### About

### 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 $\varphi =-\genfrac{}{}{0.1ex}{}{GM}{r}$

### 7.3.7.1 Equation U = mϕ

1) This expression $\varphi =-\genfrac{}{}{0.1ex}{}{GM}{r}$ is similar to the expression for gravitational potential energy, $U=-m\genfrac{}{}{0.1ex}{}{GM}{r}$. and they are related by U = mϕ.### 7.3.7.2 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).### 7.3.7.3 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).### 7.3.7.4 Independent of test mass

4) Similar to gravitational field strength $g=\genfrac{}{}{0.1ex}{}{GM}{{r}^{2}}$, gravitational potential $\varphi =-\genfrac{}{}{0.1ex}{}{GM}{r}$ is also independent of the mass of the point mass, m.### 7.3.7.5 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 $\varphi =-\genfrac{}{}{0.1ex}{}{GM}{r}$ .### 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 | $\mathrm{|g|}=\genfrac{}{}{0.1ex}{}{GM}{{r}^{2}}$ towards the centre of the source mass | $\varphi =-\genfrac{}{}{0.1ex}{}{GM}{r}$ |

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) |

### 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.Hint:

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 $\varphi =-\genfrac{}{}{0.1ex}{}{GM}{r}$

### 7.3.11 Model

### For Teachers

### Translations

### 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 |

### Credits

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

### end faq