Date: Sun, 12 Jun 2006
From: Tom deMary
Subject: Re: [SHG] Re: Skyhook visibility

Quantitative results follow.

I originally said that people at Godman Field *might* have seen
a balloon at Nashville because it was such a large reflector, and
that I did not know how to calculate the apparent brightness. It
turns out that  the math involved is pretty simple, at least to
calculate an upper limit.

The question of visibility is obviously fundamental to unraveling
who saw what, and Brad was correct to bring it up. 140 miles is
a very long distance to look through the atmosphere, after all.

One question I still have is if the balloon is 73 ft or 73 x 129 ft fully
inflated. Such a balloon is mentioned at CUFON site. I have used
73 ft in my calculations.

The answer is that the MAXIMUM brightness that a 73 ft diameter
sphere should have is -4.6 magnitude seen from 140 miles away.
That is quite bright, just brighter than Venus, in fact. But, I don't 
think that Venus could be seen in the daylight sky at Godman Field,
and a real balloon would be fainter still than my calculation. Again,
-4.6 is the most optimistic estimate, assuming diffuse (not specular)
reflection from a sphere. The balloon is certainly not a perfect
reflector, nor a exact sphere and there would be a complicated
dependence on phase angle (the angle between Sun, balloon,
and observer), so the correct answer must be less than the maximum
value which I calculated. Also not included is atmospheric absorption
which would be important attempting to see so far from Godman Field. 

I think the calculation effectively rules out seeing a 73 ft Skyhook
balloon 140 miles away.

For a 45 mile range I calculate -7.1 magnitude, and for a 15 mile
range, -9.4 magnitude. Once again these are upper limits, not
actual claims of actual brightness. A balloon would be fainter.

I tested the equation (and myself) by calculating the brightness of
the full moon, and got -12.1, which is only half a magnitude fainter
than the correct value.

The equation I used came from:

All that is required do the calculation is the cross-sectional area of
the object, the reflectivity, the phase function, and distance of the
object. I simply used 1.0 for the reflectivity (to get an upper limit
for the brightness), and reduced the phase function to 2/(3*pi)
which simply forces zero phase angle, once again so as to get 
the upper limit).

If anyone knows an optical physicist interested in flying saucers,
feel free to run this calculation by him.

I have only replied to Current Encounters since I can't send to SHG,
and all active participants are on this list, as far as I can tell.

Tom DeMary