5.5 Orbital Elements of Satellite

5.5 Orbital Elements of Satellite

A set of numerical values to define an orbit of a satellite or planet are called orbital elements. The independent orbital elements of the earth observation satellite are six elements of the Keplerian orbit.

A satellite can be considered to rotate around the earth in a plane, called the orbital plane, because the influence of gravity of the moon and the sun can be neglected as compared with the gravity of the earth.

A point in space can be expressed in the equatorial coordinate system as follows. The origin of equatorial coordinate system is the center of the earth.

The reference great circle : the equatorial plane
The origin of astronomical longitude (right ascension) : the vernal equinox
The astronomical longitude (right ascension) : 0 - 24 hours to the east from the vernal equinox
The astronomical latitude (declination) : angle from the equatorial plane ( +90 degree in the north pole ; -90 degree in the south pole)
The six elements of Keplerian orbit are ;
(1) The semi-major axis (A):
(2) Eccentricity of orbit (e) :
(3) Inclination angle (i) :
(4) Right ascension of ascending node (h)
(5) Argument of perigee (g)
(6) Time of passage of the perigee ( )

Figure 5.5.1 shows the above elements. The shape and size of an orbit can be defined by A and e, while the orbit plane can be defined by i and h. The longer axis of the orbit ellipse can be determined by g. The position of a satellite can be located by T.

Sometime the orbital elements are replaced by three dimensional geocentric coordinates and velocity for numerical analysis instead of the elements of the the Keplerian orbit.

Table 5.5.1 shows the relationship between the elements of the Keplerian orbit and the geocentric coordinates and velocity.