Definition of eccentricity in NORAD's 2-line elements

From: Ted Molczan (molczan@home.com)
Date: Fri Jun 30 2000 - 09:24:12 PDT

  • Next message: Alan Pickup: "Decay watch: 2000 Jun 30"

    I have learned that the eccentricity in NORAD's 2-line elements does not
    correspond to the epoch and argument of perigee of the elements. It is a mean
    value, corresponding to argument of perigee of zero.
    
    Background
    
    Earth's oblateness significantly perturbs the eccentricity of an orbit, as a
    strong function of orbital inclination and argument of perigee. The oblateness
    also causes the line of apsides (long axis of the orbit) to rotate, as a strong
    function of inclination. The combined effect is a long-term periodic variation
    of both eccentricity and argument of perigee.
    
    The practical effect of the oscillation in eccentricity is to cause the perigee
    distance to oscillate by as much as 15 km (for a quasi-polar orbit) during one
    rotation of the line of apsides; perigee will be closest when the argument of
    perigee is 90 deg, and furthest when argument of perigee is 270 deg.
    
    This variation is large enough to have a significant effect on the rate of
    orbital decay of orbits having low perigee heights.
    
    Until recently, I had never paid much attention to the exact definition of the
    eccentricity in NORAD's "2-line" elements. I had always assumed that the
    eccentricity corresponds to the epoch of the elements. I was forced to question
    this assumption when I could not see the expected long-term sinusoidal
    oscillation.
    
    
    Mystery Solved
    
    Examination of the SGP series of orbital models which underlie the 2-line
    elements cleared up the mystery.
    
    I learned that NORAD's 2-line elements state the eccentricity as though the
    argument of perigee were zero, i.e. as though the perigee were at the ascending
    node (i.e. over the equator, northbound)). The long-term periodic effects of
    Earth's oblateness are added by the SGP orbital models.
    
    As a result, anyone who needs the correct eccentricity at the epoch of the
    elements, will have to compute it separately. Programmers working with the SGP
    models can obtain the correct value as an output from those calculations.
    
    Ted Molczan
    
    
    
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