Fobos-Grunt: decay estimate

From: Ted Molczan (
Date: Tue Jan 03 2012 - 20:37:34 UTC

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    The mean rate of decay of the semi-major axis of the thirty-three (33) USSTRATCOM TLEs from epoch 11363.53082812 to
    12003.51878838 (2011 Dec 29 12:44 - 2012 Jan 03 12:27 UTC) was 2.0943 km/d. 
    Using the STOAG propagator and actual space weather during that period, I found that the mean rate of decay could be
    accounted for using A/m = 0.0012535 mē/kg and Cd = 2.2.
    Using those values with predicted space weather, STOAG propagates the orbit to decay on 2012 Jan 16. Estimated
    uncertainty is +/- 3 days, based on the rule of thumb of 20 percent of the time remaining to decay.
    Below is the plot of A/m estimated from historical orbital and space weather data since the orbit manoeuvres ceased,
    through Jan 02. Most of the points are at ~2 day intervals, and typically span the preceding ~2 day period. For Cd =
    2.2, the mean A/m was 0.0012789 mē/kg; those values, with predicted space weather, would advance the estimated date of
    decay to Jan 15.
    The above plot of A/m reveals no obvious long-term trend. Some of the apparent variation in A/m is due to imperfections
    in the orbital elements, orbital model and atmospheric density model; some of it may be due to actual changes in the
    object's orientation with respect to the velocity vector. In making decay estimates, the unpredictability of space
    weather (which is the basis of most atmospheric density models) adds to the uncertainty.
    In addition to STOAG, I also used Alan Pickup's Satana and Satevo programs to estimate the decay, and they also yield
    Jan 16, based on the same span of historical elements and 10.7 cm solar flux (mean = 137). 
    Satevo is based on methods developed by Dr. Desmond King-Hele. Satana employs Satevo in an effort to fit more accurate
    decay terms to TLEs, which may improve prediction accuracy. I first tried it on Rosat (1990-049A / 20638), and found
    that it forecast the correct date of decay several days earlier than Satevo and other methods; however, the
    Satana-assisted predictions were made after the decay date was obvious, and although I do not believe that this biased
    the analysis, it arguably was not a fair comparison to the other methods. Below is a plot showing Rosat decay
    predictions from several different sources:
    Satevo, with or without Satana, has been shown to produce reasonably accurate decay estimates. They are very simple and
    convenient to use, in part because their primary inputs and outputs are standard TLEs. My interest in STOAG is due to
    its more sophisticated orbital model, which includes atmospheric density, which enables estimating A/m. Knowing A/m may
    provide some useful insight into the state of Fobos-Grunt. STOAG requires more effort to assemble and format the inputs
    it requires, and its output interval is not less than one day. Also, it does not generate complete element sets that
    could be used for predictions. Which software to use is a matter of which one is best for the task at hand.
    I extracted the actual and predicted space weather data required by STOAG from data provided by, which
    compiles data issued by official sources (mainly NOAA) and presents it in a convenient format:
    Ted Molczan
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