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Orbital elements

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The orbital elements of an orbit are the set of parameters needed to specify that orbit uniquely, given a model of two ideal masses obeying the Newtonian laws of motion and the inverse square law of gravitational attraction. Because there are multiple ways of defining a motion, depending on which set of variable you choose to measure, there are several different ways of defining sets of orbital elements, each of which will define the same orbit.

There are seven degrees of freedom in this model (time, position in 3-space at that time, velocity in 3-space at that time) so all sets of orbital elements have seven parameters.

The traditionally used set of orbital elements is called the set of Keplerian elements, after Johannes Kepler, the discoverer of Kepler's laws. The Keplerian elements are:

Other orbital parameters, such as the semi-major axis, can then be calculated from the Keplerian elements.

Because the simple Newtonian model of orbital motion of idealized points in free space is not exact, the orbital elements of the orbits of real objects tend to change over time. This can often be approximated to a first approximation by adding an eighth parameter, "drag", to the Keplerian elements.

These parameters can be encoded as text in a number of formats.

The most common format is the NASA/NORAD "two-line elements" (TLE) format, originally designed for use with 80-column punched cards, but still in use because it is the most common format, and works as well as any other.


  • Explanatory Supplement to the Astronomical Almanac. 1992. K. P. Seidelmann, Ed., University Science Books, Mill Valley, California.

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