Alright William. I feel like doing some pointless math, so I'm going to attempt to calculate what your theory would imply about gravity. This may take a bit, considering how complex the math is going to be. If I make any assumptions that you feel are wrong, you can correct me, but please try to be concise about it. I don't feel like reading five paragraphs of nonsense to get what could have been said in one sentence.
First, a description. We have two balls of radius R and r, mass M and m, with their centers separated by distance D. We'll also assume that these balls have a uniform density.
Next, we have to figure out how much ambient radiation makes it through a ball. The difference between this and the radiation from the other side is gravity, according to William's theory. The only thing that'd make sense to me is some form of half-life. So, leaving the constants as unknowns, that'd be
, where
is our constant,
is the density, and
is the distance the rays had to travel through the substance. It would then make sense to assume that the force imparted by this ray would be proportional to
, which we'll need later.
The next step is to work out how this would effect a point mass. This is where things start to get tough. For each possible direction out of the point, we have to figure out how much mass the ray would pass through. This is symmetric about the line from the point to the center of the ball though. If I remember my calculus correctly, we'd only need to figure out the effects on a circle, then integrate this over the rest of the sphere.
So from the point of view of the point, for a given angle
, we need to figure out how much, if any, of the ball is in that direction. This is a really tricky calculation. I think I'll take a break here until I can figure out what to do next. (Or until someone can help me a bit with this, though I wouldn't be surprised if no one felt like it.)