Friday, May 8, 2015

EJSS gravity 06

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

symbolgφ
nameField strengthPotential
unitsN kg-1 or m s-2J kg-1
meaningForce per unit massPotential energy per unit mass
quantityvectorscalar
equation|g| = G M r 2 towards the centre of the source massϕ = - G M r 
relationship to massForce, F = G M 1 M 2 r 2 = mgPotential energy, U = -m G M r = mφ
graph
computer model if M = 500. -6.67*500/(abs(r)*r)-6.67*500/abs(r)

Model

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