When do you use $\Delta V = -GM(\frac{1}{r_1} - \frac{1}{r_2} )$ and when do you use $\Delta E_p = -GMm(\frac{1}{r_1} - \frac{1}{r_2})$

The first equation will give you the change in potential per kg between the two positions. Potential being the energy required to move 1kg from where it is to infinity. Units Joules per kg. Sometimes it is worth noting that every point in the universe has a potential value associated with it, regardless of whether there is anything there or not. (We may not be able to assign a value for potential in some exotic circumstances)

The second equation multiplies this by m and so gives the change in potential energy for an object in the move. Units are Joules

The first equation will give you the change in potential per kg between the two positions. Potential being the energy required to move 1kg from where it is to infinity. Units Joules per kg. Sometimes it is worth noting that every point in the universe has a potential value associated with it, regardless of whether there is anything there or not. (We may not be able to assign a value for potential in some exotic circumstances)

The second equation multiplies this by m and so gives the change in potential energy for an object in the move. Units are Joules

(edited 7 months ago)

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