Encyclopedia of the Solar System 2nd ed

Kuiper Belt Objects: Physical Studies 611

TABLE 3 Rotation Periods and Lightcurve Amplitudes

Name Number Prov Des Class^1 Period^2 Δm^3

136108 2003 EL 61 kbo 3.9154 0.28

15820 1994 TB kbo 6.0, 7.0 0.30

Varuna 20000 2000 WR 106 kbo 6.34 0.42

26308 1998 SM 165 kbo 7.1 0.45

32929 1995 QY 9 kbo 7.3 0.60

19255 1994 VK 8 kbo 7.8, 8.6, 9.4, 10.4 0.42

19308 1996 TO 66 kbo 7.9 0.25

47932 2000 GN 171 kbo 8.329 0.61

33128 1998 BU 48 kbo 9.8, 12.6 0.68

Pholus 5145 1992 AD cen 9.980 0.60

40314 1999 KR 16 kbo 11.858, 11.680 0.18

2001 QG 298 kbo 13.7744 1.14

(^1) Dynamical class. Kuiper Belt object (kbo) or Centaur object (cen).
(^2) Period of rotation in hours. Multiple entries indicate possible periods.
(^3) Peak to trough amplitude in magnitudes.
University of Oklahoma and Scott Sheppard of the Univer-
sity of Hawaii are responsible for many lightcurve measure-
ments. They find periods of rotation between 4 and 14 hours
(Table 3).
8.2 Amplitude
In Figure 6, Pholus has a maximum brightness of Vmax=
20 .09 and a minimum brightness of Vmin=20.69, i.e., each
time through its repeating pattern it has a maximum bright-
ness variation or lightcurve amplitude ofm=Vmin–
Vmax= 0 .60 magnitude. Since
m= 2 .5 log
Fmax
Fmin
,
the ratio of maximum to minimum brightness is Fmax/
Fmin= 1 .74. From Table 3, we see that KBOs and Cen-
taurs exhibit 0.1≤m≤1.1 magnitude.
8.3 Shape
If a KBO or Centaur lightcurve is due to the rotation of a
triaxial ellipsoid about its shortest axis, c, we can in princi-
ple determine its shape (i.e., the ratio of its axes a / b and
c/b). How? As a KBO or Centaur orbits the Sun, we ob-
serve it at different aspect angles. Aspect angle is the angle
between lines originating at the center of the body and to-
ward the Earth and the north rotational pole of the body.
Figure 7 illustrates how a change in aspect angle results in a
change in lightcurve amplitude. At point A, we are looking
at the object equator-on (aspect angle of 90◦), and we see a
lightcurve with an amplitude as large as it gets for the ob-
ject. A quarter of a revolution about the Sun later, at point
B, we are looking down the rotation axis of the body (aspect
angle of 0◦), and we won’t see any brightness variation. If we
FIGURE 6 Lightcurve for the Centaur Pholus. The brightness
pattern of two nearly equal brightness maxima and two
brightness minima (at∼0hrand∼5 hr) that differ by 0.03
magnitude (3%) repeats every 9.980 hr. The maximum
peak-to-trough brightness variation of Pholus is 0.60 magnitude.
From the lightcurve, we know that Pholus rotates once about its
axis every 9.980 hr.