Encyclopedia of the Solar System 2nd ed

608 Encyclopedia of the Solar System

interconnections between the classes. A thorough discus-
sion of KBO dynamics can be found in the chapter by
Harold Levison in this volume. [SeeComet Populations
and Cometary Dynamics.]
Classical KBOs are on orbits with perihelion distances,
q, larger than 40 AU, semimajor axes, a, between 42 and
45 AU, eccentricities, e, less than 0.1, and inclination angles,
i, less than 10◦. It appears that classical KBOs did not ex-
perience strong perturbations by Neptune and hence they
probably formed at or near their present location.
Resonant KBOs are a subset of classical KBOs that be-
came trapped in mean motion resonances during the pri-
mordial migration of the planets. The process of resonance
trapping tends to increase theeccentricityand inclination
of trapped objects. Plutinos are objects trapped in the 2:3
mean motion resonance of Neptune at a=39.6 AU, just
like Pluto.
Scattered disk objects (SDOs) are thought to have orig-
inated in the primordial inner belt, a<40 AU, and the pri-
mordial Uranus-Neptune region. They were subsequently
scattered by Neptune onto orbits with large inclination an-
gles, i> 15 ◦, large eccentricities, e>0.3, and large semi-
major axes, a>45 AU.
Centaur objects are on outer planet crossing orbits with
q>5.2 AU and a<30.1 AU. Relatively recent gravita-
tional interactions between SDOs and Neptune, and to a
lesser extent between classical KBOs and Neptune, result
in Centaur objects. Because Centaur objects cross the or-
bits of the outer planets, they are dynamically unstable and
have mean lifetimes of∼ 106 years. As mentioned above,
some Centaurs evolve into Jupiter-family comets, others
are ejected from the Solar System, and yet others impact
the giant planets. In addition, some Jupiter-family comets
evolve back into Centaurs.

5. Brightness

5.1 Apparent Magnitude

The first physical property measured for a KBO is typically
its brightness. A KBO is brightest in visible light (4000–
8000 A) by virtue of the sunlight it reflects toward the Earth. ̊
It is possible to isolate the brightness of a KBO in a partic-
ular bandpass by placing a colored glass filter in front of a
CCD camera at the focal plane of a telescope. For exam-
ple, a blue, green, or red filter in front of a CCD camera
makes it possible to measure the brightness of blue, green,
or red light from a KBO,i.e., its B (λcenter= 4500 A), V ̊
(λcenter= 5500 A), or R ( ̊ λcenter= 6500 A) magnitudes. Ta- ̊
ble 2 lists V magnitudes of the brightest KBOs. At the other
extreme of brightness, Gary Bernstein used the Hubble
Space Telescope (HST) to discover and measure the bright-
ness of the faintest known KBO, V∼28. The Centaur in
Figure 3, 1994 TA, has V=24.31±0.05. For comparison,

the Sun has V=− 26 .74 and the faintest star visible in the

sky with the unaided eye has V∼6.

5.2 Luminosity Function

There are many more faint KBOs than bright KBOs. Fig-

ure 4 comes from KBO discoveries made by a number of

surveys, and shows the number of KBOs per unit magni-

tude per square degree on the sky near theeclipticplane

as a function of brightness (R-band magnitude), a luminos-

ity function. Surveys find∼100 KBOs with 27<R<28,

∼2 KBOs with 23<R<24, and only∼0.001 KBOs with

19 <R<20, all per square degree of sky. For reference,

the full Moon occupies∼one-quarter of a square degree

of sky and the Sun has R=− 27 .10.

5.3 Absolute Magnitude

The apparent magnitude of a KBO or Centaur depends

on its heliocentric distance, r, and geocentric distance,,

in AU. For example, a KBO receding from the Sun and

Earth will become fainter and its apparent magnitude will

become larger in value. The absolute magnitude, H, of a

KBO is a way to compare theintrinsicbrightness of one

KBO with another KBO and it does not depend on distance.

The absolute magnitude of the same KBO receding from

the Sun and Earth will not change. The absolute magnitude

of a KBO is the brightness it would have if it were located at a

distance of 1 AU from the Sun and 1 AU from the Earth, and

had a Sun-KBO-Earth (phase) angle,α,of0◦. The relation

FIGURE 4 Number of KBOs per unit magnitude interval per

square degree of sky vs. R-band magnitude. There are many

more faint KBOs than bright KBOs. This is typical of small body

populations in the Solar System that have been collisionally

processed. (Courtesy of Gary Bernstein)