Encyclopedia of the Solar System 2nd ed

294 Encyclopedia of the Solar System

Some near-Earth objects’ shapes have been interpreted
as being two bodies stuck together and are referred to as a
contact binary. This interpretation is intriguing because it
leads to speculation that the two components were brought
together in a low-velocity collision and just stuck together
instead of one or both being destroyed. An alternative
interpretation is that the asteroid is so irregularly shaped
that it appears to be two pieces, but really is continuous.
Such a situation would imply a history of collisional frag-
mentation that kept the main body of the asteroid intact,
albeit severely altering its shape, but not disrupting it to-
tally. Measurements at different aspect angles are required
to truly confirm the interpretation that some objects are
contact binaries. About 16% of near-Earth objects larger
than 200 m in diameter may be contact binary systems ac-
cording to estimates.

5.3 Rotation Rates

Of 32 measured near-Earth objects with an average di-
ameter of 3 km, the mean rotation rate is 4.94±0.54
rev/day, whereas a sample of the same number of com-
parably sized, main-belt asteroids has a mean rotation rate
of 4.30±0.46 rev/day. Because the standard deviation of
these means overlaps, no statistical significance is placed
on these differences. The mean rotation rate of comets is
larger than the mean of the NEOs. Comets rotate on aver-
age more slowly than NEOs. The implications of different
rotation rates for the history of the object are discussed
elsewhere. [SeeAsteroids.] Because of their proximity to
Earth, NEOs are the smallest objects in space for which
we can measure their rotational properties. In some cases,
the rotation rates for NEOs smaller than about 150 m are
100 rev/day or faster (i.e., they have rotation periods of just a
few minutes). These objects are likely relatively strong and
intact rock fragments. Larger objects that spin substantially
slower, may be less strong “rubble piles” composed of in-
dividual fragments or fractured rock held together only by
gravity. A rubble pile must spin at a rate slower than once
every 2.2 hours, or else it will fly apart. Thus, near-Earth
objects give us insights into the likely range of internal struc-
tures occurring within small bodies in our solar system.

5.4 Size

For an object illuminated by the Sun alone, the sum of the
reflected and emitted (thermal) radiation from the object
(assuming no internal energy sources or sinks) is equal to
the total incident solar radiation upon it. Knowing where
the object is, in terms of its distance from the Sun and the
output of the Sun, the amount of incident energy on the ob-
ject’s surface can be calculated. By measuring the reflected
and reemitted (thermal) components of radiation, and with
some rudimentary knowledge of the nature of the body’s
surface materials determined from spectral measurements,

one can estimate its albedo and determine its diameter.

The two parameters, diameter and albedo, are derived in

tandem, with the requirement that the sum of reflected and

emitted components is equal to the incident solar flux. This

can be expressed mathematically as

πR^2 (F/r^2 )(1−A)= 4 πR^2 εσT^4

In this equation,Ris the object’s mean radius andFis the

solar flux, a constant. The distance from the Sun isr, andA

is a term called the bolometric Bond albedo. The emissivity

of the asteroid,ε, is assumed to be 1, and the parameterσis

the Stefan–Boltzmann constant. The temperature,T, is de-

rived from the radiated flux from the asteroid measured in

the thermal infrared spectral region. One can then solve for

the bolometric Bond albedo,A, which is the integrated re-

flected light at all wavelengths. Albedo and diameter are cal-

culated based on measurements of visible and infrared flux.

Another method of estimating the size of small asteroids

is from their measured brightness and an assumed albedo.

This method is referred to as a photometric diameter. It is

used when no thermal measurements and only visual mag-

nitudes are available. The diameter is given by the equation

logd= 3. 1295 − 0 .5 logpH− 0. 2 Hv

wherepH, the geometric albedo, is assumed, andHvis

the magnitude defined by the International Astronomical

Union magnitude system for asteroids in the V, or visual

bandpass. Unfortunately, the range of asteroid albedos is

large, from only a few percent up to 50% or more, produc-

ing considerable uncertainty in the photometric diameters.

However, the taxonomic type of the asteroid (see below),

determined from brightness measurements at several dif-

ferent wavelengths, can be used to narrow the range of

probable albedos. Notice that an object with a lower albedo,

reflecting the same amount of light, will be significantly

larger than a high-albedo object. For example, a 15th mag-

nitude object (on the bright end of any NEO) with an albedo

of 0.15, an average, “bright” asteroid, would have a diameter

of 3.4 km, whereas an asteroid with a 0.06 albedo, at the high

end of the range of dark asteroids, would be 1.6 [5.4/3.4=

1.588] times as large at 5.4 km. Keep in mind that the plot

showing the frequency of near-Earth objects as a function

of brightness and size (Fig. 10) provides only an estimate

of the size and frequency of objects and, except at the large

end of the magnitude scale, is an extrapolation and estimate

of the size of the complete population.

5.5 Mass

The mass of binary asteroids can be determined from

Kepler’s third law,P^2 /a^3 = 4 π^2 /G(Mp+ms), wherePis

the period of revolution,ais the semimajor axis, both ob-

served quantities.Gis the universal gravitational constant,