# Re: Inclination of the satellite to ecliptic plane

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

>
> 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
---------------------------------------------------------
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```
Received on Tue Dec 29 2015 - 13:47:19 UTC

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