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

ssl3molcz@rogers.com

Brian Weeden wrote:

> Ted, I agree with your overall point about the projected launch Az not
> right for a SSO orbit at 500 km, but my math is coming out differently.
>  For a latitude of 39.66 and an Az of 192.3 I get an inclination of 99.44
> degrees.  My excel formula for the inclination is
> 
> =DEGREES(ACOS(((SIN(RADIANS(B6)))*(COS(RADIANS(B5))))))
> 
> 
> where B5 = latitude and B6 = Az
> 
> I think one of us may have a math error (likely me), so if someone could
> check my formula I would appreciate it.

Your result is correct for the formula you are using, which is the commonly used first approximation, based on the
inertial azimuth. I almost always use that formula, which yields an azimuth of 189.7 deg for an orbit of inclination of
97.42 deg, launched from latitude 39.66 deg.

When the situation calls for greater precision, I include a correction for Earth's rotation found in the textbook Space
Mission Analysis and Design (aka SMAD), 3d edition, pg. 154, equation 6-42c. The simplest form of the correction, said
to be accurate to 0.1 deg for low Earth orbits, is:

= ATAN((VL / VO) * COS (inertial azimuth)),

Where VL = velocity of the launch site, = 465.5 * cos(latitude), m/s
      VO = orbital velocity, m/s

For the case at hand, the correction adds 2.7 deg to the inertial launch azimuth, resulting in 192.3 deg (including
round-off).

These formulae offer plenty of potential for big errors due to confusion regarding quadrants, but otherwise are pretty
simple to use.

SMAD provides a more precise version of the correction formula, but the above is sufficient for my purposes.

Ted Molczan

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