Orbital Description

Keplerian elements describe an orbit's physical attributes.  Satellites orbit the Earth in elliptical path's with the center of the Earth at one of the ellipse's [mathematical] focus points. The position in the orbit closest to the Earth is called perigee; the position in the orbit furthest from the Earth is called apogee

Elliptical Orbit Image

apogee - highest altitude

perigee - lowest altitide

eccen. - orbit's deviation from a circle (shape)

Orbital Size and Shape

The Keplerian elements that describe the orbit's size and shape are the semi- major axis and the eccentricity

The semi major axis describes the size of the ellipse. Semi-major axis is one half the longest distance across the ellipse (or one half the distance between apogee and perigee).  By Kepler's third law of planetary motion, you can compute the orbital period (the time it takes to make one complete orbit) from the semi major axis.  The mean motion (or orbital frequency) is the reciprocal of the period. The commonly available Keplerian elements use mean motion.

Eccentricity is shape of the ellipse.  Eccentricity is computed as the linear eccentricity (the distance from the center of the ellipse to the center of the Earth) divided by the semi major axis. A zero eccentricity describes a circular orbit; an eccentricity approaching one describes a highly elliptical orbit.

semi-major axis is half the longest distance across the ellipse

period is the time to make one orbit

mean motion is the frequency (revs per day)

Keplerian Elements

Orbital Orientation

The remaining four orbital elements orient the orbit with respect to the Earth.

The plane of the orbital ellipse is oriented by two angles: the inclination and the right ascension of the ascending node

Inclination describes the orbital plane's tilt angle with respect to the equator. Inclination also specifies the highest latitudes (North and South) over which the satellite directly overflies.  A zero inclination describes an equatorial orbit; a 90 degree inclination describes a polar orbit. Inclinations greater than 90 degrees describe orbits that move against Earth rotation (called retrograde).

An orbit's ascending node is its South-to-North equatorial crossing. The right ascension of the ascending node is the angle measured eastward from the Vernal Equinox to the ascending node.  The Vernal Equinox is the Sun's apparent ascending node (marking the beginning of the Northern hemisphere's spring.

Argument of perigee is the angle measured in the direction of satellite motion from the ascending node to perigee.

True anomaly is the angle measured in the direction of motion from perigee to the satellite's position at some defined epoch timeMean anomaly describes what the satellite's true anomaly would be if it were in a circular orbit.  You can compute mean anomaly from the orbit's true anomaly and eccentricity. The commonly available Keplerian elements use mean anomaly.

The Celestial and Orbital Mechanics Web Site is a good reference for orbital mathematics and related software, including source code.


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Ascending node is the satellite's South to North equatorial crossing

Inclination is the orbital plane's tilt

Right ascension of node is the angle from the Vernal equinox to the ascending node

argument of perigee is the angle between the acsending node and perigee

true anomaly - angle from perigee to the satellite