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. (

- Epoch (time)
- Inclination ($i,!$)
- Longitude of the ascending node (☊)
- Argument of periapsis ($omega,!$)
- Eccentricity ($e,!$)
- Orbital period ($T,!$)
- Mean longitude (Mean anomaly ($M,!$) at epoch)

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.

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.

- Ephemeris
- Orbital state vectors
- VEC2TLE software

- Keplerian Elements tutorial
- another tutorial
- Spacetrack Report No. 3, a really serious treatment of orbital elements from NORAD (in pdf format)
- Celestrak Two-Line Elements FAQ