wrote:

On Jul 3, 10:07*am, Stealth Pilot
wrote:
On Sun, 29 Jun 2008 08:24:13 -0700, AES wrote:
In article ,
Stealth Pilot wrote:

at 4,500ft (the original question) the aircraft has no shadow at all
but at the sub solar point (were you'd think the shadow should be)
there is a distinct bright area tracking along under the aircraft.

for thirty years this quietly puzzled me. it is a fact that aircraft
at altitude have no shadow. below them tracking along the ground is a
bright spot of light.

the reference I gave gives details of some original work by Fresnel
which proposed that light passing beside a gravitational mass should
be bent slightly by the mass and behind the body there should be a
bright spot. this seems to me to be the explanation for the absense of
the shadow. the mass of the aircraft acts as a gravitational lens and
this causes the bright spot.

Poisson spot, Spot of Arago, Keller edge waves. *Very much doubt
gravitational bending of light is involved.

I looked up explanations and graphics of these effects.
the poissons spot demo looks entirely different from what I see.

I'm still happy with my explanation.

Stealth Pilot

Steath, one would get sharp shadows if the sun was a point source of
light, but it's not. It's like 0.8 degrees across,
I thought it was about .5 degrees.
so rays from the
left edge of the sun will trace differently to the ground than rays
from its right edge. That's why the shadow is somewhat diffused. A
little math will tell you how high your airplane must be before an
observer on the ground will see sun all around it. It'll be when the
airplane from wing to wing is less than about a degree difference in
angle. 1 degree is about 1 meter across from 60 meters away, so if
your wingspan is 10 meters, at 600 meters distance it subtends about 1
degree and so it would just about match the sun's angular width --
that is, the airplane would be entirely within the ring of the sun. It
means the guy on the ground would not be in the dark shadow of the
airplane.
Yes, and in the case in SP's example, the plane was at 4500, and had a
wingspan of 20 feet. Using the 1:60 ratio you mentioned, 20' at 4,500
feet will look about .025 degree wide. So even if the plane were a
disk, it would block out only (.025/.5)^2 = 1/4% of the sun's surface,
WAY too small to see by eye.

It really is not driven by gravitational lensing of the
light, the airplane just isn't massive enough for that.
I agree. That's why I'd go for the diffraction theory.


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