Note 373(5): Direct Integration of the Hamiltonian

The direct integration produces the orbital differential function (16), which is known from the numerical lagrangian analysis to be that of a precessing ellipse. This function (16) can be compared directly with the non relativistic result expressed in Eqs. (20) and (27). The deviation of the relativistic orbit from the non relativistic orbit characterizes a precessing orbit. This is known from the fact that a numerical lagrangian analysis of ECE2 relativity gives a precessing orbit. There are no additional assumptions at all used in this simple analytical theory. So it is possible to deduce how a precessing orbit can be described by the differential orbital function dr / dphi. This by passes the need for numerical integration. So the exact precessing orbit is given by dr / dphi, an important result that is easy to compute and graph. The same function dphi / dr can be obtained numerically from the lagrangian. It should be possible now to make a direct comparison of this theory with the astronomical data on precession.


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