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From: Björn Gimle via Seesat-l <seesat-l_at_satobs.org>

Date: Tue, 29 Dec 2015 20:46:28 +0100

Date: Tue, 29 Dec 2015 20:46:28 +0100

Hi Vladislav, depending on your accuracy demands, the method Cees suggested may be overly cumbersome. If you have two TLE sets close to the desired time, do the calculation directly from these, and interpolate/extrapolate to your desired time. The ecliptic pole is "always" at RA=270, Dec.+66.57 degrees, so its vector is X0=0.3976 Y0=0.0000 Z0=0.9175 (Here I have ignored standard coordinate orientations, to make formulae shorter) For the elsets, pole is likewise at RAAN-90, 90-i, ie (282.3914, -8.8186) for the older one. X1=0.9651 Y1=0.2120 Z1=-0.1533 X2=0.9552 Y2=0.2530 Z2=-0.1533 The scalar product (X0*X1+Y0*Y1+Z0*Z1) is cos(ecliptical incl.) so the first ecliptical inclination is 75.93 deg, the second 76.16 deg. See attached .xlsx In the first elset for USA 249 DMSP F19 below, the RA of the pole is 12.3914-90 degrees 1 39630U 14015A 15359.24597983 0.00000130 00000-0 68437-4 0 01 2 39630 98.8186 12.3914 0010000 311.3267 48.6731 14.14033421 09 1 39630U 14015A 15361.72255199 0.00000130 00000-0 68436-4 0 06 2 39630 98.8186 14.8346 0010000 304.2889 55.7109 14.14034065 09 2015-12-29 0:15 GMT+01:00 C. Bassa via Seesat-l <seesat-l_at_satobs.org>: > Hi Vlad, > > On Mon, Dec 28, 2015 at 11:47 PM, Vladislav Gooba via Seesat-l > <seesat-l_at_satobs.org> wrote: > > How can I calculate or from where can I took these normal vectors, how > and in > > what reference system are they measured? > > The easiest solution is probably to compute the position and velocity > of the satellite using a satellite model like SGP4/SDP4 as it takes > care of the osculating elements. From position and velocity you can > compute the normal vector of the orbit by taking the cross product of > the position and velocity vectors. This normal vector is in the > reference system of SGP4/SDP4, which is, to first order, the > equatorial frame. The normal vector then points to an RA/Dec which you > can convert to ecliptic longitude and latitude. The ecliptic latitude > is then a measure for the inclination with respect to the ecliptic. > > Regards, > Cees > _______________________________________________ > > This ecliptic latitude of the orbit pole is 90-the inclination ?! -------------------------------------------------------- Björn Gimle, COSPAR 5919 59.2617 N, 18.6169 E, 51 m --------------------------------------------------------- _______________________________________________ Seesat-l mailing list http://mailman.satobs.org/mailman/listinfo/seesat-lReceived on Tue Dec 29 2015 - 13:47:19 UTC

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