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

From: Brian Weeden (brian.weeden@gmail.com)
Date: Mon Apr 02 2012 - 13:36:18 UTC

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```Thanks Ted.  Looking at SMAD further, I see now why I haven't noticed it
before.  The correction ranges from 0 degrees (for a launch due east) to 3
degrees for polar, and I had previously used this formula for due east only.

---------
Brian

On Mon, Apr 2, 2012 at 9:22 AM, Ted Molczan <ssl3molcz@rogers.com> wrote:

> 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
> >
> >
> >
> > 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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