Fobos-Grunt: decay estimate, area to mass ratio

From: Ted Molczan (ssl3molcz@rogers.com)
Date: Mon Jan 09 2012 - 03:48:02 UTC

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    I estimate decay on 2012 Jan 16 near 07:00 UTC, based on USSTRATCOM's TLE of epoch 12008.92184836 (Jan 08 22:07 UTC),
    the long-term average area to mass ratio (A/m) of 0.0012502 mē/kg, Cd = 2.2, and the space weather forecast issued by
    the USAF on Jan 08 at 21:18 UTC. 
    
    The approximate time of day of the estimated decay is reported only to reveal trends. The uncertainty is about 1.5 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 Satana/Satevo to estimate the remaining time to decay, which was about one day.
    
    Using Satana and Satevo without STOAG, yields estimated decay on Jan 16 near 09:00 UTC. I used Satana to adjust the
    decay terms of the TLEs of epoch 12003.82628145, 12006.40694296 and 12008.92184836 for a better fit. Finally, I used
    Satevo to propagate the improved version of the last TLE of this series to decay. Solar flux was set to the mean value
    during the span of the TLEs, which was 138. Satana/Satevo do not employ forecast space weather, but nevertheless yield
    reasonably reliable estimates.
    
    I decided to base the STOAG decay estimate on the long-term A/m, instead of a recent short-term value, because my
    on-going analysis reveals zero correlation between A/m and time, as shown in this plot of values derived using STOAG,
    from historical orbital and space weather data since the spacecraft's orbit manoeuvres ceased in late November 2011,
    through Jan 08 UTC: 
    
    http://satobs.org/seesat_ref/phsrm/Fobos-Grunt_area_to_mass_ratio_evolution_v11.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   0.0012408
    mean     0.0012502
    std dev  0.0000817
    points   27
    rē       0.0042 (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.
    
    The mean A/m is in good agreement with the dimensions, mass and probable orientation of the spacecraft. Recent videos by
    Thierry Legault and Emmanuel Rietsch suggest that the spacecraft's x-axis is aligned with the velocity vector:
    
    http://legault.perso.sfr.fr/phobos-grunt.html
    
    http://ercs.electronique.perso.sfr.fr/Web/Phobos_Grunt_EN.htm
    
    The greatest diameter of the bus is 3.4 m. The widest span is through the solar arrays,~7.5 m. Array width is ~2 m. The
    effective cross-sectional area for drag, of the base and protruding portion of the arrays is about 17.3 mē. Dividing by
    the mean A/m of 0.00125 mē/kg yields mass of 13,800 kg. This is within 5 percent of the most commonly cited launch
    values (last I time I searched the web): 13,200 kg and 13,500 kg. An unknown portion of the spacecraft's 529 kg supply
    of fuel and oxidizer for attitude control and ullage burns was consumed, which could increase the discrepancy to nearly
    10 percent. Given the many uncertainties, accuracy of A/m derived from drag analysis typically is limited to about 15
    percent. I am interested to know the results of analyses using different orbit and density models.
    
    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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