RE: Fobos-Grunt: decay estimate

From: Ted Molczan (
Date: Wed Dec 21 2011 - 06:34:00 UTC

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    Paul Salanitri wrote:
    > I think I've worked out what the drag profile for Phobos Grunt means.
    > The ballistic drag curve correlates with a spacecraft moving through 90
    > degrees (see image).
    > The clipping of the peak drag (when aligned with the trajectory) is where
    > the solar panels eclipse the base and therefore reduce drag).
    > Absolute maximum is slightly side on with maximum solar panel, but all the
    > base incident to the atmosphere.
    > Minimum is edge on when the solar panels present only the edge, and the
    > spacecraft sides (including hollow parts) is presented to the atmosphere.
    At launch, the spacecraft was almost totally covered with a thermal blanket, including the lattice of the cruise stage.
    > If this is correct, and nothing else changes to alter the spacecraft
    > orientation, it should return to the first "maximum" around 26 December.
    > Thoughts?
    Based on drawings and other data, I estimate that the effective area for drag is ~16 m^2 when oriented sideways into the
    velocity vector, and ~17 m^2 end-on. I have not considered other orientations. The last time I searched the web for the
    s/c mass, the most commonly quoted values were 13,200 kg and 13,500 kg. The orbit manoeuvres consumed ~100 kg of fuel (I
    am nearing completion of report on this); attitude control consumed an unknown quantity, but not more than a few hundred
    kg, limited by supply.
    Here is a plot of estimated A/m since the orbit manoeuvres ceased, at typically ~2 day intervals:
    The mean value, 0.001263 m^2/kg is in reasonable agreement with the above values of area and mass. If we assume mass is
    13,000 kg, then the mean area is ~16.4 m^2. For the same mass, the plotted range, 0.001125 m^2/kg - 0.001408 m^2/kg,
    implies a range of effective cross-section for drag of 14.6 m^2 - 18.3 m^2. Although the A/m plot shows a gradual
    variation over time, it is probably not entirely due to precession of the s/c, if at all. At least some of the variation
    probably arises from variation of Cd and errors in the modelled atmospheric density.
    Ted Molczan
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