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Planets

Planetary Parameters

Most of the parameters used to describe the characteristics of the planets are obvious, some are obscure, and several require added explanation.

The mass of a planet is determined by deriving the orbital parameters of its natural and artificial satellites. From these studies one derives the parameter GM to very high precision, but because the determination of the gravitational constant is accurate only to 0.010% (G = 6.674(28±67)×l0−8 cm3 g−1 s−2), the derived mass of a planet also has an error of 0.010%.

Six of the planets have some flattening because of their rotation. The measure of flattening is f = ( a − b )/a, where a is the equatorial radius and b is the polar radius. The volumetric mean radius is the radius that contains the same volume as the planetary shape. For the terrestrial planets, the solid surface determines the radius of the planet, while for the giant planets, which have no observable solid surface, the atmospheric pressure of 1 bar (the pressure at sea level on Earth) determines the radius. From the mass and the volumetric mean radius, a characteristic surface gravity, escape velocity, and density can be derived.

The sidereal rotation period of a planet is the time for a single rotation relative to the coordinate system tied to the vernal equinox. For the terrestrial planets, the orientation of the surface determines the rotation period. For any giant planet, which does not have an observable surface and has an atmosphere exhibiting differential rotation, two other measures are used to derive a rotation rate: the rotation of the magnetic field, which should be tied to the interior fluid of the planet, and an inferred rotation period from the hydrostatic flattening of the planet. These two methods give similar results. A planet's obliquity to orbit, which in the case of Earth is the obliquity to the ecliptic, is the angle between the planet's rotation axis and the orbital axis. The value is between 0° and 180°.

All planetary orbits are very close to elliptical. An elliptical orbit is characterized by its semimajor axis a, which is half the maximum diameter of the ellipse, and its eccentricity e, which is a measure of the deviation from purely-circular motion. The ratio of the semiminor axis b to the semimajor axis a is given by b/a = ( 1 − e2 )1/2. The position of the center of mass of the planet-Sun system is at the position ea from the center of the ellipse. The sidereal orbital period for a planet is measured relative to distant quasars rather than to the first point of Aries.

A planetary solar constant can be defined for each planet. This is the average solar power per unit area that a planet receives over an orbit. The use of the term solar constant without reference to a planet means the planetary solar constant for Earth.

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