# Gravitational potential

Read about gravitational potential in the right column before looking at the exercises.

The simulation contains two stars. The mass and radius of the second star are so small that in practice there is only one star.

## Exercises

1. Click OK on the parameter page, but don't start the simulation. Click on the Gravitational Field tab. Study the equipotential lines.
Click on neighboring lines and note that the potential difference between lines is constant.
When looking at the lines you may get the impression of looking down into a "well". Therefore we often say that the star is at the bottom of a potential well. Here is a 3D graph of a potential well: 2. Calculate the gravitational potential at the surface of the star S1.
Click close to the surface and compare with your calculated value.
3. Change the mass of S2 to 1E30 kg and the radius to 5E5 km.
Click OK and study the equipotentials.
Try to calculate the potential at the midpoint of a line connecting the two stars and compare with the value you can read by clicking in the Field window.
Click on the Field tab. Note that the field line through any point is always perpendicular to the equipotential line through the same point. Try to explain this fact.
5. Zoom out a few times and watch the equipotential lines. Try to explain that they get more circular with increasing distance from the stars.

The gravitational potential in a point P is defined by the work W done by the gravitational forces on a small mass m when it is moved from infinity to P. The gravitational potential in P is then W/m. The potential is zero infinitely far from all bodies.
At the distance r from the center of a homogeneous sphere with mass M the potential is .

The graph below shows the gravitational potential near the earth neglecting all other bodies (the moon, the sun, ...). An equipotential surface is a surface where the potential has the same value everywhere on the surface.
If the gravitational field is created by only one body the equipotential surfaces are spherical.
In a plane the equipotential surfaces appear as equipotential lines.
Orbit Xplorer can draw equipotential lines in the xy-plane when all bodies are confined to this plane. The equipotential lines are drawn with a constant potential difference between neighboring lines. They are like contour lines on a map which trace lines of equal altitude.

Electric potential can be defined in a similar way. The electric potential in a point P is W/q, where W is the work done by the electric forces moving a small charge q from infinity to P.
The difference in electric potential between two points is the electric voltage between these points. We don't have a special name for the gravitational potential difference.