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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 \(-3.95\text{ GJ}\)
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