Physicists Clarify Exotic Force
Azazel writes "A research group, including Purdue University physicist Ephraim Fischbach, has completed an experiment which shows that gravity behaves exactly as Isaac Newton predicted, even at small scales. Unfortunately for those in search of the so-called "Theory of Everything," the finding would seem to rule out the exceptions to his time-honored theories that physicists believe might occur when objects are tiny enough."
Starting with some algebra. If R'=sqrt(1-v^2/c^2), then (R'^2)*c^2+v^2=c^2. You forgot a term. Remember this sequence: simple math FIRST, then general relativity. The other way around just needlessly complicates things.
Second, your formula doesn't even support your statement that all objects travel at the speed of light. This is a nonsensical statement and I suppose it only figures that it needs nonsensical math to back it up, but wow you take it to extremes.
You cannot derive gravity or any other aspect of general relativity using Trigonometry and Newton. Sorry. I wish you could. Grading papers would a cinch, instead of worrying about Levi-Civita connectors, holonomic coordinate bases and Reimannian manifolds.
In all honesty, I am glad you are interested in physics. You should really pursue it. Portland State has some decent courses that I'm certain they would let you audit. Just remember to start with the basics before that GR class; I recommend analysis and topology as a pair of definite prerequisites.