Edelbaum's Equation

Author: Tianjiang Shuo

Website: https://cislunarspace.cn

Definition

An analytic equation derived by Edelbaum in 1961 for estimating the velocity increment required by a low-thrust spacecraft transferring between two inclined circular orbits. The key expression DV2=V12+V22−2V1V2⋅cos⁡(π⋅Δi/2)DV^2 = V_1^2 + V_2^2 - 2V_1 V_2 \cdot \cos(\pi \cdot \Delta i / 2) unifies plane-change and speed-change costs into a single compact formula, widely used for rapid preliminary analysis of low-thrust missions.

Application Value

Edelbaum's equation provides a theoretical foundation for cislunar space mission design, particularly in libration point orbit design and low-energy transfer analysis. Using this equation for trajectory optimization can effectively reduce mission propellant consumption and improve mission cost efficiency. In mission design, the analysis helps engineers understand spacecraft behavior in complex gravitational fields and guide the development of station-keeping strategies.

  • Differential Algebra (DA)
  • Plume Impingement
  • Momentum Integral (MI)

References

  • Edelbaum 1961 Propulsion Requirements for Controllable Satellites
  • Kluever 1997 Optimal Earth-Moon Trajectories Using Combined Chemical-Electric Propulsion
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Contributors: ouyangjiahong, Ou Yang Jiahong