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 ϕ = - G M r

Note:
1) This expression

ϕ = - G M r is similar to the expression for gravitational potential energy,

U

= -m G M r . and they are related by U = mφ.

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

g = G M r 2 , gravitational potential

ϕ

= - G M r is also independent of the mass of the point mass, m.
5) As distance r of the point mass from source mass increases, φ increases according to the equation

ϕ

= - G M r .

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

= - G M r

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	$\|g\|$ = G M r 2 towards the centre of the source mass	$ϕ$ = - G M r
relationship to mass	Force, $F$ = G M 1 M 2 r 2 = mg	Potential energy, $U$ = -m G M r = mφ
graph
computer model if M = 500.	-6.67500/(abs(r)r)	-6.67*500/abs(r)

Model

https://dl.dropboxusercontent.com/u/44365627/lookangEJSworkspace/export/ejss_model_gravity06/gravity06_Simulation.xhtml