Re: Heavens-Above set to south pole

From: Björn Gimle (b_gimle@algonet.se)
Date: Sun Apr 24 2005 - 06:22:01 EDT

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    Re: Heavens-Above set to south pole
    Re: Are iridium flares less common in some areas?
    
    > Fascinated by the subject I did some South Pole Iridium Flare
    > calculations with my own program. The special geometry between an
    > observer at the South Pole, the direction of the Sun and the Iridium
    > orbital planes which changes only gradually during one day leads to
    > certain days experiencing flares all the time with no-flare days in
    > between. On APR 15/16, APR 29/30, MAY 10 and MAY 14/15 (2005) you
    > can experience mag -8 monster flares every 9 minutes all day long.
    
    > My guess is that you see the flares when an orbital plane is in the
    > right place.  As J2 pushes the planes around the flares will fade
    > until the next plane comes around.
    > What's the period between peaks?
    
    The precession of RAAN is -0.4190987 degrees/day, -153.07 /year.
    Combined with Earth's movement around the Sun, 0.985 d/day, the
    next plane, 31.6 degrees away, is in place 22.5 days later, unless
    you are seeing plane 5, which has no immediate successor in the East.
    But after this period, the Sun's declination is usually quite
    different.
    
    All planes are in the same relative position after 254.17 days, but
    then solar declination is usually even more different.
    
    The separation plane 0 to plane 5 is 158 degrees, so after 369 days
    plane 5 has almost taken the position of plane 0. But all the others
    are in entirely "new" positions.  After seven years ALL planes are
    just 8.5 degrees from the initial position (equal six days later)
    so starting this December we will see the first approximate "reruns".
    After 19 years, four planes will be 3 degrees from inital positions,
    but then the Iridiums should be out of maneouvering fuel.
    
    The flares trace a mesh across the surface of the Earth, which
    depends on the declination of the Sun, and the orientation of the
    planes relative to the Sun. For some latitudes and solar declinations
    this mesh can have intersections of several traces, and/or the
    separations can phased with the day-to-day time diff of passes.
    (As an example, I noticed once that I had bright flares passing
    20 km west of me, moving a few km eastward/day at decreasing speed,
    coming to a halt 15 km east of me, then accelerating back, so the
    period of bright daily flares was about three weeks long)
    
    Since the separation of two consecutive Iridium in one plane is
    9:08 min and the Earth rotates 254 km (near the equator) in this
    time, there are large voids without bright flares.
    After three days = 43 orbits, a single Iridium appears at the same
    time, but then the Sun has changed, and the orbits precessed
    >4 degrees relative to the Sun.
    
    These pseudo-random voids and concentrations (just depending on the
    timing of passes and your longitude), and the previously discussed
    "absence" of repetition in the major factors mean that a good
    average for one place (latitude) can only be achieved by making
    many years of predictions, or using artificial elsets evenly
    spaced in RA over one year.
    
    I have investigated the use of fixed, non-drag elsets for long-term
    Iridium "predictions" and analyses.
    
    The following comments apply only to the operational, frequently adjusted
    satellites!
    
    For long-term computations, current elements are of little value,
    because they reflect (!) short-term fluctuations in mean motion, drag,
    argument of perigee etc., and when used for long intervals they
    quickly diverge. In the long run, these are regularly corrected to
    very high precision mean values, so the operational Iridia are very
    close at 360/11 degrees spacing along the orbit.
    
    The positions are also maintained relative to neighbouring planes. The
    natural way to accomplish this is to keep each individual satellite
    very close to an ideal position, which can be computed with a zero-
    drag elset. The separations between the planes are also maintained,
    but apparantly not to the same precision.
    
    A slight complication is that the orbits have a small excentricity,
    but the perigees are adjusted to remain near 80 degree orbital
    longitude, but there is no way to enforce a zero-precession in TLE-
    processing programs.
    For even higher precision in long-term predictions, average positions
    in XYZ space should simply be translated in time.
    
    I took elsets for all (operational) Iridia from one date early 2004,
    and one set from early 2005, and computed average i, e, AOP, MM,
    and the precession of RAAN (-0.4190987 degrees/day, -153.07 /year)
    Then I set these average i,e,MM in each elset, and used Vec2TLE to
    extrapolate each orbit to Epoch 05000.000. With these elsets,
    I computed the average RAAN for each plane, and set this in all
    elsets for respective plane. I also set the average AOP, and
    adjusted the Mean Anomaly accordingly.
    
    
    
    I have used Walter Nissen's suggested naming standard:
    http://satobs.org/seesat/Jun-1999/0025.html
    
    
    
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