Fobos-Grunt: decay estimate

From: Ted Molczan (
Date: Thu Jan 05 2012 - 20:50:11 UTC

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    1. Main Estimate
    The mean rate of decay of the semi-major axis of the twenty-nine (29) USSTRATCOM TLEs from epoch 11365.44119564 to
    12005.42429976 (2011 Dec 31 10:35 - 2012 Jan 05 10:11 UTC) was 2.3351 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 = 0.0012888 mē/kg and Cd = 2.2.
    Using those values with predicted space weather, STOAG propagates the orbit to decay on 2012 Jan 15 about 23 h UTC.
    Estimated uncertainty is +/- 2 days, based on the rule of thumb of 20 percent of the time remaining to decay.
    Since the decay is drawing closer, I have begun to include the approximate time of day of the estimated decay, but that
    is only to help reveal trends. My estimated uncertainty is still a couple of days, and the exact hour of decay will only
    be known with certainty a few hours before the fact. It should be noted that STOAG propagations are output at intervals
    of no less than one day, and terminate when the semi-major axis falls below 140 km; therefore, I have been using Satevo
    to estimate the time remaining to decay after the end of the STOAG data.
    2. Alternative Estimates
    I offer a few alternative estimates, to provide an indication of the sensitivity to methods and input data. 
    In recent days, the A/m has been trending higher, which tends to advance the date of decay. Shortening the orbital
    history upon which I base the A/m used in my decay estimates from five days to two days (epoch 12003.21124440 to
    12005.23998775), yields A/m = 0.0013388 mē/kg, and moves the date of decay to Jan 15 around 15 h UTC. This happens to be
    similar to Harro Zimmer's result, obtained for the same span of orbital history, using a different propagator and
    atmospheric density model:
    Below is the plot of A/m estimated from historical orbital and space weather data since the orbit manoeuvres ceased,
    through Jan 04. 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 0.0012817 mē/kg; those values, with predicted space weather, would delay the estimated date of
    decay slightly, to Jan 16 near 06 h UTC.
    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.
    I also used Alan Pickup's Satana and Satevo programs alone to estimate the decay, which yielded Jan 16 near 11 h UTC,
    based on the same span of historical orbital elements and 10.7 cm solar flux (mean = 134) as my main forecast. Unlike
    STOAG and Harro's special perturbations propagator, Satevo does not employ predicted space weather, so its accuracy
    depends on space weather not changing. Space weather cannot be forecast with great precision so this is not as great a
    disadvantage in practice as it is in theory.
    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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