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*Subject*: Re: [amsat-bb] G3RUH Plan13*From*: Phil Karn <karn@xxxxxxxx>*Date*: Wed, 10 Jan 2001 09:34:12 -0800*In-reply-to*: <2BD6C81C9D6EA149B42F93068774AD0A16C7FB@OILCLUSTERN1.omslnetwork.bm>(paul.willmott@omsl.bm)

>It is good enough, ... I ran tests comparing PLAN13 vs SGP4 (LEO), and SDP4 >(orbits over 225 minutes), and very little difference if the keps are less >than 3 weeks old, ... if the keps are old the PLAN13 starts to fail. For >keps under 3 weeks you'd see no difference in Az, El, AOS, LOS, range-rate >etc, ... which is all that counts really. PLAN13 is much faster, and easier >to understand if you are into coding. A good case can be made for using *only* SGP4/SDP4, as NORAD produces their element sets specifically for use with those "propagators". That's what they call the software that produces position and velocity vectors (the state vectors) as a function of time and a set of orbital elements. Keplerian elements like "mean motion", "argument of perigee", model an ideal two-body orbit. A simple, well-defined set of equations model this orbit. Things get fuzzy in the real world because no real earth orbit is strictly two-body. There are drag and earth oblateness effects at low altitude and sun and lunar perturbations at high altitude. And there's solar radiation pressure whenever the satellite is in the sun. Some of the real-world effects can be *approximated* with continuous "secular" changes over time to certain elements. The best known is the change in RAAN for any non-polar, non-equatorial satellite due to the earth's equatorial bulge. Another are the mean motion derivatives. They're given as constants, which is obviously incorrect for an elliptical orbit. So any orbit model with a set of elements can only approximate reality. Whenever NORAD produces a set of elements, they "fudge" them so that *their* propagators produce state vectors that match reality as closely as possibly by a least-squares measure. That's why it's important to use their propagator for best results. GPS gives another good example of matching elements to a specific propagator. A GPS satellite ephemeris is nominally also a set of Keplerian elements, but they are "fudged" (by the GPS control center) to give the best possible results when used with the official propagator given in ICD200c, the GPS reference document. Because the usual Keplerian orbit propagator does not try to model the short-term variations within an orbit, their model adds some sine and cosine coefficients to the standard Keplerian set as additional "fudge factors". The GPS specification stresses the importance of using the official propagator, along with their specified values of various physical and mathematical constants (such as pi). Using a "more accurate" propagator or values of constants can actually give *less* accurate results! Since SGP4/SDP4 are freely available in the public domain, and since modern computers are a lot faster than even a few years ago, today it makes little sense to me to use anything else with NORAD element sets. If you're interested in greater accuracy than this can provide, then your only alternative is to first produce a bunch of state vectors using the NORAD elements and SGP4/SDP4. Then feed those into a numerical integrator that models, as accurately as possible, all the significant forces acting on the spacecraft. This is how James Miller predicted the demise of AO-13, and it's how Stacy Mills more recently projected the future of AO-40 in its current orbit (apparently neglecting the force from the propellant leak). Phil ---- Via the amsat-bb mailing list at AMSAT.ORG courtesy of AMSAT-NA. To unsubscribe, send "unsubscribe amsat-bb" to Majordomo@amsat.org

**References**:**RE: G3RUH Plan13***From:*paul.willmott

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