On the nodal distance between two Keplerian trajectories with a common focus

We study the possible values of the nodal distance δ nod between two non-coplanar Keplerian trajectories A , A ′ with a common focus. In particular, given A ′ and assuming it is bounded, we compute optimal lower and upper bounds for δ nod as functions of a selected pair of orbital elements of A , wh...

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Bibliographic Details
Published in:Celestial mechanics and dynamical astronomy 2020, Vol.132 (1), Article 5
Main Authors: Gronchi, Giovanni Federico, Niederman, Laurent
Format: Article
Language:English
Subjects:
Aerospace Technology and Astronautics
Astrophysics
Astrophysics and Astroparticles
Classical Mechanics
Dynamical Systems and Ergodic Theory
Geophysics/Geodesy
Orbital elements
Original Article
Physics
Physics and Astronomy
Trajectories
Upper bounds
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Summary:We study the possible values of the nodal distance δ nod between two non-coplanar Keplerian trajectories A , A ′ with a common focus. In particular, given A ′ and assuming it is bounded, we compute optimal lower and upper bounds for δ nod as functions of a selected pair of orbital elements of A , when the other elements can vary. This work arises in the attempt to extend to the elliptic case the optimal estimates for the orbit distance given in Gronchi and Valsecchi (Mon Not R Astron Soc 29(3):2687–2699, 2013) in case of a circular trajectory A ′ . These estimates are relevant to understand the observability of celestial bodies moving (approximately) along A when the observer trajectory is (close to) A ′ .
ISSN:0923-2958
1572-9478
DOI:10.1007/s10569-019-9944-y