RE: Phobos-Grunt: latest two TLEs suggest manoeuvring or venting

From: Ted Molczan (
Date: Sat Nov 12 2011 - 16:51:55 UTC

  • Next message: Scott Tilley: "Re: Phobos-Grunt: latest two TLEs suggest manoeuvring or venting"

    USSTRATCOM has issued three new TLEs since my comments yesterday on the payload's rate of decay. They confirm that the
    apparent small increase in orbital altitude is real, and apparently it is continuing.
    Prior to the onset of this effect, which became evident in the TLEs issued after epoch day 11314.76789777, the rates of
    decay of the payload and its rocket body were roughly proportionate to their respective area to mass ratios, as would be
    expected for bodies encountering nearly identical atmospheric density, due to their nearly identical orbits.
    During the period from epoch date 11313.58425036 to 11314.76789777, the mean value of the rocket's ndot/2 decay term,
    calculated from the change in mean motion, was 0.00635 rev/d^2. During nearly the same period (epoch date 11313.58551366
    to 11314.77184893), the payload's corresponding value was 0.00155 rev/d^2. Although their orbits were similar, the
    rocket was about 9 km lower; therefore, it encountered approximately 1.2 times the atmospheric density. To facilitate
    comparison, the payload's ndot/2 should be increased by the same factor, to 0.00186 rev/d^2. Therefore, during this
    period, the payload decayed at 0.293 times the rate of its rocket body.
    The rocket body is a cylinder 10.4 m long, 3.9 m dia. Inert mass is 8367 kg. Source: Land Launch User's Guide. Several
    observers have reported regular variations in its brightness, indicating that it is tumbling. Assuming rotation about
    the transverse axis, its effective area to mass ratio for drag (A/m) is about 0.0040 m^2/kg.
    The payload is somewhat complex in shape, but overall it can be described as roughly cylindrical. Prior to launch, I
    looked for overall dimensions, but failed to find a source; however, the highly informative has many
    photos that include humans, which I used as a scale to estimate the overall length as 5 m, and the diameter as 3.4 m
    near the base and 2 m near the top. The main solar array, located near the top, consists of two deployable wings
    reportedly with total area of 10 m^2, which I estimate are 2 x 2.5 m each. 
    Several observers reported the payload stable, but its orientation and the state of deployment of its solar arrays is
    unknown. If the spacecraft's long-axis is oriented parallel to the direction of motion, and the solar arrays have not
    deployed, then the effective area for drag would be that of the cross-section through the base, about 9.1 m^2. If the
    solar arrays have deployed, then the portion that extends beyond the cross-section of the base would increase the
    effective area to about 16.3 m^2. If the spacecraft's long-axis is oriented perpendicular to the direction of motion,
    then the effective area for drag is the mean area of the side of the cylinder, about 13.5 m^2.
    Using's latest estimate of the launch mass, 13,500 kg, the smallest and largest areas yield A/m
    between 0.00067 m^2/kg and 0.0012 m^2/kg, which are respectively 0.168 times and 0.3 times the rocket body's value, in
    reasonable agreement with the ratio of their rates of decay.
    Since the orbit change(s) became evident in the TLEs, during the period from epoch 11314.95914282 through (so far)
    11316.39501126, the payload's ndot/2 decay terms have ranged between -0.000024 rev/d^2 and +0.00105 rev/d^2. The mean
    value calculated from the change in mean motion during this period is 0.000410 rev/d^2, representing a huge decrease.
    Since the rocket was now about 15 km lower than the payload, it encountered ~1.4 times the atmospheric density.
    Adjusting the payload's value for comparability, yields 0.000574 rev/d^2. During nearly the same period, from epoch date
    11314.95468762 to 11316.50998309, the rocket's mean ndot/2 increased somewhat to 0.00743 rev/d^2. 
    The ratio of the payload's rate of decay to that of its rocket was just 0.0773, far below the 0.293 ratio prior to the
    onset of the orbit change, and far below the range of values expected based on the relative area to mass ratios, between
    0.168 times and 0.3 times the rocket body's value.
    Had its orbit continued to decay at the original rate, the payload would be at least 0.9 km lower as of epoch
    11316.39501126. The probable cause appears to be manoeuvring or venting. Whether it is continuous or a series of events,
    is unclear.
    Also less clear is whether the onset correlates with one of the passes within range of Baikonur, as I speculated
    yesterday. I will continue to look into that possibility, but it now seems less likely than it did.
    I am interested and open to alternative explanations. Also, if anyone has better data on the payload's dimensions and
    mass, I would appreciate receiving it. I would also be interested to know the results of estimates of rates of decay
    based on numerically integrated motion with respect to realistic atmospheric density models, using the A/m values I
    Ted Molczan
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