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Date: Thu, 4 Mar 2010 21:56:29 -0600
To: Steve Klosko <sklosko@sgt-inc.com>,
        "jean-paul.berthias@cnes.fr" <jean-paul.berthias@cnes.fr>,
        Cerri Luca <luca.cerri@cnes.fr>,
        Eelco Doornbos <e.n.doornbos@tudelft.nl>,
        Marek Ziebart <marek.ziebart@ge.ucl.ac.uk>,
        Frank Lemoine <Frank.G.Lemoine@nasa.gov>,
        Scott Luthcke <scott.b.luthcke@nasa.gov>,
        Michiel Otten <michiel.otten@esa.int>,
        Eric Leuliette <Eric.Leuliette@noaa.gov>,
        "Mercier Flavien (contact)" <flavien.mercier@cnes.fr>,
        "ids.analysis.forum@cls.fr" <ids.analysis.forum@cls.fr>,
        "remko@altimetrics.com" <remko@altimetrics.com>,
        Nikita Zelensky <nzelensky@sgt-inc.com>
From: "John C. Ries" <ries@csr.utexas.edu>
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Subject: [ids.analysis.forum] RE: surface forces

At 8:02 AM -0500 3/4/10, Steve Klosko wrote:
>I believe what is being seen is the imperfection in the solar array 
>modeling, where we required Fairchild to deliver a droop model good 
>to the cm level.  The 28m**2 array on TOPEX is asymmetrical and we 
>believed at the time TOPEX was being built, that its thermal 
>distortion could impact the CG location of the spacecraft at the 
>several cm level.  We required Fairchild to deliver a model good to 
>1 cm to model this droop.  Obviously, this is a perturbation that is 
>isolated to TOPEX and goes into the altimeter correction model.  The 
>OD process is still made w.r.t. the CG of the spacecraft.  This 
>correction is made to locate the altimeter phase center w.r.t. CG. 
>Jason and OSTM are free of this modeling need.
>
>I see no way that this model (which to my recollection has never 
>been revisited) could perform any better than a few mm.  Since you 
>have now isolated a way to detect this error, we could probably 
>improve it.
>
>Comments?

Hi Steve,

I've been thinking about this, too. Some thoughts that may or may not 
be well-founded.

I note that the effects we are seeing seem to be strongly tied to 
large beta-prime. We've seen that the larger RMS radial orbit 
differences occur for larger beta-prime. And the TZ differences 
appear to be a one-beta-prime dependency, with differences largest at 
higher beta-prime. This is consistent with my own tests. The 
explanation that the TZ difference, dominated by the 120-days period, 
is due to the along-track difference that results from projecting the 
larger cross-track difference does seem to be compelling. But the key 
is that this has no two-beta-prime dependence.

The solar array warp will be 1/rev modulated by the beta-prime, but I 
would expect the largest oscillations of the array to be at low 
beta-prime, and the smallest at high beta-prime. If this effect is 
important, why does it seem benign at small beta prime? An additional 
question is whether the POD should not at least partially accommodate 
it, since it would be a real signal in the tracking.

Another scenario to consider. A once-per-rev radial variation will 
have the same effect as a 1/rev along-track, but it's 90 deg out of 
phase and requires twice the amplitude to get the same effect. Might 
there be radial acceleration variation that is largest for high beta 
prime? If I can imagine the configuration correctly at high beta 
prime, the satellite (being Earth pointing) might be 'nodding' back 
and forth due to the orbit inclination, illuminating the top and 
bottom of the spacecraft in a very periodic way. At low beta prime, 
the illumination is covering much more (if not all) of the spacecraft 
and perhaps this has a less systematic result. This might result in a 
two-beta-prime dependency.

Anyway, I'm thinking that the high-beta-prime dependency and the fact 
that the periodicity seems to be two-beta-prime rather than 
one-beta-prime are important clues.

Best regards,
John