RE: Updated Orbital Elements

From: Ted Molczan (molczan@rogers.com)
Date: Thu May 20 2004 - 22:16:39 EDT

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    Scott, thank you for sharing with us your orbital elements.
    
    As you noted in your follow up message, the USA 32 (19460 / 88078A) elset is
    unreliable. Quite a few others also contain unrealistic values. My guess is that
    you analyzed data over too short an arc. 
    
    For example, here is your 90050C elset:
    
    1 20691U 90050C   04141.10071233  .00000016  00000-0  24267-4 0    04
    2 20691  72.4609 231.3801 0264349 308.1211 105.3500 13.38051517    08
    
    For readers unfamiliar with the above numbers:
    http://www.satobs.org/element.html
    
    This object had not been observed for nearly 36 days, until David Brierley and
    Peter Wakelin observed it last night, producing single points on consecutive
    revolutions:
    
    9005003267504052000352220  010  12174469  +13382   20 5
    9005003201804052002251545  01   12130969  +37254   1  5             +7         S
    
    For readers unfamiliar with the above numbers:
    http://www.satobs.org/position/UKformat.html
    
    The object was only a fraction of a second late, and almost exactly on-track,
    relative these 36 day old elements:
    
    1 20691U 90050C   04105.80204169  .00000020  00000-0  24267-4 0    02
    2 20691  63.4170 307.5460 0372000   1.1505 358.8495 13.40452551    02
    
    The inclination of your elset, 72.4609 deg, is way off that of the earlier
    elset, 63.4170 deg. The inclination of most orbits either is more or less
    constant over long periods of time, or slowly changing, so this large
    discrepancy is a clear sign of a problem in the orbit determination.
    
    When the difference between prediction and observation is as small as in the
    present example, there is no real need to update the elements, but if one
    chooses to do so, then only minor changes should be made to the earlier elset.
    In this case, I would propagate the elements to the ascending node prior to the
    latest observation, and allow the differential correction to adjust only the
    mean anomaly, so that the object is placed a bit more accurately within its
    orbit.
    
    Here is the result of propagating the epoch 04105.80204169 elset:
    
    1 20691U 90050C   04141.08865757  .00000020  00000-0  24267-4 0    08
    2 20691  63.4170 217.5180 0371993   1.1194 359.0579 13.40453962    08
    
    (I know that you also used the epoch 04105.80204169 elset, because your result
    has the same B* term, 24267-4.)
    
    Here is the result after the differential correction of the mean anomaly:
    
    1 20691U 90050C   04141.08865757  .00000020  00000-0  24267-4 0    08
    2 20691  63.4170 217.5180 0371993   1.1194 359.0484 13.40453962    03
    
    Once observers have generated a large number of points over a suitably long arc,
    then the differential correction can be trusted to produce meaningful results
    for all of the elements.
    
    Also, when analyzing NOSS orbits, such as 90050C, it is important to be aware
    that this class of orbit is perturbed by the odd zonal harmonics of Earth's
    gravitational field, such that eccentricity gradually increases (in some cases,
    decreases), and the inclination slowly decreases.
    
    Scroll through its orbital history, and you will see the dramatic change the
    orbit has undergone:
    
    http://www.planet4589.org/space/elements/20600/S20691
    
    Orbital analysts need to be aware of such perturbations when assessing the
    reasonableness of their results.
    
    One final tip: always compare the residuals of your new orbit relative the
    observations from which it was derived. In the present example, I found large
    time residuals, of the order of 10 seconds - another indication of a problem.
    
    I am glad to see that you are interested in this aspect of the hobby, and I hope
    that you will keep at it.
    
    Ted Molczan
    
    
    
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