RE: Need help with web page

From: Ted Molczan (
Date: Sat Mar 18 2006 - 11:20:21 EST

  • Next message: Edward S Light: "USA 144"

    Robin Wier asked:
    > Data 2 weeks old, maybe a problem?
    Short answer: in this case, no.
    Long answer: in the olden days, which for the purpose of this discussion ended
    about 1990, most orbital elements were available only by snail mail, and very
    few people had access to elsets of more than about 20 objects. It was common to
    have to use 2+ week old elsets, even for mundane stuff like Mir predictions,
    which meant prediction uncertainties of at least several minutes.
    Today, elements of many thousands of objects in orbit are available via the
    Internet, providing millions of people access to elsets in near-real-time, all
    but guaranteeing accurate predictions. However, significantly out-dated elsets
    remain an occasional challenge. For example, hobbyists track many objects for
    which official elements are not published, but with occasional long gaps in
    coverage, due to poor visibility of the orbit or bad weather. Also, objects near
    decay have large prediction uncertainties. So, about 20 years ago, I derived a
    simple formula to estimate the prediction time error:
    Tunc =  864 * %Dunc * ndot/2 * dt^2
               n0 + 2 * ndot/2 * dt
    Tunc   = the uncertainty of the time of the satellite's passage, seconds
    %Dunc  = the uncertainty in the rate of decay, expressed as a percentage
    dt     = the time elapsed since the epoch of the elset, days
    ndot/2 = one half the rate of change of the mean motion with respect
             to time, as it appears in a 2-line elset, rev/d^2
    n0     = mean motion at the epoch, as it appears in a 2-line elset, rev/d
    The constant 864 is the number of seconds in day, divided by 100; it enables
    Tunc to be expressed in seconds of time, and %Dunc as a percentage.
    Now for a quick example, let us consider the TiPS tether, which is in a fairly
    stable orbit, for which official elements are not available. It is tracked
    fairly frequently by hobbyists, but sometimes there are gaps of several weeks
    between new elsets. The most current elset is:
    TiPS             0.0  0.0  0.0  7.2 v
    1 23937U 96029F   06064.83153168  .00000950  00000-0  68906-3 0    00
    2 23937  63.4005  63.6203 0331497   3.8035 356.1966 13.73167741    06
    which says that on day 64.83153168 of 2006, ndot/2 = 0.00000950 rev/d^2, and n0
    = 13.73167741 rev/d.
    Now let us say that we wanted to make an observation tonight, 2006 Mar 18,
    around 20:45 UTC, i.e. day 06077.8646. That would be 13.03 days since the epoch
    (77.8646 - 64.83153168).
    Now we make a judgment that the uncertainty in the rate of decay, ndot/2, is 25
    percent, so %Dunc = 25.
    We are now ready to compute the ephemeris time uncertainty:
    Tunc =   864 x 25 x 0.00000950 x 13.03^2
           13.73167741 + 2 * 0.00000950 * 13.03
         = 2.5 seconds
    So although the elset is 13 days old, its low rate of decay assures an accurate
    Ted Molczan
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