Download ModelDownload Sourceembed



7.3.8 Relationship between F and U; between g and ϕ

To understand how g is related to ϕ:

  1. Similarly, compare  g = - G M r 2 and  ϕ = - GM r in the above table.
  2. If we differentiate  ϕ = - GM r    with respect to r, we will get   d ϕ d r = - G M ( - r 2 ) , which has the same expression as g.
  3. Hence, mathematically  d ϕ d r = G M r 2 = - g
  4. To understand the meaning of g = - d ϕ d r observe the two graphs carefully, on the right side where r is positive, the gradient of ϕ vs r graph is positive but the value of g will be negative. And on the left side where r is negative, the gradient of ϕ vs r graph is negative but the value of g is positive. Thus, g = - d ϕ d r

Similarly, it can be concluded that by multiplying both sides by test mass m.

m g = - d m ϕ d r
thus F = - d m ϕ d r Activity To do

ICT inquiry worksheet 1 (E), 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. Summary

symbol g = - G M r 2   ϕ = - GM r
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 = - GM r
relationship to mass Force, F = G M 1 M 2 r 2 = mg Potential energy, U = -m G M r = mϕ
graph model g = -6.67*500/(abs(r)*r)
model phi = -6.67*500/abs(r)
computer model if M = 500.  -6.67*500/(abs(r)*r) -6.67*500/abs(r)
relationship between g and ϕ
relationship between g and φ
g = - d ϕ d r
relationship between F and U
relationship between F and U
F = - d U d r Model

  1. Run Sim


Code Language Translator Run

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

Other Resources



end faq

Testimonials (0)

There are no testimonials available for viewing. Login to deploy the article and be the first to submit your review!

Submit your review

Please deploy the article before submitting your review!

You have to login first to see this stats.

5 1 1 1 1 1 1 1 1 1 1 Rating 5.00 (2 Votes)

Article Stats

Article ID: 59
Article Category ID: 24
Deployed Users
Total # of Likes
Total # of Dislikes
Total # of Deployment 0
  • Secondary
  • Gravity
  • Chemistry
  • Atmosphere
  • Junior College
  • EasyJavaScriptSimulation
  • Android/iOS including handphones/Tablets/iPads
  • Windows/MacOSX/Linux including Laptops/Desktops
  • ChromeBook Laptops
  • Science
  • Simulations