SATELLITE DYNAMICS ON THE LAPLACE SURFACE

By S. Tremaine, J. Touma, F. Namouni. 2008

152 citations recorded by the source corpus.

The orbital dynamics of most planetary satellites is governed by the quadrupole moment from the equatorial bulge of the host planet and the tidal field from the Sun. On the Laplace surface, the long-term orbital evolution driven by the combined effects of these forces is zero, so that orbits have a fixed orientation and shape. The “classical” Laplace surface is defined for circular orbits, and coincides with the planet's equator at small planetocentric distances and with its orbital plane at large distances. A dissipative circumplanetary disk should settle to this surface, and hence satellites formed from such a disk are likely to orbit in or near the classical Laplace surface. This paper studies the properties of Laplace surfaces. Our principal results are: (1) if the planetary obliquity exceeds 68.°875, there is a range of semimajor axes in which the classical Laplace surface is unstable; (2) at some obliquities and planetocentric distances, there is a distinct Laplace surface consisting of nested eccentric orbits, which bifurcates from the classical Laplace surface at the point where instability sets in; (3) there is also a “polar” Laplace surface perpendicular to the line of nodes of the planetary equator on the planetary orbit; (4) for circular orbits, the polar Laplace surface is stable at small planetocentric distances and unstable at large distances; (5) at the onset of instability, this polar Laplace surface bifurcates into two polar Laplace surfaces composed of nested eccentric orbits.

Subfields: Aerospace Engineering, Astronomy and Astrophysics

View Paper: https://www.semanticscholar.org/paper/d4fc4d104d37d05f4b4f50a65a3bf91ccefb39bd

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Citations in the corpus

High‐inclination orbits in the secular quadrupolar three‐body problem (2009, methodology): “Vectorial methods as devel- oped by Boué & Laskar (2006, 2009); Tremaine et al. (2009) are extremely well suited for this approach.”
Greatly Enhanced Merger Rates of Compact-object Binaries in Non-spherical Nuclear Star Clusters (2017, unknown): “Finally, the equations of motion can then be conveniently written in a dimensionless form as (e.g., Milankovitch 1939; Tremaine et al. 2009): de dτ =2j× e− 5 ( e · ĵout ) j× ĵout + ( j · ĵout ) e× ĵout, (A10) dj dτ = ( j · ĵout ) j× ĵout − 5 ( e · ĵout ) e× ĵout, (A11) deout dτ = ǫsc { eout…”
Suppression of extreme orbital evolution in triple systems with short-range forces (2014, methodology): “In the following, we present the secular evolution equations to the octupole order using a geometric (vectorial) formalism (e.g. Tremaine et al. 2009; Correia et al. 2011; Tremaine & Yavetz 2014), and confirm via angular projections that they are equivalent to Hamilton’s equations for the orbital…”