# Negative GPE?

#### semc

Negative GPE???

hmm....i came across this qn which ask whether a satellite which has twice the mass of the other will have a higher gravitational potnetial energy......so the formula for GPE will be -GMm/r right? i deduce that since the mass of satellite i greater it will posses greater GPE but i was wrong
the reason i got was the satellite with bigger mass will have a more negative GPE so its GPE is lower :surprised so i was wondering is this really the case? i thought that the magnitude of the GPE tells you how much PE the object posses in the orbit?

Thanks

#### OlderDan

Homework Helper
semc said:
hmm....i came across this qn which ask whether a satellite which has twice the mass of the other will have a higher gravitational potnetial energy......so the formula for GPE will be -GMm/r right? i deduce that since the mass of satellite i greater it will posses greater GPE but i was wrong
the reason i got was the satellite with bigger mass will have a more negative GPE so its GPE is lower :surprised so i was wondering is this really the case? i thought that the magnitude of the GPE tells you how much PE the object posses in the orbit?

Thanks
It is difficult to compare things that have arbitrary reference points. If you defined the potential energy of both objects to be zero at the surface of the earth, then the more massive object would have greater GPE than the less massive object everywhere above the earth. The earth's surface is not a convenient reference point for orbital systems, so the convention is to define GPE to be zero at an infinite distance from the earth. The more massive satelite's GPE will increase at a faster rate as altitude increases. For both to have zero GPE at infinity, the more massive satellite must have less at any finite altitude. This is consistent with the expression you wrote that is based on the conventional choice of reference that GPE = 0 at infinity.

#### semc

alrite thx got it.....maybe i can argue with my teacher that i am taking reference from surface of Earth!!

#### OlderDan

Homework Helper
semc said:
alrite thx got it.....maybe i can argue with my teacher that i am taking reference from surface of Earth!!
Actually, you would be on firm footing if you did, though I'm not recommending it. Only changes in potential energy have physicsal signifigance. The choice of reference point is completely arbitrary, and a matter of convenince. There are good reasons for choosing the reference of zero at infinity, but obviously we often choose the zero to be elsewhere when we are doing problems near the earth's surface.

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