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7.3.7 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 Equation U = mϕ

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.
 ϕ = - G M/r Scalar quantity

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

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).
 ϕ = - G M/r Independent of test mass

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. Vary according to inverse law with distance r

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

 ϕ = - G M/r

7.3.8 Activity to do

ICT inquiry worksheet 1 (C) and (D), as well as the "G field and potential" EJS here. The HTML5 version is below, the Java worksheet customization to HTML5 is work in progress.

7.3.9 Summary

symbol g ϕ
name Field strength Potential
units N kg-1 or m s-2 J kg-1
meaning Gravitational force per unit mass Gravitational 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 g = -6.67*500/(abs(r)*r)
φ = -6.67*500/abs(r)
computer model if M = 500.  -6.67*500/(abs(r)*r) -6.67*500/abs(r)

7.3.10 Modeling

Try to input your own model for potential until you achieve a close fit to the data set graph from potential.
What is the value of M is the model?
no need to key in x10-11
abs in JavaScript is absolute |   | that always make the value positive.
try something like -6.67*500/abs(r) in the equivalent for ϕ = - G M r

7.3.11 Model

  1. Run Sim


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Software Requirements


Android iOS Windows MacOS
with best with Chrome Chrome Chrome Chrome
support full-screen? Yes. Chrome/Opera No. Firefox/ Samsung Internet Not yet Yes Yes
cannot work on some mobile browser that don't understand JavaScript such as.....
cannot work on Internet Explorer 9 and below



This email address is being protected from spambots. You need JavaScript enabled to view it.; Anne Cox; Wolfgang Christian; Francisco Esquembre

end faq




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  • Secondary
  • Gravity
  • Chemistry
  • Periodicity
  • Junior College
  • Science
  • Simulations