the kinetic energy as well, because the velocity of the satellite
in a lower orbit will be bigger
 
willem2 said:
You need to include the kinetic energy as well, because the velocity of the satellite
in a lower orbit will be bigger

How would I include the kinetic energy?

Would I approach it as this?

GPE = gravitational potential energy
KE = kinetic energy


GPEfinal + KEfinal = GPEinitial + KEinitial + Workof external force ?
 

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