Encyclopedia of the Solar System 2nd ed

Kuiper Belt: Dynamics 597

FIGURE 6 The inclination of the classical

Kuiper Belt objects as a function of their

absolute magnitude. The horizontal dashed line

ati= 4 ◦separates the cold from the hot

population. The vertical dotted line is plotted at

H= 5 .5. The distribution on the left side of the

dotted line is clearly different from that on the

right-hand side. The largest classical objects are

all in the hot population.

are actuallycausedby the different inclinations. For ex-
ample, it has been suggested that the higher average im-
pact velocities of the high inclination objects could cause
large-scale resurfacing by fresh water ice and carbonaceous
materials, which could be gray in color. However, a similar
color-inclination trend should be observed also among the
plutinos and the scattered disk objects, which is not the case.
A careful analysis shows that there is no clear correlation
between average impact velocity and color.
In summary, the significant color and size differences
between the hot and cold classical objects imply that these
two populations are physically different in addition to being
dynamically distinct.

5. Size Distribution of the Trans-Neptunian

Population and Total Mass

As briefly described in Section 1, the disk out of which the
planetary system accreted was created as a result of the
Sun shedding angular momentum as it formed. As the Sun
condensed from a molecular cloud, it left behind a disk of
material (mostly gas with a little bit of dust) that contained
a small fraction of the total mass but most of the angular
momentum of the system. It is believed that the initial solid
objects in the protoplanetary disk were pebble-sized, of the
order of centimeters in size. These objects formed larger
objects through a process of accretion to form asteroids and
comets, which in turn accreted to form planets (or the cores
of the giant planets which then accreted gas directly from
the solar nebula). Understanding this process is one of the
main goals of astronomy today.

There are few clues in our planetary system about this

process. We know that the planets formed, and we know

how big they are. Unfortunately, the planets have been so

altered by internal and external processes that they preserve

almost no record of their formation process. Luckily, we also

have the Asteroid Belt, the Kuiper Belt, and the scattered

disk. These structures contain the best clues to the planet

formation process because they are regions where the pro-

cess started, but for some reason, did not run to completion

(i.e., a large planet). Thus, the size distribution of objects

in these regions may show us how the processes progressed

with time and (hopefully) what stopped them. The Kuiper

Belt and the scattered disk are perhaps the best places to

learn about the accretion process.

Because the size of the object is not a quantity that can

be easily measured (one needs to make hypotheses on the

intrinsic reflectivity of the objects, or albedo), and the ab-

solute magnitude is readily obtained from the observations,

astronomers generally prefer the absolute magnitude dis-

tribution, instead of the size distribution. The magnitude

distribution is usually given in the form

LogN(<H)∝Ha,a> 0

where N is the cumulative number of objects brighter

than absolute magnitudeH. The slope of this distribution,

a, contains important clues about the physical strengths,

masses, and orbits of the objects involved in the accretion

process.

For example, there are two extremes to the accretion

process. If two large, strong objects collide at low veloci-

ties, then the amount of kinetic energy in the collision is