How Gravity Relates to the Electric Force

Gravity is due to an imbalance in the electric force which makes electric repulsion a tiny bit weaker than electric attraction.

This means that Newton's law is in fact a variation on Coulomb's law, and we should therefore be able to establish a formal relationship between the two.

It's not enough to say that G is a proxy for k, and that M1 and M2 represent total charge while q1 and q2 represent net charge. However, it's a good starting point.

As we will see, the relationship between Coulomb's law and Newton's universal law of gravity can be formally quantified and explained.

Coulomb's law compared to Newton's law

How G relates to k

First off, we need to realize that the two constants k and G are related in that they both transform an intermediate result into force. Both of the above equations yield result in Newton, and this is only because of k and G.

With the only other difference between the two equations being q1 and q2 vs M1 and M2, we should be able to find a relationship between these quantities simply by dividing G by k.

k and G have been measured to be:

k = 8.98755 10^9 kg m^3/C^2s^2 , where C is charge expressed in Coulomb

G = 6.6743 10^-11 m^3/kg s^2

Dividing G by k we get:

G/k = (6.6743 10^-11)/(8.98755 10^9) C^2/kg^2

G/k = 7.426 10^-21 C^2/kg^2

How G/k relates to inherent charge imbalance in matter

The thing to note about this result is that we have C squared divided by kg squared.

The reason for this is that we naturally get a square if we multiply q1 with q2 or M1 with M2. To get a result that relates one mass quantity to one charge quantity, we need to take the square root of G/k.

This yields the magnitude of the electric imbalance inherent in neutral matter. It relates matter expressed in kg to its inherent charge imbalance expressed in C, and we will call this value p for short:

p = (G/k)^1/2

p = 8.618 10^-11 C/kg

What this means

We can now use p to transform matter measured in kg into charge imbalance measured in C. For every 1 kg of matter, we have an imbalance of 8.618 10^-11 C.

If we put two neutral 1 kg masses next to each other, with only 1 mm of separation, we get a force corresponding to 0.067 mN.

To get a corresponding force by simply charging the two masses we need to add 538 million electrons to one of the masses and subtract 538 million electrons from the other mass.

This may sound like a lot, but there are 3.055 10^24 atoms in a kg of gold, and each atom of gold has 79 electrons. The total number of electrons corresponding to 1 kg of matter is therefore roughly 2.4 10^20 million electrons.

The imbalance in the electric force caused by 1 kg of matter is in other word a mere 5 10^-15 percent of the total number of electrons present in the material.

This means that a measurement in an electric lab has to be precise to 17 digits after the decimal point to even start registering the effect of gravity. No wonder then that gravity has never been measured in such a laboratory.

Our proxy is a variable

If gravity is due to a minuscule imbalance in the electric force, it's likely to be dependent on other electric factors as well, such as capacitance and charge. This makes p a variable rather than a constant, and by extension we get that G is a variable too.

It follows that two bodies don't necessarily have the same value for p. A small body with little capacitance will have a different p than a large body with a lot of capacitance.

From observations we can further infer that it is the large bodies that have the greatest values for p, because large bodies seem to be more gravitationally strong, relative to their sizes, than small bodies.

With this in mind we can put together a modified version of Newton's formula as follows.

Newton's formula expressed in terms of k and p

It's now possible to convert mass expressed in kg into a charge imbalance expressed in C. By multiplying p with M we get units corresponding to point charges and we can therefore express Newton's law as follows:

Newton's law expressed in terms of k and p

Instead of G, we get p1 and p2 which relate the masses M1 and M2 to their respective charge imbalances.

With this transformation in place, Coulomb's law can be used for both gravity and the electric force. These two forces have thus been formally joined together, leaving us with no need for the gravitational constant G.