E1: Start with the default situation of a single point object.

Rotate the 3D projection around the V axis (z) and control so that the distribution is of rotational symmetry in the xy plane.

E 2: Tilt the projection to see the xy plane from below.

Shift the yellow V plane with the slider and observe its intersection with the potential contour. Consider thoroughly what you see! (the intersection line is an equipotential line of Potenial V in the xy plane. The magenta colored plot is not a 3 dimensional potential function!).

E 3:  Choose among the specific projections and study the effect of shifting the V plane.

E 4:  Choose the projection with perspective. Shift the distance above the xy plane − by means of slider z − for which the distribution is calculated. It will become less pronounced.

What do you see? (the xy potential distribution in a plane parallel to the xy plane, at a distance z from it. Again, this is not a 3D potential distribution!).

E 5:  Now try to get a conception of the 3D potential distribution itself. It should be of rotational symmetry to any straight line that passes the origin ~ point symmetry.

E 6:  Choose the 2 body case. Repeat the experiments described above.

Now the distribution is no longer of rotational symmetry, but just symmetric in respect to the y axis. When you shift the V plane, you will see ranges where an equipotential line encloses both sources; this is the near field. Then you can see ranges, where it disaggregates into two separate equipotential lines; this is the far field. In between there exists a neutral point; here in the case of two celestial bodies a satellite (a third object) could be positioned without attractive force to any one of the two others. Reflect why such a neutral point is instable, and hence why the satellite will need small corrective propulsions.

E 7:  Change the distance between the objects with slider R. Playing around with R, z and V you can study situations for a great range of parameters.

E 8: With slider b<1 change the relation of the size of both objects. b defines the relation of the second object to the first one. This simulates for example a star with a smaller companion.

E 9:  Repeat the experiments for the case of 3 bodies. Now sliders b and c are active to define the relative sizes. This may simulate a sun, earth and moon situation (not in respect of the real distances!).

E 10:  Choose the dipole and reflect what determines the difference to the 2 body case. Is there an axis of symmetry which leads to the 3D configuration of the equipotential lines? Observe how fast the potential declines with distance, compared to the 2 body situation (of equal polarity).

E 11:  Study the quadrupole. Here the fast decline with distance is still more striking. Why?

E 12:  Edit the formulas and speculate in advance what you should see and why!