Length Scaling In Spacecraft Dynamics

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This research evaluates the length-dependence of a number of space environmental accelerations, both orbital and angular. Many non-gravitational effects accelerate a smaller body more than a larger body, thanks to ratios such as area-to-mass that vary inversely with characteristic length. This research studies these accelerations, and the corresponding dynamics, with an interest in applying the results to methods of propellant-free spacecraft propulsion. After surveying space environmental accelerations, the analysis focuses on three particular cases: solar radiation pressure, aerodynamic drag, and the Lorentz force. Each of these accelerations has an explicit dependence on length-scaling, such that millimeter-scale bodies experience characteristically larger magnitudes of acceleration than typical spacecraft. For the case of solar-radiation pressure, a flat integrated circuit is considered as a low-cost, feasible solar sail with passive, locally and/or globally stable attitude control. The modified orbital and attitude dynamics are considered for heliocentric, geocentric, and three-body orbits. For aerodynamic drag, a similar thin-plate integrated circuit bus is considered for atmospheric re-entry. Here, the spacecraft's cross-sectional area-to-mass ratio drives the magnitude of drag. So, small bodies can remove orbital kinetic energy very efficiently. Further, length-scaling laws for thermodynamics and fluid mechanics show that a very small spacecraft can even survive the intense re-entry thermal environment without burning-up or requiring active control. Research on the Lorentz force has found that an orbiting body with an electrostatic charge can interact with a planetary magnetic field and experience a force. In this case, the driving parameter is the electrostatic charge-to-mass ratio, a quantity that depends on the inverse square of characteristic length. This analysis presents a proposal for a small spacecraft that can demonstrate the Lorentz force in Earth orbit. A sample low charge-to-mass mission is proposed, wherein the Lorentz force is considered for Jovian capture and orbit circularization. The Lorentz force is also evaluated in relation to the so-called Earth Flyby Anomaly, in which an unknown acceleration affected the orbit of six spacecraft as they were executing Earth gravity assists. This research finds that the Lorentz force cannot be associated with the unknown acceleration, in spite of having similar characteristics.

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