This paper presents a new theory for the solar gravitational field based on the inclusion of a vector potential. A magnetic-like flux modeled as the curl of the vector potential is produced by steady state mass currents in the sun, analogous to electromagnetic phenomena, and complements Newton's static force. We show that the effects of the vector potential and the magnetic-like flux appear in the observed planetary orbits, with the potential setting the orbit inclinations and the flux driving their spin configurations. A Fourier relationship exists between object position and velocity based on a specific angular momentum constant (sigma-slash) for the solar field, and the orbital states are derived from a standing wave equation which treats orbital energy E as its separation constant. The constant sigma-slash may be compared to the reduced Planck constant h-bar of the atomic field divided by the electron mass m, but without particle statistics and related constraints. The planets are located at nodes of the wave equation; however, the populations depend on the availability of mass at the time the solar system was formed and not all allowed states are occupied. Theory results for planetary orbit inclinations and mean radii agree with observations to the third significant digit. Body precessions for the Earth and Mars are also modeled for orbit level reference frames based on the presence of the potential and the flux. Base values for the Earth's Chandler Wobble and its far-term nutation are derived correctly for the first time, using the Earth's observed oblateness and the southward movement of the Tropic of Cancer as inputs. The nutation results provide an average of about 106,000 years for the period of the Earth's Ice Ages, in good agreement with the Milankovic theory. The results for Mars are speculative because of the lack of required observational data. The analysis additionally includes chapters devoted to (1) the advance of the perihelion of the planet Mercury's orbit, and (2) anomalies observed in the trajectories of Pioneer 10 and 11 spacecraft. Three plausible sources are analyzed for the perihelion advance -- the general theory of relativity computation, the gravitational equivalent of Larmor precession, and effects of a quadrupole moment in the solar equatorial plane. Application of the flux to the trajectories of the two Pioneer spacecraft provides an explanation for the onset of observed anomalies, their magnitudes, and gradual extinctions. In the final chapter we summarily compare electromagnetic and atomic quantum theories with the new gravitational theory, concluding that gravity waves propagate at the speed of light. We address the differences between the two fields, especially their fine structure constants, and apply the equivalent of Maxwell's equations to gravity waves. Also included is a discussion of why the special theory of relativity provides a wrong velocity result for Doppler shifts of light rays from distant galaxies. We end the presentation with a qualitative assessment of the impact of clusters of stellar gravitational vector potentials on cosmology theory.