Plane...shadow?

Question

Would a plane in the air make a shadow bigger than the plane, smaller than the plane, or equal in size to that of the plane?

Answer 1

the shadow would be bigger then the plane. But if the plane where to tilt over and its wing where in a vertical position, It would be smaller (and then the plane would crash)

Answer 2

Good question!

There are many things that affect a shadow.

- If the sun were a point source directly above the plane, in theory, it would cast a shadow that is bigger be larger the higher the plane. (However, the altitude of airplanes is very small relative to the distance to the sun, and for practical purposes, the light is parallel.)

- In practical terms, the sun is not a single point, but has edges that emit light. Also that light is affected by our atmosphere and is distorted like light through a magnifying glass. Light is being reflected by the atmosphere and ground. The shadow is being eliminated by scattered light at higher altitudes.

- Another practical matter is that an airfield is very level. Typically, most of the earth is not flat and changes to the elevation will affect the size of the shadow (positive or negative) depending on the position of the sun.

I'm sure there are other factors to consider, but I'm interested in other less "practical" answers to this theoretical question.

Answer 3

The sun is so far away, 93,000,000 mi, that its rays are essentially parallel when they hit the plane. The shadow on the surface of the Earth will be the same size as the plane. The surface of the Earth is essentially flat under the plane. The atmosphere will cause the shadow lines to blur, so that there will not be a sharp outline of the shadow.

Answer 4

Due to diffraction effects, the outer edges of the shadow get filled in with light, the more so the higher the plane is, at relatively modest heights, that is heights such that initially, the plane's outline somewhat more than covers up the Sun's disk. It ultimately essentially ceases to exist as a well-defined shadow.

At greater heights, you can also think about the FRACTION
' f ' of the disk of the Sun that you would see occulted (### See WARNING... , below) if you were to look at the same plane crossing across its disk higher and higher up. So much of the rest of the Sun will be illuminating any given part of the Earth's surface, that f ---> 0 as the plane passes higher and higher across the Sun's disk, and the "occultation effect" becomes negigible.

This is an exaggerated version of the "Umbra/Penumbra" effect that occurs in solar eclipses. The Umbra is the COMPLETEY dark region of FULL SHADOW, which no part of the Sun's light can reach if the Moon is too close to the Earth. (The Umbra, when present, is always surrounded by the PENUMBRA, a region of PARTIAL ILLUMINATION, and therfore PARTIAL SHADOW.)

However, the Umbra is not necessarily always present. As it happens, the Moon's orbit has an eccentricity of about 5%. That eccentricity is sufficient to carry the Moon just that little bit further away such that "annular solar eclipses" take place, in which a bright rim of Sun is still visible all around the Moon's "shadow." What that means is that there is now NO UMBRA; only the Penumbra is left.

In actuality, the Moon's average distance from the Earth is such that annular solar eclipses are slightly more common than total eclipses. If we could back the Moon off more and more, even that Penumbra would fill in and tend to no practical effect at all. (A moment's thought shows that the EXTENT of those partial shadows would in fact grow very slightly smaller as the angular size of the plane --- or the Moon --- were to becom very much smaller than the angular size of the Sun's disk.)

All of the effects described for the shadow of the plane or Moon are natural consequences of observations of shadows or eclipses made by mankind for many tens of thousands of years.

### WARNING, WARNING, WARNING: This is of course a "thought experiment." Under NO circumstances should you actually attempt to look at the Sun with your naked eye!

Live long and prosper.

LATER EDIT --- Oh, there IS one effect we've all been FORGETTING so far! We've all been assuming that the Earth's SURFACE is PERPENDICULAR to the Sun's rays. In general, that's NOT TRUE, of course.

Then, because of DE-PROJECTION EFFECTS, at low altitudes the plane's shadow will be LARGER than that idealized MINIMUM shadow size by a de-projection factor of 1/cos i, where ' i ' is the "angle of incidence" between the normal to the surface and the direction of the Sun at the point and time in question.

That "incidence" effect is macroscopic, and would in fact swamp all the other effects previously described, at low enough altitudes, particularly when the plane was at rest on the ground.

Sorry about missing that de-projection effect the first time around!

Answer 5

That depends on the height. The higher the plane is, the smaller its shadow looking at it from the plane. (Similarly, when you see a plane in the sky it looks smaller than its actual size). Seen from the ground, the shadow will be bigger.

Answer 6

Bigger... but not very much!

Remember that you are talking about a light source 93,000,000 miles away. The distance between the plane and the ground is maybe 10 miles.

The angular dimension of the sun is 1922 arc-seconds.

You also need to take the contour of the ground into consideration. If you are measuring point-to-point, the above answer applies. If you are measuring surface area, although the point-to-point length may be the same, the surface length may vary quite a bit if the shadow covers "peaks and valleys."
.

Answer 7

The shadow of an object blocking the light from a single source is always larger than the object blocking the light. This is always true.

Since the sun is so much larger than the plane, light from the sun may invade part of the shadow making it dimmer or even invisible to the naked eye, but the shadow is still there.

Answer 8

Both. Because of their great height they usually cast a complex shadow.

Answer 9

I believe fringing effects make it smaller and gradually disappear with increasing elevation.

Answer 10

bigger