Introduction to Planetary Science

290 chapter 14
Figure 14.8. Relation of the Main ring of Jupiter to the
inner satellites: Metis and Adrastea, Amalthera, and Thebe.
The outer edge of the Main ring coincides with the orbits
of Metis and Adrastea whose periods of revolution resonate
with the period of Amalthea (Science Brief 14.7.1). In
addition, the Main ring is located inside the Roche limit
for objects having a density of 20g/cm 3 in a region where
particles cannot accrete to form a solid body because of
tidal forces exerted by Jupiter. The satellites of Jupiter
are located outside the Roche limit, except Metis and
Adrastea, both of which appear to be rocky objects having
superior mechanical strength. Adapted from Hartmann
(2005, Figure 3.14)
For this reason, rings can exist only inside the
Roche limit. Particles that orbit a planet outside
of the Roche limit could, in principle, form a
larger solid body in case that body can withstand
the stresses caused by planetary tides.
The Roche limit r R is expressed by the
equation (Hartmann, 2005, p. 60):
r R = 244
1/3 M
S
R (14.1)
where M is the density of the planet, R is its
radius, and S is the density of the satellite. In
case M = S, the Roche limit is r R = 244 R.
Note that equation 14.1 implies that the Roche
limit for a satellite orbiting a planet such as
Jupiter decreases with increasing density of the
satellite. In other words, satellites composed of
rocks can approach more closely than satellites
composed of ice before they are broken up by
the tidal force of the planet. Therefore, the rings
that orbit the large gas planets may have formed
when objects composed of rocks or ice came
too close to a planet and were broken up by
tidal forces. Alternatively, particles that initially
formed a disk around a planet at the time of its
accretion may have been preserved in the rings
by the fact that tidal forces prevented them from
coalescing into a satellite.
An additional constraint on ring particles is
provided by the Poynting-Robertson effect which
arises from the way in which centimeter-sized
particles in stable orbits absorb and reradiate
sunlight (Duncan and Lissauer, 1999). The effect
causes particles to lose energy and to spiral
toward the mother planet. As ring particles
descend into lower orbits, they are further slowed
by atmospheric friction and eventually fall into
the atmosphere of their mother planet. Consequently,
a gap is observed between the top of the
atmosphere and the innermost ring of a planet.
14.4 The Spacecraft Galileo
Much of what is known about Jupiter and its
satellites was learned during flybys of the robotic
spacecraft Pioneers 10 and 11 and by Voyagers
1 and 2. The Voyagers recorded spectacular
images of Jupiter and its Galilean satellites,
which provided a great deal of information that