Mathematical Foundations of the Solar Gravitational Maneuver under Controlled Spacecraft Gravitational Response

Source abstract

This paper develops the mathematical foundations of a conditional Solar Gravitational Maneuver for a spacecraft whose mechanical response to the existing solar gravitational field is prescribed by a dimensionless coefficient Z g (t), while the spacecraft inertial mass and the solar field itself remain unchanged. The physical mechanism capable of producing Z g ≠ 1 is not derived here; it is treated as a separate gravitational-response problem. In the solar-dominant two-body approximation, constant Z g gives an ordinary Kepler problem with μ eff = Z g μ , while scalar response modulation preserves the direction of ☉ the specific angular momentum. For time-dependent response, the orbital mechanical energy satisfies dε/dt =-(μ /r) dZ ☉ g /dt. The general post-switch escape threshold is Z crit = v²r/(2μ), and for switching at ☉ perihelion of an initial Kepler ellipse it reduces to Z crit ,p = (1+e)/2, showing that complete decoupling is not mathematically required for escape. Because the switching leverage scales as 1/r, perihelion is the natural location for response change, subject to thermal and actuator constraints. Numerical Solar-System examples are used only to illustrate the conditional trajectory consequences. Conventional propulsion remains necessary for angular-momentum reduction, vector steering, rendezvous, and capture. The paper therefore addresses the celestial mechanics that follows from a prescribed Z g (t), not the technology by which such a response might be produced.