By Fredrik Nygaard, November 2016
In my essay titled “The Gravity Mystery”, published September 2016, I pointed out that both gravity and capacitance of our planet appear to have increased over time. I postulated from this that charge held in capacitors may be the cause of gravity.
I called this hypothesis the Capacitor Model of Gravity, and although I did not elaborate on it, I claimed that it would support the theory that Earth is both hollow and expanding. I also claimed that the Capacitor Model is fully compatible with other gravity related observations.
I did not include a theoretical backing of my claims because I did not have a ready formula at the time. However, this has now changed, and I will in this paper present a simple formula that makes the Capacitor Model mathematically equivalent to Newton’s model in all but a few cases, namely at the centre of large bodies and for close interaction between two or more large bodies.
Starting with the basic fundamentals related to capacitors, I will show that there is nothing about the Capacitor Model, or dipole gravity in general, that automatically makes it incompatible with observed facts.
Characteristics of Capacitors
A capacitor is a charge carrying object. Anything that can hold charge without resorting to a change in chemistry is a capacitor, and since almost everything fits this description to some extent, we can say that capacitors are just about everywhere.
However, some capacitors are more efficient than others. We can create an efficient capacitor by placing two charge carrying plates close together with a suitable insulator, a so-called dielectric, placed in between them.
The charge carrying ability of a capacitor is known as its capacitance, and this ability is inversely related to the distance between the charge carrying plates. Capacitance increases when the distance between the plates is reduced. If the dielectric of a capacitor is made thinner, the capacitance of that capacitor increases.
It should also be noted that capacitance is a dipole phenomenon. Charged capacitors have a “plus” and a “minus” side.
Charge Held in Capacitors
Standard physics tells us that charge held in capacitors results in no external effect, but much speculation has considered whether this is true. Many argue that charge held inside capacitors can, in some way, affect their external environment.
Approaching the subject from various angles, those arguing that there must be some external effect due to charge held in capacitors generally believe that this effect is likely to be what we refer to as gravity. However, the effect is so small that only truly enormous capacitors are able to hold enough charge to produce a measurable effect.
Our planet and other stellar bodies such as our moon and sun are sufficiently large to produce gravity. Smaller bodies like asteroids and comets also produce gravity, but to a lesser extent. Small bodies such as rocks, boulders, animals and humans, hold too little charge to produce any detectable gravity.
Earth as a Hollow Capacitor
We know for a fact that Earth is a capacitor, and we know that it is likely to be an efficient one due to its chemical composition. Even if our planet is solid to the core, the capacitance of our planet is enormous. But should it be the case that our planet is hollow, then its capacitance would be much greater still, because a hollow Earth implies a relatively thin dielectric crust, and therefore higher capacitance.
The Gravity Atom
Since capacitance is a dipole phenomenon, and we assume gravity to be directly linked to this phenomenon, we must also assume that gravity at the atomic level is a dipole. And since gravity acts on mass, which is an attribute of subatomic matter, it must operate at the subatomic level. Just like mass, gravity is a property related to the subatomic.
We have no idea if such a thing as a gravity atom exists. No one has ever been able to locate such an entity. However, from a mathematical perspective the notion of a gravity atom serves a useful purpose in that it helps us explore the overall phenomenon of gravity. We will therefore discuss gravity atoms as if they really exist. Since we have no way of knowing what such an atom would look like, we might as well choose to define it in the simplest possible terms.
We will therefore define the gravity atom as a perfect sphere with one half charged opposite to the other half. From this, we will derive a formula for describing gravity mathematically.
Gravity atoms only exist inside charged capacitors, and they line up according to the electrical field that creates them. Their negative poles face towards the negatively charged plate, while their positive poles face towards the positively charged plate.
Note that for a spherical capacitor, hollow or not, gravity atoms will all be facing radially out from the centre. They will all have one end pointing in and the other end pointing out. Ref fig 2.
Problems With The Dipole Model
In my essay “The Dipole Model of Gravity and the Expanding Earth”, published January 2016, I made an extensive general analysis of dipole gravity. One of the troubling conclusions I arrived at was that dipole gravity will not produce a centre of gravity at the geometrical centre of stellar bodies. The centre of gravity would appear to be located relatively close to the observer. This in turn, made it difficult to calculate changes to gravity with altitude.
In my essay, “Universal Gravity Based on a Dipole Model”, published February 2016, it proved extremely hard to explain orbits when using a dipole model.
The problems with dipole gravity seemed insurmountable. However, I had overlooked an important possibility that can be derived directly from the fact that dipoles only exhibit repelling properties with respect to other dipoles.
If gravity atoms are distinct from mass, as the Capacitor Model implies, we get that gravity atoms may always attract mass, regardless of which poles are used. Only when gravity atoms interact with other gravity atoms will there be a dipole effect for sure.
Dual Behaviour of Dipoles
If gravity and mass are two separate things, then we can liken gravity on mass interaction with the way magnets act with respect to iron filings. While magnets attract or repel each other depending on the arrangement of their poles, they uniformly attract iron filings. Iron filings are never repelled by magnets, regardless of which poles are used. Likewise, mass may always be attracted by gravity. Only gravity atoms interacting with other gravity atoms will display dipole properties.
And if we add to this an assumption that dipole on dipole interaction between gravity atoms taper off at a more rapid rate than dipole on mass interaction, we get attraction in all cases, except when two gravitationally charged surfaces of identical polarity are located very close to each other.
Keeping in mind that only truly enormous capacitors can be said to be sufficiently charged to produce any measurable gravity, the repelling aspect of gravity will only come into effect on the inside of gravitational bodies, and when two or more gravitational bodies are in close encounter with each other. Ref fig 2.
Defining Gravity for the Capacitor Model
From the above speculations we can now define the gravity atom as follows:
1. It is a dipole
2. It is a perfect sphere
3. It attracts mass equally with both poles
4. It acts as a dipole, only in respect to other gravity atoms
5. It obeys the inverse square law when it interacts with mass
6. It obeys the inverse cube law  when it interacts with other gravity atoms
7. It acts unhindered by intervening matter
8. It exists only inside charged capacitors
9. It lines up with the electrical field within capacitors
Dipoles Behaving like Monopoles
Now, if we consider point 1, 2 and 3 of the above definition, we get that gravity atoms are indistinguishable from monopoles when it comes to how they act on mass. This is because perfectly spherical dipoles that act equally with both poles are mathematically equivalent to monopoles.
And if we include point 7 from the above list we get the exact same mathematical starting point that Newton used to develop his shell theorem.
Adding to this the inverse square law by including point 5, we get that gravity as described by Newton, and gravity as described by the Capacitor Model are identical as long as dipole effects due to mutually repelling gravity atoms can be ignored. We get a centre of gravity located at the geometrical centre of our planet, and we get the same results that Newton got for both orbits and changes in gravity with altitude.
Dipoles Behaving Like Dipoles
As far as neutral bodies are concerned, the Capacitor Model of Gravity is completely Newtonian in its predictions. At large distances we get Newtonian predictions for gravitationally charged bodies as well. This is due to the fact that the dipole on dipole effect tapers off according to the inverse cube law. At large distances, the dipole effect becomes insignificant.
However, the dipole effect is important inside gravitationally charged bodies. At the inside of such a body, gravity acts with an attracting force on mass as it always does. However, there will be mutual repulsion between gravity atoms because these all line up with their positive end facing in towards the centre. Ref Fig 2.
This opens for the possibility that gravitationally charged bodies may be hollow. In fact, if the repelling force between gravity atoms is strong enough to overcome the attracting force between gravity atoms and mass, gravitationally charged bodies cannot avoid having a cavity at their centre when they are in their equilibrium state.
Furthermore, we get that neutral bodies and gravitationally charged bodies will be affected differently by changes in gravity of a nearby gravitational body. While an increase in gravity of our planet will result in a direct increase in pull on gravitationally neutral bodies like ourselves, this will not be the case for our moon. Our moon, being a gravitationally charged body, will be affected by both an increase in attraction and an increase in repulsion.
This follows from the same logic used to explain the possibility of a cavity inside gravitationally charged bodies. Our moon and our planet are facing each other with mutually repelling gravity atoms. Only the gravity atom on mass interaction is producing an attracting force. The gravity atom on gravity atom interaction is producing a repelling force.
Depending on the distances involved and the exact relative strength of the two opposing forces, we get anything from an overall increase to an overall decrease in attraction between an expanding planet and its moons.
The fact that our moon is receding from us, can at least in part, be explained by the dipole effect.
When looking into anything that has to do with gravity, it has to be remembered that gravity is a weak force. Our universe is awash in electromagnetic activity which no doubt plays an important role. Our receding moon may for instance be affected more by electrostatic repulsion between itself and our planet than by the dipole effect theorized in this paper.
However, gravity is a major force in our solar system, and it behaves pretty much exactly as predicted by Newton. Any theory of gravity which aims to replace or improve upon Newton’s theory, must therefore make the same predictions for orbits and altitudes as does the standard model. Very little deviation can be tolerated.
The fact that the Capacitor Model matches Newton’s model as well as it does is in other words essential. Without such a close match the Capacitor Model would not be able to stand up to scrutiny. However, with the match being as close as it is, I expect that the Capacitor Model will be very difficult to refute.
From the above analysis, we get that the Capacitor Model of Gravity is mathematically equivalent to Newton’s model when it comes to orbits and changes in gravity with altitude. The only difference is that gravity in the Capacitor Model is not caused by mass acting on mass, but by charge-induced gravity in capacitors acting on mass. The dipole effect can then be ignored for large distances.
However, the dipole effect is important at short distances. The dipole effect allows for hollow, expanding planets, it explains how gravity may increase due to expansion, and why moons may recede from expanding planets even as gravity grows stronger.
We have arrived at a mathematical model that solves all the problems laid out in “The Gravity Mystery”, and we can conclude that there is nothing about dipole gravity that makes it automatically incompatible with observed facts. The possibility that our planet may be expanding due to internal pressures can no longer be dismissed on a purely theoretical basis.
The Gravity Mystery:
The Dipole Model of Gravity and the Expanding Earth:
Universal Gravity Based on a Dipole Model:
 Michael Faraday looked into the possibility that gravity had an electromagnetic origin.
 Thomas Townsend Brown did extensive research into a possible connection between capacitance and gravity.
 The inverse cube law is an arbitrary choice. The important point is that it is of a higher order than the inverse square law that governs gravitational attraction.