Interpretations of Orbits and Gravitational Attraction

Subject: Interpretations of Orbits and Gravitational Attraction
Date: Sun, 30 Nov 2008 07:23:42 EST

1) If the angular momentum in the previous note is a constant of motion then it follows that J is constant in a relativistic Kepler orbit for example, and that del J = 0. In this case there emerges the general law of orbits with constant angular momentum:

R = omega T

a result which has been obtained in a different way in previous work. The details of the orbit are obtained from the orbital theorem of paper 111, a new geodesic method which does not use the incorrect Einstein field equation. In galaxies omega T is equal to R but J is increasing in the non Newtonian region because v is constant. In a binary pulsar J is not constant and the orbit spiral inwards. This is perhaps describable by the opposite situation to a galaxy, where the stars spiral outwards. So there emerges a self consistent and very powerful description of orbits using the field equation plus orbital theorem of paper 111.

2) If we wish to interpret g as the usual centrally directed acceleration due gravity along a staright line (or what appears to us as a straight line on the earth), then we use omega approaching zero and

del g = 4 pi G rho = c squared R

to obtain the Newton inverse square law and the non-relativistic Kepler laws. In this case g is regarded as a straight line. If one imagines a circle with infinite radius, g (or the static E of Coulomb’s law) is the tangent to the circle:

g = c squared (T sup 010 i + T sup 020 j + T sup 030 k)

In the k axis g = c squared T sup 030 k

and points along k. In the spherical polar system g points along the radial coordinate r, and in both cases is generated by torsion in the limit of zero spin connection. Then orbits are generated as usual by a balance of gravitational attraction and centripetal repulsion.