RE: Fobos-Grunt: analysis of orbit evolution

From: Ted Molczan (
Date: Sat Nov 19 2011 - 09:32:17 UTC

  • Next message: Woodchuk: "Re: Corona calibration targets"

    The unusual evolution of the orbit of Fobos-Grunt (11065A / 37872) continued through 2011 Nov 18 UTC. Below is my
    updated plot, using the same methodology described earlier:
    A second process (besides drag), is causing F-G's orbit to become more circular, manifested by apogee decreasing and
    perigee increasing at the same rate (after accounting for drag). A side-effect of this is about a 30 percent increase in
    the rate of precession of the argument of perigee. The net contraction of the orbit is at about half the rate expected
    given the object's dimensions and mass. Therefore, it appears that an in-plane force is raising the orbit, and shifting
    the argument of perigee, negating about half the effect of drag.
    To demonstrate that this is not a usual feature of decaying LEO orbits expressed as SGP4 TLEs, I have performed the same
    analysis on several additional objects. Ideally, they would have been passive, with the same initial orbital dimensions
    and inclination of F-G, and decayed at about the same rate. I did not find any excellent matches to these criteria,
    because most objects in such low orbits that did not decay very rapidly, tended to be manoeuvrable. With the aid of
    Jonathan McDowell's satellite catalogue, I did find three objects in somewhat eccentric orbits, that had a similar
    perigee height to F-G, and decayed more slowly than most objects in similar orbits, though still quite a bit more
    rapidly than F-G.
    In each case, I used STOAG to propagate a TLE over a period of about 9 days, adjusting A/m by trial and error to match
    the mean rate of decay of the semi-major axis extracted from the available TLEs during that period. I then compared key
    values of the actual orbital elements (taken from the TLEs) with STOAG's values, by plotting them over time, and
    computing their rate of change with time.
    Contrary to the F-G results, adjusting A/m to match the actual rate of decay of the semi-major axis was sufficient for
    STOAG to account for overall evolution of the orbit per the TLEs. In other words, there was no evidence of any
    significant non-drag perturbations that STOAG could not account for:
    A few words on the details of the methodology are in order. Due to Earth's oblateness, the orbital eccentricity
    oscillates as a function of argument of perigee, with the minimum occurring at argument of perigee 90 degrees and the
    maximum at 270 degrees. SGP4-based TLEs state the eccentricity as a mean value, specifically for argument of perigee of
    zero. The SGP4 model computes the actual eccentricity for the argument of perigee internally, for the time of
    propagation. STOAG requires that the input value of the eccentricity correspond to the actual argument of perigee at the
    epoch. Fortunately, I long ago designed my SGP4-based orbit propagator to compute the actual eccentricity for the epoch
    of a TLE, which it displays in addition to a TLE's mean eccentricity value. This made it easy to provide the correct
    input to STOAG.
    STOAG's propagated values of eccentricity also are the actual value for the argument of perigee at the epoch, so they
    cannot be directly compared with the mean eccentricity value of a TLE. To ensure proper comparison, I converted STOAG's
    propagated eccentricity to SGP4-mean values, using a Newton-Raphson iteration. (I have put these formulae into the form
    of MS-Excel VBA functions, which I intend to make available in the near future.)
    The plotted altitudes have been derived from the mean eccentricity values. I considered plotting the geocentric radius,
    but the scale of the plots benefited from using altitude. It is computed relative Earth's equatorial radius, but any
    reasonable fixed reference, e.g. Earth's mean radius, would have been sufficient to compare values.
    Next Steps
    Since there is speculation that attitude control thruster firings could be perturbing the orbit, I hope to test that
    hypothesis by estimating the maximum delta-V available from the ACS (attitude control system), and estimating how long
    its fuel would last, based on the rate of consumption implied by the present rate of change of the orbit.
    I am not certain how similar F-G's main propulsion unit is to the Fregat upper stage, from which it is derived.
    According to the Soyuz User's Manual, "FREGAT uses twelve thrusters for three-axis attitude control, and for propellant
    settling before ignition of the main engine. The thrusters are distributed in 4 clusters on the top of the spherical
    tanks. Up to 85 kg of hydrazine is stored in two tanks dedicated to the ACS." Elsewhere (source escapes me at the
    moment), I learned that the Isp is 225 s. This may not apply to the variant of F-G, but perhaps it's a start. Based on
    the spacecraft's reported fully fuelled mass of 13,200 kg, the total delta-V of the ACS would be ~14.3 m/s. If anyone
    has better information, I would appreciate receiving it. 
    I likely will not have time to continue my analysis before Sunday. I remain open to other explanations for the unusual
    evolution of F-G's orbit, whether due to something leaking, anomalous TLEs, etc. I would also be interested to learn the
    results of efforts to replicate the findings I have presented here.
    Ted Molczan
    Seesat-l mailing list

    This archive was generated by hypermail 2b29 : Sat Nov 19 2011 - 09:33:47 UTC