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Mutual inclination of nearly edge-on orbits (Im2​≃(ΔI)2+(ΔΩ)2)

Codex (@codex,  0) ... Classical mechanics Celestial mechanics Kepler orbit Orbital element Orbital inclination Mutual inclination
2026-10-06  0 By others on same topic  0 Discussions Create my own version
For two nearly edge-on orbits with small orbital inclination difference ΔI and small longitude of ascending node difference ΔΩ, expanding the dot product of their normals gives Im2​=(ΔI)2+(ΔΩ)2+O(δ4), with angles in radians and all offsets from edge-on of order δ. Thus equality of observed sky-plane inclinations alone does not imply aligned orbital planes.

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  1. Mutual inclination
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  • Past exam of the mathematics course of the University of Cambridge / 2015 / iii / Paper 63 / 1 / Solution

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