RE: A method of estimating pre-launch elements

From: Ted Molczan (molczan@rogers.com)
Date: Tue Jun 25 2002 - 02:39:10 PDT

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    The launch took place on 2002 Jun 24 at 18:23 UTC - one minute later
    than planned.
    
    The elements appear to be converging as follows:
    
    1 27453U 02032A   02176.10887502 -.00025567  00000-0 -11350-1 0    84
    2 27453  98.7874 243.1851 0011378 331.9446 112.5061 14.23079723    48
    
    Apart from being one minute late, the mean motion is somewhat greater
    than the one I derived using NOAA 16 as a proxy:
    
    1 70000U          02176.10040685  .00000200  00000-0  11164-3 0    19
    2 70000  98.7886 242.6421 0009705 275.1802 115.0094 14.10880075    40
    
    The difference seems small, but by the time of Ralph McConahy's
    observations, the object was running about 4.8 min ahead and 5.5 deg
    from the sky-track predicted by my elements:
    
    http://satobs.org/seesat/Jun-2002/0177.html
    
    27453 02 032A   8834 F 20020625054457200 17 35 1354237+181865 36 S+055
    10
    27453 02 032A   8834 F 20020625054508900 17 35 1342823+226114 36 S+055
    10
    27453 02 032A   8834 F 20020625054536000 17 35 1315075+329475 36 S+060
    10
    27453 02 032A   8834 F 20020625054544100 17 35 1305191+357900 36 S+060
    10
    
    Had the launch not been delayed by one minute, my prediction time error
    would have been one minute greater.
    
    Could I have done better? I decided to take a closer look at the launch
    circumstances and initial elements of all NOAAs that were launched into
    the present standard 850 km orbit. I have appended the results.
    Following the name of each satellite is its date and time of launch. I
    obtained the data from Jonathan McDowell's web site, at the URLs cited
    in my earlier post.
    
    As I compiled the data, a pattern quickly became apparent: 
    
    - launches near 10:00 UTC had initial mean motion near 14.11 rev/d and
    inclination near 98.90 deg
    
    - launches near 15:52 UTC had initial mean motion near 14.22 rev/d and
    inclination near 98.75 deg
    
    This must be by design, and my guess is that it has to do with the
    perturbation caused by the sun's gravity, that strongly affects
    sun-synchronous orbits. This perturbation varies somewhat depending upon
    the orientation of the orbital plane with respect to the sun. In some
    cases, it causes orbital inclination may vary by more than one degree
    over a long period, causing the plane to wander away from its original
    location.
    
    Sun-synchronous satellites that must maintain a very precise orbital
    plane compensate for solar gravity and other perturbations by making
    frequent small manoeuvres. This is true of most Earth resources
    satellites, such as ERS, Landsat, Spot and RadarSat.
    
    The NOAA satellites are not manoeuvrable, probably because they are not
    required to maintain quite as precise planes as the Earth resources
    satellites. My guess is that their initial plane, mean motion and
    inclination are selected to achieve a mean plane-location during the
    planned mission that is close to some desired mean value.
    
    In any case, knowing that the planned launch time of NOAA 17 was closer
    to the 15:52 UTC time than to the 10:00 UTC launch times, it would have
    been prudent to use as my proxy one of the 15:52 UTC launches, such as:
    
    NOAA 15  1998 May 13 15:52:04 UTC
    1 25338U 98030A   98134.12823554 +.00001287 +00000-0 +59324-3 0 00115
    2 25338 098.7158 164.0280 0010413 339.2361 020.8393 14.22773088000061
    
    Using the ten step process described in my earlier post, and taking into
    account the one minute late launch time, yields:
    
    1 70000U          02176.23305037  .00000200  00000-0  89247-4 0   117
    2 70000  98.7158 243.2926 0010413 339.2361  20.8393 14.22773088    64
    
    At the time of Ralph McConahy's observations, this elset would have been
    just 3.3 s late and within 0.1 deg of the satellite's sky track.
    
    This lesson learned is that by making a more thorough study of past NOAA
    launches, I could have selected a proxy orbit that would have produced a
    much more accurate pre-launch elset - in this case, about 100 times more
    accurate.
    
    Ted Molczan
    
    
    Launch date and time, and initial elements of 850 km NOAA satellites
    prior to NOAA 17
    
    NOAA 6   1979 Jun 27 15:51:59 UTC
    1 11416U          79178.91752047  .00000926           00000-0 0    31
    2 11416  98.7392 207.8071 0011227 280.8958  79.1177 14.22139740    40
    
    NOAA 7   1981 May 29 10:53    UTC
    1 12553U          81174.49904749 -.00000008           00000 0 0    18
    2 12553  98.9001 129.0551 0012452 299.2665  60.7261 14.12002827    00
    
    NOAA 8   1983 Mar 28 15:52    UTC
    1 13923U          83087.91741999 -.00000009           00000-0 0    34
    2 13923  98.7529 118.1785 0015621 262.2376  97.7036 14.22297001    37
    
    NOAA 9   1984 Dec 12 10:42    UTC
    1 15427U          84347.70411840  .00000082           49999-4 0    38
    2 15427  98.9245 296.3557 0014661 268.2803  91.6724 14.11364999    31
    
    NOAA 10  1986 Sep 17 15:52    UTC
    1 16969U          86261.40966530 -.00000009           00000 0 0    25
    2 16969  98.7498 289.4101 0012749 273.7777  85.9107 14.22475423   101
    
    NOAA 11  1988 Sep 24 10:02:00 UTC
    1 19531U          88270.30806841  .00001049           59671-3      72
    2 19531  98.9044 210.0942 0011178 256.6974 103.3183 14.10632414   263
    
    NOAA 12  1991 May 14 15:52    UTC
    1 21263U          91135.19924078  .00026887           12316-1      39
    2 21263  98.7337 164.8826 0011869 262.5003  97.3407 14.21373634    72
    
    NOAA 13  1993 Aug 09 10:02    UTC
    1 22739U 93 50  A 93222.31462920 -.00000019  00000-0  00000+0 0   109
    2 22739  98.9084 163.5700 0008992 280.7119  79.3074 14.10849591   126
    
    NOAA 14  1994 Dec 30 10:02    UTC
    1 23455U 94089A   94364.88900946 -.00014416  00000-0 -79395-2 0    38
    2 23455  98.8861 303.8954 0008755 314.2394  45.8013 14.11496091    67
    
    NOAA 15  1998 May 13 15:52:04 UTC
    1 25338U 98030A   98134.12823554 +.00001287 +00000-0 +59324-3 0 00115
    2 25338 098.7158 164.0280 0010413 339.2361 020.8393 14.22773088000061
    
    NOAA 16  2000 Sep 21 10:22    UTC
    1 26536U 00055A   00265.76707352 -.00020078  00000-0 -11203-1 0    13
    2 26536  98.7886 210.5136 0009705 275.1802 115.0094 14.10880075    42
    
    
    
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