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Orbital elements

    The elements of an orbit are the 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. (See also: orbital state vectors).

    Keplerian elements

    The traditionally used set of orbital elements is called the set of Keplerian elements, after Johannes Kepler and his Kepler's laws. The Keplerian elements are:
    Keplerian elements can be obtained from orbital state vectors using VEC2TLE software or by some direct computations.
    Other orbital parameters, such as the semi-major axis, can then be calculated from the Keplerian elements. In many cases, the semi-major axis is used as an orbital element instead of period. The elements can be seen as defining the orbit by degrees:
    • The semi-major axis (or the period, interchangeably) fixes the size of the orbit.
    • The eccentricity fixes its shape.
    • The inclination (orange in Fig. 2) and longitude of the ascending node (green) fix its plane.
    • The argument of perihelion (blue) orients the orbit within its plane.
    • The epoch (or mean anomaly, interchangeably) (red) fixes the object in time on its orbit.

    Because the simple Newtonian model of orbital motion of idealized points in free space is not exact, the orbital elements of real objects tend to change over time. For artificial satellites grazing the fringes of the atmosphere, an eighth parameter (" drag") may be added. For the planets and moons it is more usual simply to add a time term to the elements.

    Two line elements

    Keplerian elements parameters can be encoded as text in a number of formats. The most common of them 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.
    Line 1Column Characters Description-----  ---------- -----------1        1       Line No. Identification
    3        5       Catalog No.
    8        1       Security Classification
    10        8       International Identification19       14       YRDOY.FODddddd34        1       Sign of first time derivative35        9       1st Time Derative45        1       Sign of 2nd Time Derivative46        5       2nd Time Derivative51        1       Sign of 2nd Time Derivative Exponent52        1       Exponent of 2nd Time Derivative54        1       Sign of Bstar/Drag Term55        5       Bstar/Drag Term60        1       Sign of Exponent of Bstar/Drag Term61        1       Exponent of Bstar/Drag Term63        1       Ephemeris Type65        4       Element Number69        1       Check Sum, Modulo 10
    Line 2Column Characters Description----- ---------- -----------1 1 Line No. Identification 3 5 Catalog No. 9 8 Inclination 18 8 Right Ascension of Ascending Node27 7 Eccentricity with assumed leading decimal35 8 Argument of the Perigee44 8 Mean Anomaly53 11 Revolutions per Day (Mean Motion)64 5 Revolution Number at Epoch69 1 Check Sum Modulo 10

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

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