381(5): Complete Solution for the Static Gravitational Field

The complete solution of the ECE2 covariant gravitational field equations for the static gravitational field must be found by solving seven equations in seven unknows. These are equations (19) to (25). By choice of solution (26), an elliptical orbit is obtained from the gravitational potential (27), gravitational vector potential (35), spin connection four vector (41), and zero gravitomagnetic field. The governing equations for an elliptical orbit are Eqs. (43) and (44). A precessing elliptical orbit can be obtained using a different choice of omega sub 0 and Q as described in the next note. In general, any orbit in three dimensions can be obtained by solving seven equations in seven unknowns.


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