The Energy Equation of an Ether Theory of Gravity: Consistency with Special Relativity and the Orbit Equation

In the ether theory of gravity studied here, gravity is the inflow of a granular, incompressible medium toward bodies that condense it into matter, and mass is not its source. A body accelerates as a=k0 ve, and along its motion the acceleration is reduced by 1/γ 2. This paper treats only the consequences for energy and orbits, and gives the steps in full. (i) Integrated along the motion, the law gives the energy equation E=γmc 2e −φ, in which γ and e −φ are one exponential of the energy exchanged with the ether. (ii) Put into the force equation of special relativity, the same law gives the work Δ(γmc 2) for every direction of motion, reduces to E=γmc 2 far from the sinks, and satisfies Eloc 2=π 2c 2+m 2c 4 at every point; integration of the equations of motion confirms the algebra to 10−13. (iii) The Hamiltonian of the energy equation gives an orbit equation whose first-order form reproduces the perihelion advance 6πGM/[c 2a(1−e 2)], that is 42.98″ per century for Mercury, with β=γPPN=1 and no adjustable constant. The perihelion test does not separate this theory from general relativity; the exponential metric differs from the Schwarzschild metric at second order, and the points that remain open are listed. The scripts that produce every number are in the Supplementary Material.