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> Let's say I suspend a pipe, 1cm inside diameter and
> 10m long, over the Earth at a point within the
> ecliptic.  At the moment when the Sun's GP coincides
> with my "zenith-pipe", for how long a time will I see
> the light of the Sun making it all the way through the
> pipe?

Your pipe is 1000x as long as it is wide, so a pinhole at
the bottom could see a piece of sky whose diameter is
about arctan(1/1000) = roughly 3 minutes of arc.  Since
the whole bottom of the pipe is open, a piece of sky twice
as wide is visible from somewhere at the bottom of the pipe.

The sun is about 30 minutes of arc wide.  From when the sun
starts to peek into the bottom of the pipe, until the last
piece of the sun's disk leaves, it must move 36 minutes of
arc across the sky (sun's width plus pipe's view).

The sun appears to move 360 degrees every 24 hours, or
15 degrees per hour, or 15 minutes (of arc) per minute (of
time).  So it will take about 2.4 minutes for the sun to
move from starting to peek into the pipe until leaving it.

If, instead of a pipe, you had a telescope with cross-hairs,
the sun's disk would move across the cross-hairs in just 2
minutes.

Clear?
        -- Bill

   

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