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What is Gravitational Potential? 

 Occasionally, another concept is defined with respect to gravitational potential energy. We define it here primarily to avoid possible confusion with the gravitational potential energy. Gravitational potential, Vg, is defined as the potential energy that a unit mass (usually 1 kilogram) would have at any point. This is sometimes useful because it assigns each point in space a definite gravitational potential value, irrespective of mass.

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More About Potential 

In our discussions so far, we have only considered gravitation in terms of the gravitational force itself. Another valuable concept in the study of gravitation (and indeed, in analogous fashion, electric fields and electrostatics) is the concept of gravitational potential. The concept of gravitational potential and potential energy also enables the solution of certain types of problem that are difficult to solve by other means, as we shall see.

In essence, gravitational potential is concerned with the work that needs to be done by anexternalentity to bring a system of masses into a certain configuration, taking into account the gravitational attraction between those masses. To illustrate this, consider the set up in the following diagram:




We consider the work that an external agent would have to do in moving our massmfrom an infinite separation to some separationRfrom massM. I find it slightly easier to consider this problem the other way round – what work needs to be done to move the mass m from Rto infinity. Because the gravitational force is attractive, separating the masses requires a positive amount of work from the external agent. (Imagine doing the job yourself – if you had to separate masses that were attracted to each other in this way, you yourself would be doing positive work, and would get tired as a result).

Thus, bringing the masses together requiresnegativework from the external agent. By definition, the work done in moving through the distance r (Δx in the diagram above is)


To evaluate the total work done in moving from infinity to a separationR, it is necessary to use integral calculus on the above expression. The result is found to be:


To evaluate the total work done in moving from infinity to a separationR, it is necessary to use integral calculus on the above expression. The result is found to be:

The expression above, describing the work that has to be done by an external agent in bringing the masses together, is referred to as thegravitational potential energy.

The gravitational potential is then defined as the work that needs to be done by the external agent on a UNIT mass, so that


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