Encyclopedia of the Solar System 2nd ed

Solar System Dynamics: Regular and Chaotic Motion 811

b

a

FIGURE 23 Tw oCassiniimages of the Saturnian satellite
Hyperion show the unusual shape of the satellite, which is one
cause of its chaotic rotation. Panel (a) is a true color image, while
panel (b) uses false color and has better resolution because it was
obtained at closer range. [Courtesy of NASA/JPL/Space Science
Institute.]

a tumbling motion, such that its axis of rotation is not fixed
in space.
Voyagerobservations of Hyperion indicated a spin pe-
riod of 13 days, which suggested that the satellite was not
in synchronous rotation. However, the standard techniques
that are used to determine the period are not applicable if it
varies on a timescale that is short compared with the times-
pan of the observations. In principle, the rotational period
can be deduced from ground-based observations by looking

FIGURE 24 A single surface of section plot of the orientation

angle,θ, and its time derivative,θ ̇, obtained from the numerical

solution of Eq. (10) using the valuese=0.1 andω 0 =0.89,

which are appropriate for Hyperion. The points cover a much

larger region of the phase space than any of those shown in Fig.

22, and although there are some remaining islands of stability,

most of the phase space is chaotic.

for periodicities in plots of the brightness of the object as a

function of time (the lightcurve of the object). The results

of one such study for Hyperion are shown in Fig. 25. Since

there is no recognizable periodicity, the lightcurve is con-

sistent with that of an object undergoing chaotic rotation.

Hyperion is the first natural satellite that has been observed

to have a chaotic spin state, and results fromCassiniimages

confirm this result. Observations and numerical studies of

Hyperion’s rotation in three dimensions have shown that its

14.0

14.2

13.8

13.6

Time (days)

60

Mean Opposition Magnitude

02040

FIGURE 25 Ground-based observations by J. Klavetter of

Hyperion’s lightcurve obtained over 13 weeks (4.5 orbital

periods) in 1987. The fact that there is no obvious curve through

the data points is convincing evidence that the rotation of

Hyperion is chaotic. (Courtesy of the American Astronomical

Society.)