# Gravitational Potential (symbol: φ and units: J kg-1)

The gravitational potential, φ , at a point due to the gravitational field set up by a mass M is defined as the work done per unit mass in bringing a point mass from infinity to that point.

Mathematically, it can be shown that $$

Note:

1) This expression $$

2) Gravitational potential is a scalar quantity. (i.e. it has no direction and a negative value simply means it is less than zero).

3) This expression implies that φ is also always negative (less than zero) and by convention, the gravitational potential at infinity is also taken to be zero (maximum).

4) Similar to gravitational field strength $$

5) As distance r of the point mass from source mass increases, φ increases according to the equation ϕ

Try to input your own model for potential until you achieve a close fit to the data set graph from potential.

hint:

What is the value of M is the model?

no need to key in x10

^{-11}

abs in java is absolute | | that always make the value positive.

try something like -6.67*500/abs(r) in the equivalent for ϕ

# Summary

symbol | g | φ |

name | Field strength | Potential |

units | N kg^{-1} or m s^{-2} | J kg^{-1} |

meaning | Force per unit mass | Potential energy per unit mass |

quantity | vector | scalar |

equation | ||

relationship to mass | Force, F | Potential energy, U |

graph | ||

computer model if M = 500. | -6.67*500/(abs(r)*r) | -6.67*500/abs(r) |