# Re: G3RUH Plan13

```>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

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