# FWD> Tether orientation and

John_Kiffmeyer@machome.com
Fri, 15 Mar 96 16:10:54 -0800

```FWD> Tether orientation and mag
To seesat-l@iris01.plasma.mpe-garching.mpg.de
CC RMN@aaocbn2.aao.gov.au

TETHER ORIENTATION
The problem of deriving the 3-D orientation is relatively
easy to describe,
but will need a bit of effort to code it.

The simplest thing to recognise is that if it is vertical,
then it will be
seen as perpendicular to the horizon no matter where you see
it from, at
what angle or distance.  If you were lucky enough to have it
pass high in
the sky and the tether diminished to a point, then that
defines the
orientation.  Some simple geometry would then define the
in-orbit orientation.

In general terms, however, you could define a rectangular
coord system centred
on the satellite with Z up (extension of the radius vector)
and X forward in
the orbital plane, and Y normal (perpendicular) to the
plane.  Two estimates
of the tether orientation (angle relative to the observer's
zenith) are needed
to make a determination and these should be from as wide an
arc as possible
during one pass, or from well separated observers during the
same pass.  (It
is assumed that tether orientation is stable over a period
of several minutes).

The observer's spatial coordinates and the observed
orientation for each
observation have to be transformed into the satellite
coordinate system as
defined above.  These define two planes that contain the
tether.  It is then a
simple procedure of finding the intersection of the two
planes.

Other than the transformation of coordinates, this is
formally equivalent to
determining the radiant of a meteor.  Of course, more than
two observations
can be combined, in which case a least squares solution is
used for the
intersection of all the planes.

Regarding Paul Maley's request for the magnitude of the
tether, it is not
possible to give a number that is comparable with stellar
magnitudes.  The
brightness to the naked eye is greater than in binoculars,
as the brightness
decreases linearly with magnification until the seeing disk
is resolved.
It may be possible to define mags/arcmin or some such, but
this is not trivial.
Naked-eye visibility relative to the sky background may be
the easiest way
of defining the visibility, but you will require estimates
of the naked-eye
limiting magnitude and how obvious the tether is.  The
tether is a strange
intermediate between a point source (star) and an extended
source (sky
background) as it is only resolved in one dimension.

Rob McNaught

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Date:	 Thu, 14 Mar 1996 15:41:43 +1100 (EST)
From: 	"Robert H. McNaught, Anglo-Australian Observatory"
<RMN@aaocbn2.aao.gov.au>
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Subject:  Tether orientation and mag
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