Fobos-Grunt: decay estimates, area to mass ratio update

From: Ted Molczan (ssl3molcz@rogers.com)
Date: Wed Jan 11 2012 - 04:21:50 UTC

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    1. Summary
    
    For more than two weeks, Jan 15 and 16 have been the most commonly estimated dates of decay. As of the end of Jan 10,
    estimates had yet to converge, ranging between Jan 15 11:18 UTC and Jan 16 18:00 UTC. A comparison plot appears in
    Section 3.
    
    2. My Estimates
    
    I estimate decay on 2012 Jan 16 near 18:00 UTC, based on USSTRATCOM's TLE of epoch 12010.75855006 (Jan 10 18:12 UTC),
    the long-term average area to mass ratio (A/m) of 0.0012523 mē/kg, Cd = 2.2, and the space weather forecast issued by
    the USAF on Jan 10 at 21:04 UTC.
    
    The approximate time of day of the estimated decay is reported only to reveal trends. The uncertainty is about 1.2 days,
    based on the rule of thumb of 20 percent of the time remaining to decay. The exact hour of decay will only be known with
    certainty a few hours before the fact.
    
    I used primarily STOAG, but since its output is at no less than one day intervals, and ceases when the semi-major axis
    falls below 140 km, I used Satevo to estimate the remaining time to decay, which was about one day.
    
    The STOAG estimate moved 11 h later since the previous estimate, mainly because the USAF significantly reduced the
    forecast solar flux for the coming days.
    
    Using Satana with Satevo yields estimated decay on Jan 15 near 19:00 UTC. I used Satana to adjust the decay terms of the
    TLEs of epoch 12008.7992824, 12009.71815112 and 12010.75855006 for a better fit. Finally, I used Satevo to propagate the
    improved version of the last TLE of this series to decay. Without Satana, Satevo estimates decay on Jan 16 near 00:00
    UTC. Solar flux was set to the mean value during the span of the TLEs, which was 136. Satana and Satevo do not employ
    forecast space weather, but nevertheless yield reasonably reliable estimates.
    
    3. Comparison of Estimates of Multiple Sources
    
    I offer the following plot of recent estimates by The Aerospace Corporation, Paul Salanitri, Harro Zimmer and myself.
    For at least the past couple of weeks, Jan 15 and 16 have been the most common estimates, and as those dates draw closer,
    most estimates now include the hour of day. Since the uncertainties range from half a day to several days, the times are
    mainly useful to show trends. To facilitate comparison, I have included only those predictions that include the hour of
    day.
    
    http://satobs.org/seesat_ref/phsrm/Fobos-Grunt_decay_estimates_v1.pdf
    
    The spreadsheet and data used to generate the plot is here:
    
    http://satobs.org/seesat_ref/phsrm/Fobos-Grunt_decay_estimates_v1.xlsx
    
    4. Updated Area to Mass Ratio
    
    I have extended my analysis of the evolution of A/m to Jan 10. The values were derived using STOAG, from historical
    orbital and space weather data since the spacecraft's orbit manoeuvres ceased in late November 2011.
    
    http://satobs.org/seesat_ref/phsrm/Fobos-Grunt_area_to_mass_ratio_evolution_v12.pdf
    
    Most of the points are at ~2 day intervals, and typically span the preceding ~2 day period. The following statistics are
    based on an assumed value of Cd of 2.2:
    
             A/m, mē/kg
    minimum  0.0010954
    maximum  0.0013982
    median   0.0012441
    mean     0.0012523
    std dev  0.0000808
    points   28
    rē       0.0002 (A/m vs. time)
    
    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 changes in the object's orientation with respect to the velocity vector.
    
    Since A/m is not correlated with time, my recent STOAG decay estimates have been based on the long-term mean. I had been
    using the latest 5-day value, but the statistics to-date provide no reason to believe that recent values will be more
    reliable than the long-term mean.
    
    5. Space Weather Data
    
    I extracted the actual and forecast space weather data required by STOAG from data provided by Celestrak.com, which
    compiles data issued by official sources (mainly NOAA) and presents it in a convenient format:
    http://celestrak.com/SpaceData.
    
    Ted Molczan
    
    
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