Integrating the gravity formula?

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SUMMARY

The discussion focuses on integrating the gravity formula, specifically ##g = \frac{GM}{r^{2}}##, leading to the result ##v_{g} = -\frac{GM}{r}##. This result represents gravitational potential, analogous to electric potential in electromagnetism. The conversation highlights that multiplying this potential by a second mass yields gravitational potential energy, and differentiating it returns to the original gravitational field strength relationship.

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  • Knowledge of electromagnetism concepts, especially electric potential.
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Mr Davis 97
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I decided to integrate the formula ##g = \frac{GM}{r^{2}}##, and I ended up getting ##v_{g} = -\frac{GM}{r}##. What is the meaning of the latter formula, and is it useful in anyway?
 
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It's equivalent to the gravitational potential (not the gravitational potential energy). In other words, if you're familiar with electromagnetism, it's analogous to the electric potential V. Multiplying by a second mass will give you the gravitational potential energy, and then taking the derivative after that will give you the force. Taking the derivative of what you have now would give you your original relationship, which is the strength of the gravitational field.
 

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