Tether brightness and analysis

Robert H. McNaught, Anglo-Australian Observatory (RMN@aaocbn2.aao.gov.au)
Fri, 15 Mar 1996 10:38:07 +1100 (EST)

Stephen Thompson wrote

>In a previous life I was a variable star observer, mostly with binoculars. 
>I observed eclipsing binaries, cepheids and long period 'Mira type' stars. 
>One of the techniques that I used often was to compare the surface 
>brightness of the out of focus disks of stars.
>
>It should be possible to do the same with the tether.  This would not 
>necessarily give the same results as photometric or CCD measurements, but a 
>comparison of the surface brightness of the out of focus tether with the 
>surface brightness of equally out of focus reference star images would 
>probably give reproducible results that would at least be quantified.  One 
>pitfall of this method is that it is sensitive to the colors of stars so it 
>would be best to use reference stars that are about the same color as each 
>other, and if possible the tether.  To do this right would require that all 
>observers use the same reference star series.

Stephen's comment contains part of the truth but I'm afraid that whilst you
can resolve the length of the tether there is no easy way of getting around
the problem of a star being effectively 0-dimensional and the tether
1-dimensional. This is made most apparent by imagining what happens when you
defocus the sky (2-dimensional); it stays the same surface brightness.  The
tether will thus still be intermediate between the 0-D and 2-D cases,
disappearing more gradually than a star as you defocus.

However there IS a way to get around this by making the tether as 0-dimensional
as possible.  With the tether having an intensity per unit length (actual
length, not angular) one must somehow measure the total light.  It is perhaps
possible to condense the image of the tether to a nearly stellar point using a
strongly curved convex mirror or hub-cap or reversing your binoculars.  This
is the same technique as used in estimating the magnitude of the eclipsed Moon.
If the tether were still resolved in reversed binoculars, defocusing WOULD
work, as you are then spreading the TOTAL light, not just a segment.  There are
several such technique used by comet observers and with some care this could
produce quite reasonable results

There is one other complication in analysing the brightness.  As I assume the
tether can be likened to a cylinder, it is thus capable of producing specular
reflections with the right geometry.  However such a geometry cannot occur at
night if the tether is vertical.  With knowledge of the surface roughness,
this effect could be predicted.  It is thus necessary to use the angle of the
Sun relative to the specular condition in addition to the phase angle.

One final thought.  As the specular condition can only occur in daytime for a
vertical tether, could it be bright enough to become visible?

Rob McNaught