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mistake in proof of gravitational potential equation?
Hi, I have a problem in deriving an equation for the gravitational potential.
Well, I think that the graviational potential is the work done by external forces in moving a unit mass Mp from infinity to that point through distance d, and so I converted the equation in this way:
when M is the mass of a planet creating the gravitational field and r is the distance between M and Mp,
V= (work done) / (mass)
=F.d / Mp
=(G*M*Mp/r^2)*d/ Mp
... and I got nowhere.
However, my text states that the distance from the infinity to the point mass Mp should be r as well. So the text says that
V= (work done) / (mass)
=F.r / Mp
=(G*M*Mp/r^2)*r/ Mp
and in this way the correct equation, V=-GM/r (negative sign is added afterwards) shows up.
But I don't understand why the text can set both the distance from the infinity to the point mass Mp and the distance between M and Mp as r.
To make the problem more complicated, my teacher has said that there might be a typo or two in the text, which makes the understanfing very difficult. So it might be included in this context, I don't know...
If anyone could explain me this, please help me by doing so...
I would really really appreciate your advise!
Hi, I have a problem in deriving an equation for the gravitational potential.
Well, I think that the graviational potential is the work done by external forces in moving a unit mass Mp from infinity to that point through distance d, and so I converted the equation in this way:
when M is the mass of a planet creating the gravitational field and r is the distance between M and Mp,
V= (work done) / (mass)
=F.d / Mp
=(G*M*Mp/r^2)*d/ Mp
... and I got nowhere.
However, my text states that the distance from the infinity to the point mass Mp should be r as well. So the text says that
V= (work done) / (mass)
=F.r / Mp
=(G*M*Mp/r^2)*r/ Mp
and in this way the correct equation, V=-GM/r (negative sign is added afterwards) shows up.
But I don't understand why the text can set both the distance from the infinity to the point mass Mp and the distance between M and Mp as r.
To make the problem more complicated, my teacher has said that there might be a typo or two in the text, which makes the understanfing very difficult. So it might be included in this context, I don't know...
If anyone could explain me this, please help me by doing so...
I would really really appreciate your advise!