RE: Lacrosse 5 and USA 129 elements

From: Ted Molczan (molczan@rogers.com)
Date: Thu May 12 2005 - 16:21:52 EDT

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    Allen Thomson wrote:
    
    > Ted said,
    > 
    > > I have been unable to make sense of many of the time residuals in
    > > the Lacrosse 5  data set.  In particular, many of my obs appear 
    > > to be several 10ths of a second late relative the others - this is
    > > true of entire passes.
    > 
    > 
    > Are there sufficient post-launch observations for the other Lacrosse 
    > missions to tell whether they also exhibited this behavior?
    > (The antecedent of "they" is meant to be ambiguous.)
    
    To my knowledge, only Lacrosse 4 has been tracked nearly as closely as Lacrosse
    5, within the first week or so following orbit circularization. I have just
    completed an analysis of 40 positions obtained by Paul Gabriel and myself:
    
    Lacrosse 4      18.0  4.5  0.0  3.6 v
    1 26473U 00047A   00245.37621282  .00000718  00000-0  14454-3 0    05
    2 26473  67.9930   1.2775 0004612 270.4404  89.6192 14.61484425    08
    Arc 2000 Aug 23.42 - Sep 01.39, WRMS residuals = 0.026 deg
    
    Only a few points had time residuals in excess of 0.15 s. I note that the
    typical frozen orbit of a 68 deg Lacrosse had already been achieved. This
    consists of a mean argument of perigee of 270 deg, and a mean eccentricity near
    0.0004.
    
    Lacrosse 5 has yet to achieve the typical frozen orbit of a 57 deg Lacrosse,
    which consists of a mean argument of perigee of 90 deg, and a mean eccentricity
    near 0.0004. Our tracking reveals that the argument of perigee is between about
    170 and 180 deg:
    
    Lacrosse 5       0.0  0.0  0.0  3.4 v
    1 28646U 05016A   05131.96464533  .00000042  00000-0  10000-4 0    02
    2 28646  57.0094  87.6328 0004183 172.2400 187.8679 14.53350437    00
    Arc 2005 May 05.10 - 11.99, WRMS residuals = 0.047 deg
    
    It may be that an argument of perigee near 180 deg is required, or at least
    desirable, prior to making the manoeuvre to establish the desired frozen value,
    whether 90 deg or 270 deg. For example, Seasat (78064A / 10967), had argument of
    perigee = 174 deg, before manoeuvring to 278 deg:
    
    http://www.planet4589.org/space/elements/10900/S10967
    
    1 10967U          78237.90713672  .00000790           00000-0 0   313
    2 10967 108.0190 103.5586 0009648 174.5828 185.5369 14.31953582  8572
    
    1 10967U          78238.95500845  .00000790           00000-0 0   326
    2 10967 108.0219 105.6962 0001457 278.2590  77.3469 14.29719006  8727
    
    (Though Seasat has long been dead, it has naturally maintained the frozen
    argument of perigee, as inspection of the above archive reveals.)
    
    EO-1's argument of perigee also was near 180 deg prior to manoeuvring to near 90
    deg:
    
    http://www.planet4589.org/space/elements/26600/S26619
    
    1 26619U 00075A   00345.36201492 -.00011868  00000-0 -27188-2 0   451
    2 26619  98.2168  50.2940 0007144 176.1515 183.9663 14.55537197  2704
    
    1 26619U 00075A   00346.73623477  .00003029  00000-0  68099-3 0   505
    2 26619  98.2145  51.6492 0003821  95.7415 264.4020 14.57187415  2909
    
    As was Icesat's:
    
    http://www.planet4589.org/space/elements/27600/S27642
    
    1 27642U 03002A   03021.84791254 -.00002268  00000-0 -21401-3 0   141
    2 27642  94.0085 185.5224 0010987 199.4818 160.6010 14.93547263  1314
    
    1 27642U 03002A   03023.52287413  .00002625  00000-0  24746-3 0   156
    2 27642  94.0069 186.3729 0010900 201.7235 158.4032 14.93818209  1567
    
    1 27642U 03002A   03023.92676826  .00001787  00000-0  17689-3 0   178
    2 27642  94.0101 186.5833 0010199 158.6939 201.4718 14.92154200  1623
    
    1 27642U 03002A   03026.20827824 -.00003258  00000-0 -33027-3 0   180
    2 27642  94.0117 187.7451 0010123 115.8321 244.3953 14.90786074  1968
    
    1 27642U 03002A   03026.94662729 +.00000966 +00000-0 +99503-4 0 00208
    2 27642 094.0114 188.1218 0010018 113.8092 246.4152 14.90793975002072
    
    1 27642U 03002A   03033.52348385  .00003383  00000-0  34097-3 0   256
    2 27642  94.0089 191.4772 0012245  96.2243 264.0378 14.91264490  3052
    
    1 27642U 03002A   03034.53000706  .00003152  00000-0  31775-3 0   265
    2 27642  94.0066 191.9882 0012277  92.1579 268.1053 14.91270475  3208
    
    None of this explains the several second time residuals that have cropped up in
    tracking Lacrosse 5 at argument of perigee near 180 deg. Perhaps it is making
    small adjustments to argument of perigee and/or eccentricity, that result in the
    greater than normal time residuals.
    
    I expect that in the near future, Lacrosse 5 will rotate its argument of perigee
    to nearly the typical 57 deg Lacrosse mean  value of 90 deg, at which point our
    residuals will settle down.
    
    Some suggested reading on frozen orbits:
    
    Earth Observing - 1 (EO-1) Ascent Strategy
    http://www.ai-solutions.com/Resources/Papers/EO1AscentStrategy.PDF
    
    Phase Plane Analysis and Observed Frozen Orbit for the Topex/Poseidon Mission
    http://jpltrs.jpl.nasa.gov/1995/95-1462.pdf
    
    Orbital Mechanics with MATLAB - Methods of Orbit Design
    http://www.cdeagle.com/ommatlab/odesign.pdf
    
    Ted Molczan
    
    
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