4 Encyclopedia of the Solar System
TABLE 1 Orbits of the Planets and Dwarf PlanetsaPeriod
Name Semimajor Axis (AU) Eccentricity Inclination (◦) (years)Mercury 0.38710 0.205631 7.0049 0.2408
Venus 0.72333 0.006773 3.3947 0.6152
Earth 1.00000 0.016710 0.0000 1.0000
Mars 1.52366 0.093412 1.8506 1.8808
Ceresb 2.7665 0.078375 10.5834 4.601
Jupiter 5.20336 0.048393 1.3053 11.862
Saturn 9.53707 0.054151 2.4845 29.457
Uranus 19.1913 0.047168 0.7699 84.018
Neptune 30.0690 0.008586 1.7692 164.78
Plutob 39.4817 0.248808 17.1417 248.4
Eris (2003 UB 313 )b 68.1461 0.432439 43.7408 562.55aJ2000, Epoch: January 1, 2000.
bDwarf planet.central body, and the conservation of angular momentum
and energy. Parameters for the orbits of the eight planets
and three dwarf planets are listed in Table 1.
Because the planets themselves have finite masses, they
exert small gravitational tugs on one another, which cause
their orbits to depart from perfect ellipses. The major ef-
fects of these long-term or “secular” perturbations are to
cause theperihelionpoint of each orbit to precess (rotate
counterclockwise) in space, and the line of nodes (the inter-
section between the planet’s orbital plane and the ecliptic
plane) of each orbit to regress (rotate clockwise). Additional
effects include slow oscillations in theeccentricityand
inclinationof each orbit, and the inclination of the planet’s
rotation pole to the planet’s orbit plane (called the obliq-
uity). For the Earth, these orbital oscillations have peri-
ods of 19,000 to 100,000 years. They have been identified
with long-term variations in the Earth’s climate, known as
Milankovitch cycles, though the linking physical mechanism
is not well understood.
Relativistic effects also play a small but detectable role.
They are most evident in the precession of the perihelion of
the orbit of Mercury, the planet deepest in the Sun’s grav-
itational potential well. General relativity adds 43 arcsec/
century to the precession rate of Mercury’s orbit, which is
574 arcsec/century. Prior to Einstein’s theory of general rel-
ativity in 1916, it was thought that the excess in the preces-
sion rate of Mercury was due to a planet orbiting interior to
it. This hypothetical planet was given the name Vulcan, and
extensive searches were conducted for it, primarily during
solar eclipses. No planet was detected.
A more successful search for a new planet occurred in
- Two celestial mechanicians, U. J. J. Leverrier and
J. C. Adams, independently used the observed deviations
of Uranus from its predicted orbit to successfully predict
the existence and position of Neptune. Neptune was found
by J. G. Galle on September 23, 1846, using Leverrier’s
prediction.
More complex dynamical interactions are also possible,
in particular when the orbital period of one body is a small-
integer ratio of another’s orbital period. This is known as
a mean-motion resonance and can have dramatic effects.
For example, Pluto is locked in a 2:3 mean-motion reso-
nance with Neptune, and although the orbits of the two
bodies cross in space, the resonance prevents them from
ever coming within 14 AU of each other. Also, when two
bodies have identical perihelion precession rates or nodal
regression rates, they are said to be in a secular resonance,
and similarly interesting dynamical effects can result. In
many cases, mean-motion and secular resonances can lead
to chaotic motion, driving a body onto a planet-crossing or-
bit, which will then lead to its being dynamically scattered
among the planets, and eventually either ejected from the
solar system or impacted on the Sun or a planet. In other
cases, such as Pluto and some asteroids, the mean-motion
resonance is actually a stabilizing factor for the orbit.
Chaos has become a very exciting topic in solar system
dynamics in the past 25 years and has been able to explain
many features of the planetary system that were not pre-
viously understood. It should be noted that the dynami-
cal definition of chaos is not always the same as the gen-
eral dictionary definition. In celestial mechanics, the term
“chaos” is applied to describe systems that are not perfectly
predictable over time. That is, small variations in the ini-
tial conditions, or the inability to specify the initial condi-
tions precisely, will lead to a growing error in predictions
of the long-term behavior of the system. If the error grows