Mathematical Fact Sheet
Notes on the Fact Sheets
Most values listed in the factsheets are from the following sources:
- Astronomical Almanac, 2000, 2001
- Global Earth Physics, American Geophysical Union, 1995
- Astrophysical Quantities, C.W. Allen, 1981, 2000
Bulk Parameters
Mass (1024 kg) Mass of the body in 10^24 kilograms
Volume (1010 km3) Volume of the body in 10^10 km^3
Equatorial radius (km) Radius of the body at the equator in kilometers
Polar radius (km) Radius of the body at the poles in kilometers
Volumetric mean radius (km) Radius of a sphere with the same volume as the body
Core radius (km) Radius of the planet core in kilometers
Ellipticity (Flattening) The ratio (equatorial - polar radius)/(equatorial radius),
dimensionless
Mean density (kg/m3) Average density of the body (mass/volume)
in kilograms/(meter^3)
Surface gravity (m/s2) Equatorial gravitational acceleration at the
surface of the body or the 1 bar level, not including
the effects of rotation, in meters/(second^2)
Surface acceleration (m/s2) Effective equatorial gravitational acceleration
at the surface of the body or the 1 bar level,
including the effects of rotation, in meters/(second^2)
Escape velocity (km/s) Initial velocity required to escape the body's
gravitational pull in kilometers/second
GM (x 106 km3/s2) Gravitational constant times the mass of the body
in 10^6 kilometers^3/seconds^2
Visual geometric albedo The ratio of the body's brightness at a phase angle of
zero to the brightness of a perfectly diffusing disk
with the same position and apparent size, dimensionless.
Bond albedo The fraction of incident solar radiation reflected back
into space without absorption, dimensionless.
Also called planetary albedo.
Visual magnitude V(1,0) The visual magnitude of the body if it were one AU
(1.496 x 10^8 kilometers) from the Earth at a phase
angle of zero, dimensionless.
Solar irradiance (W/m2) Solar energy on the body in Watts/(meter^2)
Black-body temperature (K) Equivalent black body temperature is the surface
temperature the body would have if it were in
radiative equilibrium and had no atmosphere,
but the same albedo, in Kelvin.
Topographic range (km) Difference in elevation between the highest and lowest
points on the planet's surface, in kilometers.
Moment of inertia (I/MR2) The moment of inertia of the body expressed as
the rotational inertia divided by the body's (mass
x radius^2). A hollow spherical shell has a moment of inertia
of 2/3, a homogeneous sphere 0.4
J2 (x 10-6) The ratio of the difference in the moments of inertia
to the mass of the body times the radius^2,
(C-A)/(M R^2), x 10^-6, dimensionless
Number of natural satellites The number of moons orbiting the planet, as certified by the IAU
Absolute magnitude (Comets) The magnitude of the comet at 1 AU for Y = 10, where Y is the
photometric parameter giving the observed dependence of the
magnitude on heliocentric distance, also designated H(10).
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Orbital parameters
Instantaneous values referenced for Julian Date 2451800.5 (13 September 2000)
[Astronomical Almanac 2000, p. E3]
Semimajor axis (106 km) Mean distance from the Sun (or other central body in the
case of satellites) from center to center in 10^6 kilometers
Sidereal orbit period (days) The time it takes the body to make one revolution about
the Sun relative to the fixed stars in days.
Tropical orbit period (days) The average time for the body to make one revolution
about the Sun from one point in its seasonal orbit to
the equivalent point (e.g. equinox to equinox) in days.
For Earth, this equals exactly 1 year.
Synodic period (days) The time interval between similar configurations in the
orbit (e.g. opposition) of the body and Earth, in days.
Perihelion (106 km) The point in a body's orbit closest to the
Sun, in 10^6 kilometers.
Aphelion (106 km) The point in a body's orbit furthest from
the Sun, in 10^6 kilometers.
Mean orbital velocity (km/s) The average speed of the body in orbit,
in kilometers/second.
Max. orbital velocity (km/s) Maximum orbital velocity, at perihelion,
in kilometers/second.
Min. orbital velocity (km/s) Minimum orbital velocity, at aphelion,
in kilometers/second.
Orbit inclination (deg) The inclination of the orbit to the ecliptic, in degrees.
For satellites, this is with respect to the planet's equator.
Orbit eccentricity A measure of the circularity of the orbit, equal to
(aphelion - perihelion distance)/(2 x semi-major axis).
For the Galilean satellites, the forced eccentricity is given.
For a circular orbit eccentricity = 0. Dimensionless.
Sidereal rotation period (hrs) The time for one rotation of the body on its axis
relative to the fixed stars, in hours. A minus sign
indicates retrograde rotation.
Length of day (hrs) The average time in hours for the Sun to move from the
noon position in the sky at a point on the equator back
to the same position, on Earth this defines a 24 hour day.
Obliquity to orbit (deg) The tilt of the body's equator relative to the body's
orbital plane, in degrees.
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Mean orbital elements
250-year least squares fit elements referenced to J2000 (Global Earth Physics, p. 14)
Longitude The point in a body's orbit around the Sun, defined from
0 to 360 degrees. The 0 point of longitude is defined as
the first point of Aries. This is the position of the Sun
as seen from Earth at Earth's vernal equinox, so at the
vernal equinox the Earth is at a longitude of 180 degrees.
Longitude of ascending node (deg) The longitude in a body's orbit at which it crosses
the ecliptic plane with increasing latitude (i.e.
crosses the ecliptic from south to north).
Longitude of perihelion (deg) The longitude in a body's orbit at which it reaches
the point closest to the Sun.
Mean longitude (deg) The longitude a body was at in its orbit at 12:00
Universal (Greenwich) Time on January 1, 2000,
also known as J2000 or Julian Day 2451545.0
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Atmospheres
Surface Pressure: Atmospheric pressure at the surface, in bars, millibars
(mb = 10^-3 bar), or picobars (10^-12 bar).
Surface Density: Atmospheric density at the surface in kilograms/meters^3.
Scale height: The height interval in which the atmospheric pressure changes by a
factor of e = 2.7183
Average temperature: Mean temperature of the body over the entire surface in Kelvin.
Diurnal temperature range: Temperature range over an average day in Kelvin.
Wind speeds: Near surface wind speeds in meters/second
Atmospheric composition: Relative composition by volume of gasses in the atmosphere.
Mean molecular weight: Average molecular weight of the atmospheric constituents in
grams/mole
Atmospheric composition (by volume): Relative volume of constituents in the atmosphere,
by percentage or ppm (parts per million).
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Related Definitions
Astronomical Unit (AU) - The mean distance from the Sun to the Earth = 149,597,900 km.
Bar - A measure of pressure or stress. 1 bar = 10^5 Pascal (Pa) = 10^5 kg m^-1 s^-2
Ecliptic - An imaginary plane defined by the Earth's orbit.
Equinox - The point in a body's orbit when the sub-solar point is exactly on the equator.
Gravitational Constant - Relates gravitational force to mass,
= 6.6726 x 10^-11 meters^3 kilograms^-1 seconds^-2
Opposition - An orbital configuration in which two bodies are on exact opposite sides of
the Sun or are on the same side of the Sun forming a line with the Sun
(neglecting inclination)
Phase Angle - The angle between the Earth and Sun as seen from the body.
Sub- and Superscripts
If some of the numbers or units on the fact sheets look a little strange, it may be that the browser you are using doesn't support sub- and superscripts. Such browsers include versions of Netscape and Mosaic below 2.0. On your browser, the number formatted to look like 10 to the minus 15 power (10 followed by a superscripted -15) looks like 10-15. If "10-15" looks like "10-15" to you, you will have trouble reading parts of the factsheets. In the explanation of units, we've included a description of the units in the form where, for example, 10^24 equals 10 to the 24 power.
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