# Speed Of Light and Gravitational Force

I have been studying gravity for a while on an under graduate level. I have an equation that was derived that uses the speed of light to calculate the gravitational force between two objects. No G needed. Do any of you know of any like equations available that I could compare it with or study?

I know, why not show the equation... well honestly, I do not want to appear an idiot before I do necessary research so any guidance would be appreciated. The only variables are the two masses, distance between them to calculate the force, plus the speed of light and a use of the area of space. (no made up numbers).

Thanks for the guidance.

Einstein's equation in GR contains the gravitational constant, so there is no way around it unless you want to depart from that theory. Either your formula is not consistent with GR, or you are using units where G=1. I'm assuming G is not somehow embedded into any of your other quantities, e.g. the area you speak of?

There is no need to be afraid of posting your equation here. If it weren't for equations, physics would be a sorry state of affairs!

In Newtonian gravity, the attracting gravitational force between two homogeneous spherical objects of masses M1 and M2, the centres of which are separated by a distance R, is

F = G*M1*M2/r^2

acting on each object along the line connecting them. For small masses and large R, your formula should reduce to this one in order to be consistent with Newtonian gravity.

Torquil

When I reduce it to solve for G from Newton's famous equation, it comes out looking odd, I calculate G = (64*pi^10) / c^2. Hope this helps.

Thanks

nicksauce
Homework Helper
There is no equation that relates gravitational force without using G. And your supposed equation, G = (64*pi^10) / c^2, is not even dimensionally correct.

Consider $$MT^2/r^3$$ with M being a mass, T is the period of an orbiting satellite, r is the distance between the center of mass of M and satellite. Consider this a constant, using Kepler's constant. We will call this constant K for these purposes. There are a lot of cool calculations you can do with this, they are measurable. I suggest using Solar Mass for M, sidereal year in seconds for T, and AU for r. These are all measurable and can eliminate G.

$$F=G*M*m/r^2$$

Newton's equation can be calculated without G using K (which is the same for any mass, orbiting period and distance between objects, so you only need one accurate measurement, much like G).

Another concept is that any mass's "Kepler" number (for lack of better naming) can be obtained by K/M written

$$M_{k}$$

or

$$m_{k}$$

Now use this equation

$$F=(4\pi^2M)/r^2m_{k}$$

or you can use

$$F=(4\pi^2Mm)/Kr^2m$$

I believe you will find these units are correct, as K has $$kg^1, s^2, (r^-3)$$ units and is in the denominator, so we match G's units, but with more of a real observable type of units. That is the start of my construct. The equation I had stated above G = (64*pi^10) / c^2 was only to show where c was brought in to correlate with G.

Hope this helps see where I started.

Thanks!