Amanda L' Proctor, Douglas P' Hamilton

1
An Explanation for the High Inclinations of
Amalthea and Thebe
Amanda L. Proctor, Douglas P. Hamilton Kevin P.
Rauch University of Maryland
ABSTRACT
Formation of Planetary Systems
Introduction
Two of the inner Jovian satellites, Amalthea and
Thebe, have unusually large inclinations for
regular satellites. We propose that these small
moons obtained their inclinations during passages
of Io resonances across their orbits. We
investigate the resonant kicks to the moonlet
inclinations analytically and numerically using
the sophisticated N-body integrators HNBody and
HNDrag. We determine that Io formed between 4.04
and 4.92 Rj, by showing that the 42 resonance
must have crossed over Thebe, but could not have
affected Amalthea. This means that Amalthea's
current orbit can be fully explained by the 31
resonance with Io. In addition to the 42
resonance, Thebe may also have been affected by
the 53 and 64 resonances.
Regular satellites, those that formed from the
planetary debris disk, should have nearly zero
inclinations. However, Amalthea and Thebe have
large inclinations. Could these inclinations be
the result of the passage of Io resonance's
across their orbits, as Io moved outward by
tides?
- How do planetary systems form? In particular,
how are planetary locations determined? - In many
ways, the Jovian system resembles a miniature
Solar System. Insight gained in one system can
often be applied to the other.
Satellite a(Rj) e i(deg)
R(km) Mass(kg) Amalthea 2.536
0.002 0.366 100 1x1019 Thebe
3.100 0.02 1.094 50
1x1018 Io 5.900 0.04 0.04
1821 8.93x1022 Europa 9.384
0.01 0.47 1565 4.8x1022
Ganymede 14.967 0.00 0.21 2634
1.48x1023 Callisto 26.339 0.01
0.28 2403 1.08x1023
Resonances/Tides - Two objects are in resonance
if their mutual perturbations add coherently over
time. The simplest orbital resonance, a mean
motion resonance, occurs when the ratio of the
orbital periods is a rational number. - A mn
resonance is (m-n)th order in eccentricities or
inclinations. First and second order resonances
are most efficient at exciting eccentricities and
inclinations. - Around an oblate planet, each
mean motion resonance splits into a fine
structure, similar to how the energy levels of a
Hydrogen atom are split by a magnetic field. -
Tides damp orbital eccentricities, but do not
affect inclination - the latter remain as fossil
records of past resonant activity.
Rings, Satellites and Io Resonances
Resonance Passages
Vertical heights of the jovian rings (cyan),
vertical oscillations of the moons (red), and the
vertical strengths of Io resonances
(yellow).
Scenarios for the origin of Amalthea's
inclination (left) and Thebe's inclination
(below).
Io and its resonances if Io were at 4Rj (above),
when Io was at 5Rj (right), and the current
configuration of the Jovian System (far right).
The current observed vertical oscillations of
Amalthea and Thebe are 1160km and 4300km,
respectively.
Conclusion
Small Moon Stability
Metis and Adrastea
The Cassini spacecraft recently undertook an
unsuccessful search for new km-sized moons. Many
radial locations are unstable in the context of
our model.
Io formed between 4.04 and 4.92 Rj as determined
from the resonant interactions detailed in the
table below. Since Io, Europa, and Ganymede
participate in the Laplace resonance today, the
latter two satellites must have formed exterior
to 6.35 and 10.08 Rj,
Could the small moonlets Metis and Adrastea have
been affected by a 41 resonance with Io? -
Perhaps, but the inclination of these moonlets
are not known. The main ring, shown left, is
30km thick. This thickness is similar to the
inclination kick which Io could have delivered.
- Io starts at 4.92 Rj and drifts outward by
tides. - Moonlets (with radial oscillaions shown
in yellow) that cross the semimajor axis of
Amalthea or Thebe (shown in red) are
destroyed.I - Our assumptions are conservative
since 1) Io probably formed closer to Jupiter,
and 2) Thebe and Amalthea have non-zero
eccentricities.
respectively. Finally, the existence of non-zero
inclinations for Amalthea and Thebe indicate that
these satellites have not been catastrophically
disrupted in the past several billion years. This
limits the flux of 1 km-sized comets to Jupiter
to not more than one per thousand years.
Top Galileo data for Jupiter's Rings, Burns et
al. 1999. Bottom Keck data from dePeter et al.
1999.