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I would like some assistance in understanding the ratio of change in energy between two objects.

In this case, if object A goes from rest to an altitude (h) above earth but does not begin an orbit versus object B goes from rest to the same altitude and then proceeds to orbit the earth.

The variables are as follows:

Re=radius of earth

h=altitude

G=universal gravitational constant

M=mass of earth

m=mass of object(A=B, also known as A and B are the same)

I'll need to transcribe my findings, which until now when comparing to my professors simplication are slightly off, a little later.

I was told my error might occur in the initial change of energies for the respective objects, and this may very well be true. However, I did come across great challenges at first when trying to find a GCF for the variable laden energies.

What I've been using prior to simplication:

Object A = change in Eg = Eg2 - Eg1

Object B = change in total energy = Ek - Eg1

Eg as known is a negative value while Ek is positive.

Any help is appreciated and I understand little help may be offered since I've yet to put up the actual attempts, but when I have more time I'll transcribe my most recent effort into mspaint.

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# Homework Help: Ratio between change in Energy(Gravitational Potential)

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