Re: Geodetic precision

From: Bruno Tilgner (
Date: Sat Aug 18 2001 - 08:41:42 PDT

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    WGS and NORAD models
    Orbital elements per se are not in any way referenced to a geodetic
    datum, they are referred to an inertial reference frame. However,
    TLEs are not classical orbital elements. They are massaged in a
    special and undocumented way to give the best possible results
    over a certain time span with the NORAD models. This becomes clear
    by inspecting the code which begins by recovering the original
    mean motion and semi-major axis.
    This reconstitution of two variables (which in fact are not independent
    of each other) involves the WGS72 values of the Earth's equatorial
    radius and angular velocity. If one changed this to WGS84 one would
    probably introduce an error and not recover the original mean motion
    and semi-major axis.
    The NORAD models give the position of a satellite in an earth-centered
    inertial reference system in units of earth radii. The algorithm uses
    the J2, J3 and J4 spherical harmonics of the gravitational field. It
    is at this point where it could make sense to use their WGS84 values.
    I have made a test of SGP4 with all WGS72 constants replaced by their
    WGS84 values. The position of a satellite, expressed in units of Earth
    radii, changes in the 7th decimal place only. This is in the 100 m
    range. I recall having read that the intrinsic accuracy of the TLEs
    at epoch is in the order of 500 m. The error introduced by using WGS72
    instead of WGS84 is smaller than that, so in summary, it does not seem
    useful to replace WGS72 constants by those of WGS84 which are very close
    to each other anyway. There are far more important sources of error
    elsewhere in the algorithms, notably in the atmospheric density model.
    I'd appreciate any comments.
    Bruno Tilgner
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