Gravitational Potential
Definitions
- Gravitational potential energy is defined y the amount of work required to move a mass from infinity to a point in the gravitational field.
- We often talk about the change in gravitational energy and use the delta sign (\(\Delta\)) to signify change.
- This definition does not include "per unit mass" which is what separates it from gravitational potential, and makes it energy.
Equation for Gravitational Potential
\[V=-\frac{GM}{r}\]
Gravitational Potential
- If I have a unit mass, which is at a point in a gravitational field with a value of -20MJ kg\(^{-1}\)
- This means it would take 20MJ of energy to move it to infinity.
The radius of the earth is 6370km and it has a mass of \(5.97\times10^{24}\). Calculate the gravitational potential on the surface of the earth.
-
\[\frac{-6.67\times10^{-11})\times(5.97\times10^{24}}{6370000}=-62511616.95\]
-
\[-62511616.95\div 1000000=-62.5MJ\]
The mass of the earth is \(5.97\times10^{24}\) and it has a radius of \(6370\)km. Calculate the GPE of a 75kg satellite at a height of 1200km.
- \(\frac{(-6.67\times10^{-11})\times(5.97\times10^{24})\times(75)}{(6370+1200)\times10^3}=-3945168428\)
- \(-3945168428=-3.95\times10^9J\) or \(-3.95\text{ GJ}\)