The keplerian osculating elements

The keplerian osculating elements in the current time locate the orbit and satellite position in the geocentric inertial frame GEI .

It is possible to use various sets of the Keplerian elements. The tradition of IKI is to use the set as follows:

Date and universal time (UT)
Semi-major axis                       a 
Eccentricity                          e
Inclination                           i 
Right ascension of the ascending node  
Perigee argument                      
Latitude argument                     u 

Instead of the Semi-major axis and Eccentricity it is possible to use alternative parameters:

• Apogee geocentric distance Ra, or hight above the Earth's reference elipsoid Ha.
• Perigee geocentric distance Rp, or hight above the Earth's reference elipsoid Hp.

The connections between these parameters are as follows:

a = (Rp + Ra)/2, e = (Ra - Rp) /2a

The inclination is the orbit plane inclination to the Earth's equatorial plane (corresponding to the used GEI frame).

The nodes line is the intersection line of the orbit plane and the Earth's equatorial plane.

The ascending node is the point of the nodes line, where satellite transfers the equatorial plane from the south hemisphere to the north one.

The right ascension of the ascending node is the angular location of one relative to the X GEI axis. This angle is measured along the Earth's equator from the spring equinox (counter-clockwise from the North pole view point).

The perigee argument locats the perigee on the orbit plane relative to the ascending node. This angle is measured along the orbit (counter-clockwise from the North orbit's pole view point).

The latitude argument locats the satellite current position on the orbit plane relative to the ascending node. This angle is measured along the orbit (counter-clockwise from the North orbit's pole view point).

Dr. Victoria Prokhorenko vprokhor@iki.rssi.ru
Space Research Institute (IKI)
Russian Academy of Sciences
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Last updated 16 April 98