RE: North Korea satellite: NOTAMs inconsistent with claimed sun-synchronous orbit

From: Ted Molczan (ssl3molcz@rogers.com)
Date: Mon Apr 02 2012 - 12:34:11 UTC

  • Next message: Ted Molczan: "RE: North Korea satellite: NOTAMs inconsistent with claimed sun-synchronous orbit"

    David Tiller asked:
    
    > It seems that there are two parameters that are used to compute the particulars of a sun-
    > synchronous orbit - orbital altitude is used to derive the correct orbital inclination which
    > then drives the launch azimuth based on latitude. Your analysis assumes that the stated
    > launch altitude is correct and the launch azimuth is incorrect.
    > 
    > What orbital altitude would be correct for a sun-synchronous orbit assuming that the launch
    > azimuth will be as the DPRK stated?
    
    The defining property of a sun-synchronous orbit is that its rate of planar precession exactly negates the -0.9856 deg/d
    (westward) precession due to Earth's motion about the sun. That is accomplished by taking advantage of the perturbation
    due to Earth's oblateness that causes an orbit's plane to precess, which is a function of its size, shape and
    inclination. The rate of planar precession varies in direct proportion to the cosine of the inclination; therefore, to
    achieve the required +0.9856 (eastward) precession requires a retrograde inclination, i.e. >90 deg.
    
    North Korea's NOTAM's for of its upcoming launch correspond to a launch azimuth of about 181 deg, which corresponds to
    an inclination of approximately 88.7 deg, which would not support a sun-synchronous orbit at any altitude, since it is
    not retrograde. 
    
    The lowest orbit that would survive for at least one revolution before decay, ~140 km, requires an inclination of 96.13
    deg to be sun-synchronous, which requires a launch azimuth of about 190.6 deg for a direct ascent trajectory. The 500 km
    orbit announced by North Korea requires a 97.42 deg inclination to be sun-synchronous, which requires an approximately
    192.3 deg launch azimuth.
    
    Ted Molczan 
    
    
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