The Formula Revisited

After being challenged to come up with a mathematical formula for the capacitor model, I've come up with several versions, all of which have Newton's formula as its main part.

The main part derives directly from the fact that the capacitor model suggests that gravity dipoles attract inertia universally regardless of which end is used. They act therefore as a mono-poles, just as Newton suggested. This means that Newton's shell theorem applies to this part of the formula. The long range attracting force can be calculated from the center of objects, and we get:

F = GM(q1)M(q2)/r^2

where

G is the gravitational constant
M() is a function for inertia based on charge quanta
q1 is the total charge carrying quanta in object 1
q2 is the total charge carrying quanta in object 2
r is the distance between the centers of object 1 and 2

This is basically Newton's formula with variable mass, as described by Halton Arp.

The short range repelling force due to dipoles acting against each other is far less straight forward to describe, and it is probably a mistake to include it as a specific formula at this point.

However, the repelling force needs to be mentioned, since it is responsible for the hollow assumed to exist inside planets, moons and stars. It is also assumed to produce a short range repulsion between large objects, should they come into close contact with each other.

The short range repelling force is likely to obey the inverse cube law. However, dipoles do not conform to Newton's shell theorem, so the force will appear to emanate from some point other than the center of objects. The apparent origin may even change with distance and geometry. This force may have more in common with the energy hill described in chemistry, where compounds resists spontaneous binding, than regular gravitational pull.

The repelling force may best be described as an unknown complex function of q1, q2 and r.

ShortRangeRepellingForce(q1, q2, r)

That would give us the full formula:

F = GM(q1)M(q2)/r^2 - ShortRangeRepellingForce(q1, q2, r)

The exact nature of the short range repelling force may never be discovered. However, there should be measurable evidence for its existence in the form of hollows inside planets and a resistance to collisions between stellar objects.

Anyone feeling up to the task can go ahead and make a formula for the repelling force based on the integral of dipoles arranged in a sphere. Such a task is far beyond my capabilities in integral calculus, so I'm not going to attempt it. But it might be fun for someone who's good in this kind of stuff.

Alternatively, we can wait and see what sort of data turns up as we delve deeper into the exact nature of hollow planets. There might one day be enough data to derive from them a formula for the short range repelling force.

On further deliberation I have since come to the conclusion that the repelling force described above is nothing more mysterious than the electrostatic force. From this we get a repelling electric force that acts between surfaces, and an attracting gravity that acts from the centre of bodies.

Attracting gravity, repelling electrostatics

This solution can in turn be used to explain the remarkable stability of orbits. It can also be used to defend the position that planets are hollow at their core.