Nodal regression

From: Matson, Robert (ROBERT.D.MATSON@saic.com)
Date: Thu Dec 04 2003 - 13:34:11 EST

  • Next message: FrankReedCT@aol.com: "Re: ISS occulting.../precession"

    Hi Thomas,
    
    On the subject of orbital precession (i.e. nodal regression) you asked:
    
    > So, what would account for such a huge precession of the plane of orbit?
    
    The earth's equatorial bulge.
    
    > The most significant torque (or force acting in a non-center-directed way)
    > on the ISS would seem to be gravitational tugging by the moon & sun (which
    > I'd think would largely balance out, over the course of an orbit),
    > atmospheric drag, and the solar wind.
    
    The earth's non-spherical shape overwhelms all of these for LEO
    satellites in non-polar orbits.
    
    > Do more compact satellites (such as Hubble, for example) have a similar
    > orbital precession?
    
    Yes.  Nodal regression is a function of altitude and orbital inclination.
    The lower the altitude and the lower the inclination, the greater the
    nodal regression rate per day (the maximum possible is about 9 degrees/day).
    The rate of change of the right ascension of ascending node (RAAN) due
    to earth's J2 zonal coefficient is given by:
    
    delta Omega = -1.5 * n * J2 * (Re/a)^2 * cos i * (1-e^2)^-2
    
    where n is mean motion in deg/day
          Re is earth's equatorial radius
          a is the semi-major axis in km
          e is eccentricity
          i is orbital inclination
          J2 = .00108263
          delta Omega is in deg/day
    
    Since n is a function only of a, the formula can be simplified.  After
    substituting all the constants, you get:
    
    delta Omega = -2.06474E+14 * a^(-3.5) * cos i * (1-e^2)^-2
    
    For a circular orbit, the last term is unity.  So, try plugging in
    51.6 degrees for the inclination, and an altitude of 380 km (a=6758 km):
    
    delta Omega = -2.06574E+14 * 3.94127E-14 * cos 51.6 = -5.06 deg/day
    
    (the negative sign indicating westward movement of the RAAN).
    
    --Rob
    
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