About
7.3.8 Relationship between F and U; between g and ϕ
To understand how g is related to ϕ:
 Similarly, compare $g=\genfrac{}{}{0.1ex}{}{GM}{{r}^{2}}$ and $\text{\varphi}=\frac{\text{GM}}{r}$ in the above table.
 If we differentiate $\text{\varphi}=\frac{\text{GM}}{r}$ with respect to r, we will get $\genfrac{}{}{0.1ex}{}{d\varphi}{dr}=\genfrac{}{}{0.1ex}{}{GM}{({r}^{2})}$, which has the same expression as g.
 Hence, mathematically $\genfrac{}{}{0.1ex}{}{d\varphi}{dr}=\genfrac{}{}{0.1ex}{}{GM}{{r}^{2}}=g$
 To understand the meaning of $g=\genfrac{}{}{0.1ex}{}{d\varphi}{dr}$ 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, $g=\genfrac{}{}{0.1ex}{}{d\varphi}{dr}$
Similarly, it can be concluded that by multiplying both sides by test mass m.
$mg=\genfrac{}{}{0.1ex}{}{dm\varphi}{dr}$
thus
$F=\genfrac{}{}{0.1ex}{}{dm\varphi}{dr}$
7.3.8.1 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.7.3.8.2 Summary
symbol  $g=\genfrac{}{}{0.1ex}{}{GM}{{r}^{2}}$  $\text{\varphi}=\frac{\text{GM}}{r}$ 
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  $\mathrm{g}=\genfrac{}{}{0.1ex}{}{GM}{{r}^{2}}$
towards the centre of the source mass 
$\text{\varphi}=\frac{\text{GM}}{r}$ 
relationship to mass  Force, $F=\frac{G{M}_{1}{M}_{2}}{{r}^{2}}$ = mg  Potential energy, $U=m\genfrac{}{}{0.1ex}{}{GM}{r}$ = mϕ 
graph  
computer model if M = 500.  6.67*500/(abs(r)*r)  6.67*500/abs(r) 
relationship between g and ϕ 
$g=\genfrac{}{}{0.1ex}{}{d\varphi}{dr}$


relationship between F and U  $F=\genfrac{}{}{0.1ex}{}{dU}{dr}$ 
7.3.8.3 Model
Translations
Code  Language  Translator  Run  

Software Requirements
Android  iOS  Windows  MacOS  
with best with  Chrome  Chrome  Chrome  Chrome 
support fullscreen?  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 
Credits
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
 http://iwant2study.org/lookangejss/02_newtonianmechanics_7gravity/ejs/ejs_model_GField_and_Potential_1D_v8wee.jar
end faq
Testimonials (0)
There are no testimonials available for viewing. Login to deploy the article and be the first to submit your review!
You have to login first to see this stats.