612 Encyclopedia of the Solar System
FIGURE 7 Changes in aspect angle result in changes in
lightcurve amplitude. When the object is at point A, the angle
between two lines originating at the center of the body and
toward the Earth and the north rotational pole of the body, the
aspect angle, is 90◦. We see the object with an equator-on aspect
and the lightcurve of the object has its maximum amplitude.
When the body moves to point B, the aspect angle is 0◦and we
are looking down on the rotational pole. At point B, the object
does not exhibit any brightness variation; its lightcurve amplitude
is zero. By monitoring changes in the lightcurve amplitude of a
body as it orbits the Sun, it is possible to calculate the shape of
the body. (Courtesy of Ron Redsteer and NAU Bilby Research
Center)
observe the amplitude change of a body’s lightcurve over a
significant portion of the object’s revolution about the Sun,
it’s possible to use a computer to search through all possible
combinations of shape and orientation of the rotation axis
to find a shape that best simulates the observed amplitude
changes.
Figure 8 shows three lightcurves of Pholus from 1992,
2000, and 2003. The x-axis is labeled with the rotational
phase of Pholus. The rotational phase interval of 0 to 1 is
equal to a time interval of 9.980 hr, the time it takes Pholus
to complete one rotation about its axis. The amplitude of
the lightcurves grew from 0.15 to 0.39 to 0.60 magnitude.
A computer search of orientations of the rotation axis and
shapes for Pholus yields four possible orientations for the
rotational axis, all with the same shape of a / b=1.9 and
c/b=0.9. Pholus appears to have a significantly elongated
shape.
The amplitude measurements of Pholus span little more
than 10% of its 92-year period of revolution about the Sun.
Confirmation of the shape for Pholus will require addi-
tional amplitude measurements two or three decades into
the future.
KBO shape measurements require amplitude measure-
ments over more than a century. Yet, we can still say
something about the shapes without waiting a century. For
FIGURE 8 Evolution of Pholus lightcurve. (a) The lightcurve
observed by Marc Buie and Bobby Bus in 1992 has an amplitude
of 0.15 magnitude. (b) The lightcurve observed by Tony
Farnham in 2000 has an amplitude of 0.39 magnitude. (c) The
lightcurve observed by Bill Romanishin and Guy Consolmagno
in 2003 has an amplitude of 0.60 magnitude. The period in 1992,
2000, and 2003 remained constant at 9.980 hr; however, the
increasing amplitude indicates that we were seeing Pholus more
equator-on with each passing year between 1992 and 2003.