RE: correction of obs 9/1/04

From: Ted Molczan (molczan@rogers.com)
Date: Mon Sep 06 2004 - 11:32:26 EDT

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    Steve Newcomb wrote:
    
    > At 1.16.10 UTc NROL-1 and rocket were under beta draco in 
    > telescope field of view, so actually above. And it has also 
    > been pointed out to me that 47 draco could be the double I 
    > saw instead of 39 draco. I don't know for certain which 
    > double star it was, they are both close to a 5 mag and an 8 
    > mag star. Maybe there are other doubles in the area close to 
    > these mag that I have not found. Five years ago the only 
    > stars I could identify was the big dipper. Below are revised 
    > points if it were at 47 draco .
    > 
    > 28385 04 034B   8539 G 20040901012544040 17 25 1848587+592331 68
    
    Using my three positions and your original one (based upon 39 Draconis):
    
    28385 04 034B   2701 G 20040901005917130 17 25 1540326+161016 68 R
    28385 04 034B   2701 G 20040901010243750 17 25 1604058+251534 68 R
    28385 04 034B   2701 G 20040901010330500 17 25 1609463+271046 68 R
    28385 04 034B   8539 G 20040901012544040 17 25 1821437+584267 68
    
    and allowing the differential correction to adjust all but drag and mean
    anomaly, I obtained the following solution, for which WRMS residuals = 0.142
    deg:
                                                              186 X 23559
    1 70000U          04245.01789074  .00000000  00000-0  00000-0 0    01
    2 70000  60.2703 232.2359 6406027 297.8724 356.8937  3.52300605    02
    
    This solution is in serious disagreement with your observation that the cloud
    passed about 1.5 deg above (non-inverted view) beta Draconis at 01:16:10 UTC. It
    has the Centaur passing directly over the star at 01:17:27.6 UTC, more than 1
    min late.
    
    Replacing your 39 Draconis-based point with your 47 Draconis-based point:
    
    28385 04 034B   8539 G 20040901012544040 17 25 1848587+592331 68
    
    and performing the same analysis, I obtained the following solution, for which
    WRMS residuals = 0.03 deg:
    
                                                              937 X 19453
    1 70000U          04245.01789074  .00000000  00000-0  00000-0 0    01
    2 70000  58.2348 230.2271 5588718 302.6820 358.3180  4.07168784    02
    
    The perigee height of 937 km was at least 500 km to high, but this result places
    the Centaur 0.9 deg directly above beta Draconis as 01:16:11 UTC, in excellent
    agreement with your report.
    
    Depending on how I perform the analysis, I get two different solutions.
    
    Fixing eccentricity manually to maintain perigee height near the apogee of one
    of my parking orbits, 416 km above 6371 km mean Earth's radius, I get:
                                                              418 X 16550
    1 70000U          04245.01789074  .00000000  00000-0  00000-0 0    01
    2 70000  58.0561 230.1366 5430000 295.8537 358.9124  4.79504135    06
    
    Since inclination seems close to 58 deg, I performed an alternative analysis,
    fixing the inclination at that value, and letting eccentricity vary, with this
    result:
                                                              267 X 16020
    1 70000U          04245.01789074  .00000000  00000-0  00000-0 0    01
    2 70000  58.0000 230.1055 5426414 294.1861 358.8949  4.96442126    09
    
    This results in perigee of 267 km, which also is reasonable.
    
    Both of these solutions remain with a few a seconds of your beta Draconis
    appulse.
    
    I have not found any doubles similar in magnitude to 39 Draconis and 47
    Draconis, so I am reasonably confident that the Centaur's mean motion is roughly
    4.8 to 5 rev/d.
    
    I hope to add positions from at least one or two of several photos of the
    propellant cloud I have received from amateur astronomers, once I have received
    their final time reductions. However, all of the new data falls within the
    existing arc; therefore, I doubt it will improve the orbit much, if at all.
    
    Ted Molczan
    
    
    
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