Gravitational fields (A2)?!

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It'sTheArtLife
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#1
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#1
Hi,

I do AQA A2 Physics and feel as though I'm really struggling with the Gravitational Fields topic. I don't understand Gravitational Potential Energy or the link and difference between that and Gravitaional Potential. If someone could maybe give me the definition, equation (uniform and radial), units, and graph (if there is one) I'd really appreciate it.
Also, what is the link between Gravitational Force and Gravitational potential? I think it's something to do with work done and graphs but I really don't know...
Thanks a lot!
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username1560589
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Gravitational potential is the gravitational potential energy per unit mass at a point.
Gravitational field strength is the gravitational force per unit mass at a point.
Gravitational potential energy is usually defined as the work needed to move an object from infinity to a point(it is negative).

Have you studied integral calculus and improper integrals? The equations and some of the relationships will probably make more sense if you have.

For radial about a point of mass M,
gravitational potential is -GM/r, gravitational potential energy is -GMm/r.

For uniform a distance h up from some arbitrary point, it doesn't make sense to define gravitational potential energy the same way as before(we get -infinity) and in any case uniform is usually an approximation so we define gravitational potential energy to be the work done to move an object from some arbitrary point(same one as in our definition of h for simplicity) to a point. Gravitational potential energy is gmh, gravitational potential is gh and gravitational field strength is g.
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#3
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(Original post by It'sTheArtLife)
Hi,

I do AQA A2 Physics and feel as though I'm really struggling with the Gravitational Fields topic. I don't understand Gravitational Potential Energy or the link and difference between that and Gravitaional Potential. If someone could maybe give me the definition, equation (uniform and radial), units, and graph (if there is one) I'd really appreciate it.
Also, what is the link between Gravitational Force and Gravitational potential? I think it's something to do with work done and graphs but I really don't know...
Thanks a lot!
In addition to what Morgan said, for a uniform field the gravitational potential energy is defined as the energy of an object as a result of its position in the field. Here we do not refer to such a point as infinity as we assume that the gravitational field strength is constant throughout the field. This results in the classical definition of it, that is GPE=mgh where, for a radial field, g=-\dfrac{GM}{r^2} . This would give the gravitational potential energy as GPE= -\dfrac{GMmh}{r^2} where h is the distance from the surface the mass causing the field to the object in the field and r the distance from the centre of the mass causing the field. Of course, if h was given as the distance from the center of the mass to the center of the object, the above equation would become GPE=- \dfrac{GMmr}{r^2}= -\dfrac{GMm}{r}.
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It'sTheArtLife
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(Original post by Mehrdad jafari)
In addition to what Morgan said, for a uniform field the gravitational potential energy is defined as the energy of an object as a result of its position in the field. Here we do not refer to such a point as infinity as we assume that the gravitational field strength is constant throughout the field. This results in the classical definition of it, that is GPE=mgh where, for a radial field, g=-\dfrac{GM}{r^2} . This would give the gravitational potential energy as GPE= -\dfrac{GMmh}{r^2} where h is the distance from the surface the mass causing the field to the object in the field and r the distance from the centre of the mass causing the field. Of course, if h was given as the distance from the center of the mass to the center of the object, the above equation would become GPE=- \dfrac{GMmr}{r^2}= -\dfrac{GMm}{r}.
(Original post by morgan8002)
Gravitational potential is the gravitational potential energy per unit mass at a point.
Gravitational field strength is the gravitational force per unit mass at a point.
Gravitational potential energy is usually defined as the work needed to move an object from infinity to a point(it is negative).

Have you studied integral calculus and improper integrals? The equations and some of the relationships will probably make more sense if you have.

For radial about a point of mass M,
gravitational potential is -GM/r, gravitational potential energy is -GMm/r.

For uniform a distance h up from some arbitrary point, it doesn't make sense to define gravitational potential energy the same way as before(we get -infinity) and in any case uniform is usually an approximation so we define gravitational potential energy to be the work done to move an object from some arbitrary point(same one as in our definition of h for simplicity) to a point. Gravitational potential energy is gmh, gravitational potential is gh and gravitational field strength is g.
Thank you both for replying! I've made this to help me learn about each aspect... Would you mind having a look and pointing out any improvements/corrections/links between each thing? Also, is the area under the Gravitational Force - Distance graph the GPE? Thanks again!
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(Original post by It'sTheArtLife)
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Thank you both for replying! I've made this to help me learn about each aspect... Would you mind having a look and pointing out any improvements/corrections/links between each thing?
I would say that's fine.

Also, is the area under the Gravitational Force - Distance graph the GPE? Thanks again!
Yes, that's why the integral of Newton's inverse square law formula results in the formula of GPE.
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