632 Encyclopedia of the Solar System
3. Dynamics and Evolution
3.1 Gravity and Keplerian Orbits
In the planetary system, solar gravitation determines the or-
bits of all bodies larger than dust particles for which other
forces become important. But even for dust, gravity is an
important factor. Near planets, planetary gravitation takes
over. However, the basic orbital characteristics remain the
same. Two types of orbits are possible: bound and unbound
orbits around the central body. Circular and elliptical orbits
are bound to the Sun; the planets exert only small distur-
bances to these orbits. Planets, asteroids, and comets move
on such orbits. Objects on unbound orbits will eventually
leave the solar system. Typically, interstellar dust particles
move on unbound, hyperbolic orbits through the solar sys-
tem. Similarly, interplanetary particles are unbound to any
planetary system and traverse it on hyperbolic orbits with
respect to the planet. [SeeSolarSystemDynamics.]
A Keplerian orbit is a conic section that is characterized
by its semimajor axisa, eccentricitye, and inclinationi. The
Sun (or a planet) is in one focus. Theperiheliondistance
(closest to the Sun) is given byq=a(1−e). Circular orbits
have eccentricitye=0, elliptical orbits have 0<e<1, and
hyperbolic orbits havee>1 andais taken negative. The
apheliondistances (furthest from the Sun) are finite only
for circular and elliptical orbits. The inclination is the angle
between the orbit plane and the ecliptic (i.e., the orbit plane
of Earth).
Dust particles in interplanetary space move on very dif-
ferent orbits, and several classes of orbits with similar char-
acteristics have been identified. One class of meteoroids
moves on orbits that are similar to those of asteroids, which
peak in the Asteroid Belt. Another class of orbits that rep-
resents the majority of zodiacal light particles has a strong
concentration toward the Sun. Both orbit populations have
low to intermediate eccentricities (0<e< 0 .6) and low
inclinations (i< 40 ◦). These asteroidal and zodiacal core
populations satisfactorily describe meteors, the lunar crater
size distribution, and a major portion of zodiacal light ob-
servations. Also, spacecraft measurements inside 2 AU are
well represented by the core population. [SeeMain-Belt
Asteroids.]
3.2 Radiation Pressure and the Poynting–Robertson
Effect
Electromagnetic radiation from the Sun (most intensity is
in the visible wavelength range atλmax= 0. 5 μm) being
absorbed, scattered, or diffracted by any particulate ex-
erts pressure on this particle. Because solar radiation is
directed outward from the Sun, radiation pressure is also
directed away from the Sun. Thus, gravitational attraction
is reduced by the radiation pressure force. Both radiation
pressure and gravitational forces have an inverse square
FIGURE 11 Ratioβof the radiation pressure force over solar
gravity as a function of particle radius. Values are given for
particles made of astronomical silicates (from Gustafson et al.,
2001) in various shapes: sphere (solid curve), long cylinders
(dashes), and flat plates (dots).dependence on the distance from the Sun. Radiation pres-
sure depends on the cross section of the particle and grav-
ity on the mass; therefore, for the same particle, the ratio
βof radiation pressure,FR, over gravitational force,FG,is
constant everywhere in the solar system and depends only
on particle properties:β=FR/FG∼Qpr/sρ, whereQpris
the efficiency factor for radiation pressure,sis the particle
radius, andρis its density.
Figure 11 shows the dependence ofβon the particle size
for different shapes. For big particles (sλmax), radiation
pressure force is proportional to the geometric cross section
giving rise to the 1/s-dependence ofβ. At particle sizes
comparable to the wavelength of sunlight s≈λmax,β-values
peak and decline for smaller particles as their interaction
with light decreases.
A consequence of the radiation pressure force is that
particles withβ>1 are not attracted by the Sun but rather
are repelled by it. If such particles are generated in inter-
planetary space either by a collision or by release from a
comet, they are expelled from the solar system on hyper-
bolic orbits. But even particles withβvalues smaller than
1 will leave the solar system on hyperbolic orbits if their
speed at formation is high enough so that the reduced solar
attraction can no longer keep the particle on a bound orbit.
If a particle that is released from a parent body moving on a
circular orbit hasβ>^1 / 2 , then it will leave on a hyperbolic
orbit. These particles are termedbeta-meteoroids.
Because of the finite speed of light (c≈300,000 km/s)
radiation pressure does not act perfectly radial but has an
aberration in the direction of motion of the particle around
the Sun. Thus, a small component (approximately propor-
tional tov/c, wherevis the speed of the particle) of the ra-
diation pressure force always acts against the orbital motion