User:Inconspicuum/Physics (A Level)/Gravitational Potential

Gravitational potential is the gravitational potential energy given to objects per unit mass:

$V_{grav}={\frac {E_{grav}}{m}}={\frac {-{\frac {GMm}{r}}}{m}}={\frac {-GM}{r}}$

For short changes in distance Δh (Δh << r), gravitational potential energy is given by:

$E_{grav}\approx mg\Delta h$,

where

$g={\frac {-GM}{r^{2}}}$

So, for short changes of distance, gravitational potential is equal to gΔh. Gravitational potential is measured in Jkg^-1.

Equipotentials

On a field diagram, lines can be drawn which, like contours on a map, show all the points which have the same gravitational potential. These lines are known as equipotentials. Equipotentials are always perpendicular to field lines, and get closer together as the field strength increases, and the density of field lines increases. Over short distances, equipotentials are evenly spaced.

Summary of Gravity

You should now know (if you did the gravity section in the right order) about four attributes of gravitational fields: force, field strength, potential energy and potential. These can be summarised by the following table:

Force $F_{grav}={\frac {-GMm}{r^{2}}}$	→ integrate → with respect to r and × by −1	Potential Energy $E_{grav}={\frac {-GMm}{r}}$
↓ per unit mass ↓
Field Strength $g={\frac {-GM}{r^{2}}}$	→ integrate → with respect to r and × by −1	Potential $V_{grav}={\frac {-GM}{r}}$