In case there is any doubt, the following is my final answer - unless
of course I find other mistakes! 8^)
On Dec 29, 2009, at 8:44 AM, Horace Heffner wrote:
Hi Rick,
Coincidentally, I saw something similar yesterday (Dec 28, 2009)
around noon AKST, (about 11 orbits later) west of Palmer AK, but
heading SW. It was one small finger width at arms length above the
horizon. It had a periodic (about 10 second) flash to it, so I
assumed it might be a booster, but strange it was heading SW, not
SE or NE, or just S. Of course a U-turn is not a typical satellite
maneuver, nor did I see that!
The altitude h to the directly overhead sun midline is given by:
h = r_earth * ( SQRT(1 + sin^2 theta) -1)
Given time after sunset t we have:
theta = (t/(8.64x10^4 s))*(2*Pi) radians = (t/(1440 min))*(2*Pi)
radians
Earth radius, r_earth, at Hawaii is about 3951 mi. Here are some
numbers:
t (min) theta (radians) h (miles)
1 0.00436331944 0.03760073165
5 0.02181659722 0.93976780755
10 0.04363319444 3.75594358
20 0.08726638889 14.973936498
30 0.13089958333 33.506081478
60 0.26179916667 130.1553394
90 0.39269875 279.3533269
Since the above is time after total sunset, you don't have to
correct for the angular width of the sun. However, even total
sunset is not good enough to black out an object though, due to
light diffraction. Clearly not enough time, i.e. "shortly after
sunset", passed to rule out an airplane.
Best regards,
Horace Heffner
http://www.mtaonline.net/~hheffner/
