Subject: Re: [ids.analysis.forum] RE: surface forces
From: [email-masked]
To: "John C. Ries" <[email-masked]>
Cc: Eric Leuliette <[email-masked]>, Eelco Doornbos <[email-masked]>, "Mercier Flavien (contact)" <[email-masked]>, Frank Lemoine <[email-masked]>, "[email-masked]" <[email-masked]>, "[email-masked]" <[email-masked]>, Cerri Luca <[email-masked]>, Marek Ziebart <[email-masked]>, Michiel Otten <[email-masked]>, Nikita Zelensky <[email-masked]>, "[email-masked]" <[email-masked]>, Scott Luthcke <[email-masked]>, Steve Klosko <[email-masked]>
Date: Fri, 5 Mar 2010 12:35:37 +0100

Dear all,

At the risk of introducing a bright red herring, I would like to mention
a software problem that I ran into last year and which could have a
signature similar to what you are all seeing (beta & two-beta signal).

In multi-step numerical integrators you have to be careful with the
zero transitions of the wing from the box-wing model, which typically
do not occur for SRP but you can get them for IR, albedo or drag.
When the panel rotates "through zero" in the direction of the Earth,
the projected wing area for IR first decreases more or less linearly,
can even be zero for a split second and immediately starts increasing
again. This implies a discontinuity in the first and higher derivatives
of any surface forces that are looking sideways at the solar panel.

Multi-step integrators really don't like jumps in higher derivatives.
The result can be non-negligible errors in the computed acceleration,
which is the same as having an additional perturbation on the satellite.
Arcs with two such occurrances per revolution (~20 per day...) will
definitely come out worse than arcs that do not have any of these
zero-crossings at all. Without having checked it in detail, I suppose
that these movements are governed by the beta angle, and as it
affects the absolute value of the projection (2-per-rev) there could
well be a spectral peak at two beta as well.

This thing happened here in a new implementation - perhaps you
have all fixed such mishaps years ago in your own software. In that
case just ignore this mail, but keep in mind that the problem may be
numerical rather than physical.

Best regards and good luck on this,

Henno