Fobos-Grunt: analysis of orbit evolution

From: Ted Molczan (ssl3molcz@rogers.com)
Date: Thu Nov 17 2011 - 07:58:23 UTC

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    The orbit of Fobos-Grunt (11065A / 37872) continues to evolve in unexpected ways. To the previously noted low rate of
    decay and possibly propulsive orbit change(s), we add the puzzling rise of its perigee altitude. These observations
    relate to USSTRATCOM's TLEs, which remain the only orbital data available to the public.
    
    In an effort to determine whether the perigee rise could be explained by gravitational perturbations not modeled by SGP4
    (the orbital model of TLEs), I compared the actual orbital elements against those yielded by propagating the earliest
    reliable TLE data using the STOAG (Semi-analytic Theory of mOtion under Air drag and Gravity) software. I propagated the
    epoch 11313.39819696 TLE through day 11319, varying the area to mass ratio, A/m, by trial and error to match the actual
    rate of decay of the semi-major axis.
    
    The value of A/m found to explain the observed rate of decay of the semi-major axis, 0.654 km/d, was 0.000634 m^2/kg,
    one half the expected value of approximately 0.00129 m^2/kg, based on the object's known dimensions and mass. Despite
    their forced agreement on the overall rate of decay, STOAG and the TLEs differed greatly regarding the evolution of the
    perigee and apogee, as summarized:
    
                       STOAG    TLEs    Diff
                       km/d     km/d    km/d
    Semi-major axis   -0.654   -0.654   0.000
    Mean perigee      -0.247   +0.386  +0.633
    Mean apogee       -1.062   -1.694  -0.632
    
    It is evident that in addition to drag, some unknown force raised the perigee at the rate of +0.633 km/d, but lowered
    the apogee at nearly the identical rate.
    
    It should be noted that running STOAG with A/m set to zero, reduced the overall rate of decay to zero, and revealed
    negligible non-drag perturbations of perigee and apogee of -0.025 km/d and +0.025 km/d, respectively; therefore, the
    observed evolution probably does not have a natural cause.
    
    The analysis also revealed that the argument of perigee is precessing at more than 1.3 times the expected rate. Since
    the STOAG rate is close to the value predicted by SGP4, the observed rate probably is a side-effect of the decreasing
    eccentricity.
    
    Comparison of the rate of precession of the RAAN revealed close agreement among STOAG, SGP4 and the observed TLE values,
    which tends to confirm the uniqueness of the findings with respect to the argument of perigee.
    
    I have plotted the above results on two graphs, available here:
    
    http://satobs.org/seesat_ref/phsrm/Fobos-Grunt_orbit_evolution_v1.pdf
    
    The unexpected low rate of decay and the unusual perturbation affecting eccentricity and argument of perigee probably
    are manifestations of the same unknown force acting on the orbit. The STOAG model is sufficiently complete to rule out
    natural forces that could have such a large effect over so short a time; therefore, I am left with the possibility of
    thruster firings or venting. The former seldom have such a large effect; however, on an NSF forum, contributor Patchouli
    wondered whether the Fregat-derived propulsion stage could be firing thrusters to settle propellants - an interesting
    idea that I intend to follow up.
    
    I remain open to other possible explanations. I doubt that errors in the TLEs could explain all of the observed effects,
    but could the perturbation be creating some side-effects in the elements that are more apparent than real?
    
    In closing, I caution that my experience using STOAG (and programs like it) is extremely limited. I ran a few tests to
    familiarize myself with its operation and accuracy. I was impressed with its ability to accurately propagate USA 193
    (06057A / 29651) from 2007 Jan 1 until just prior to its unnatural demise in 2008 Feb, using a value of A/m well within
    10 percent of what I believe to be correct. It also handled the object's frozen orbit very well, with argument of
    perigee remaining in the vicinity of 90 deg at all times. The program appears not to propagate mean anomaly, which
    somewhat limits its usefulness, but it appears to be helpful in evaluating long-term perturbations of LEO orbits. A
    description of STOAG, as well as source code and binaries is available here:
    
    http://www.asu.cas.cz/~bezdek/density_therm/pohtd/
    
    I would be interested to learn the results of similar evaluations, using semi-analytic and numerical models.
    
    Ted Molczan
    
    
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