  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: (i) if the planetary obliquity exceeds 68.875 deg there
is a range of semimajor axes in which the classical Laplace surface is
unstable; (ii) 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; (iii) there is also a "polar" Laplace surface perpendicular to the
line of nodes of the planetary equator on the planetary orbit; (iv) for
circular orbits, the polar Laplace surface is stable at small planetocentric
distances and unstable at large distances; (v) at the onset of instability this
polar Laplace surface bifurcates into two polar Laplace surfaces composed of
nested eccentric orbits.
