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 > > > > =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 > > > _______________________________________________ > Seesat-l mailing list > http://mailman.satobs.org/mailman/listinfo/seesat-l > -------------- next part -------------- An HTML attachment was scrubbed... URL: http://mailman.satobs.org/mailman/private/seesat-l/attachments/20120402/3e6348a7/attachment.html _______________________________________________ Seesat-l mailing list http://mailman.satobs.org/mailman/listinfo/seesat-l
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