# Gravitational Binding Energy

#### Stratosphere

I read about the gravitational binding energy and I figured out how to derive it but what is the significance of it, what does it tell us? It also says something about the suns internal energy, how would I find this?

Gravitational binding energy equation
$$U=\frac{3GM^{2}}{5R}$$

#### qraal

I read about the gravitational binding energy and I figured out how to derive it but what is the significance of it, what does it tell us? It also says something about the suns internal energy, how would I find this?

Gravitational binding energy equation
$$U=\frac{3GM^{2}}{5R}$$
The equation tells us how much energy is needed to remove a spherical object's mass beyond its own gravitational attraction and how much energy has to be dissipated as heat for that object to become gravitationally bound from gas/dust falling from far away ("infinity".) Thus protostars are very hot from the energy being released by their mass contracting in size, converting gravitational potential energy into heat.

An important equation in astrophysics is the Virial equation:

$$U + 2K = 0$$

which means the binding energy is twice the kinetic energy and negative in sign for a bound system. Because temperature is a measure of average kinetic energy then the equation can be used to work-out the average temperature of an object, like the Sun. Also the temperature of a cluster of stars is determined by the Virial Theorem and the binding energy equation, telling us a lot about how that system will evolve through time gravitationally.

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