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<p>This study presents the orbital dynamics of a spacecraft moving along a planar trajectory in the shape of a generalized parabola. The analysis method used is inspired by Siacci’s theorem, since the acceleration is decomposed into a central component and a tangential component. This allows us to obtain the expression for the continuous thrusts of the spacecraft as a function of the orbital distance, in cases where the thrust is parallel or perpendicular to the trajectory. Numerous original solutions are presented, which are then applied, for example, to the organization of orbital rendezvous or to suggest alternatives to the classical Hohmann transfer. In the latter case, <InlineEquation ID="IEq1"> <EquationSource Format="MATHML"><math> <mi mathvariant="normal">Δ</mi> <mi>v</mi> </math></EquationSource> <EquationSource Format="TEX">$\Delta v$</EquationSource> </InlineEquation> and flight time comparisons are carried out, in particular with simulations of Earth-Saturn transfers.</p>

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New analytic solutions with thrust tangential or perpendicular to the flight direction: a class of generalized parabolas

  • 期刊论文

  • 发表日期：

    2026年7月14日

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  • Eric Guiot

摘要

This study presents the orbital dynamics of a spacecraft moving along a planar trajectory in the shape of a generalized parabola. The analysis method used is inspired by Siacci’s theorem, since the acceleration is decomposed into a central component and a tangential component. This allows us to obtain the expression for the continuous thrusts of the spacecraft as a function of the orbital distance, in cases where the thrust is parallel or perpendicular to the trajectory. Numerous original solutions are presented, which are then applied, for example, to the organization of orbital rendezvous or to suggest alternatives to the classical Hohmann transfer. In the latter case, Δ v $\Delta v$ and flight time comparisons are carried out, in particular with simulations of Earth-Saturn transfers.