A flat, circular UFO is traveling (in daylight) from Rome to San Diego well
above the Earth's atmosphere at a constant velocity of .5C; what will
be the size of the UFO's shadow that is cast on Earth, and what will
be the alignment of the shadow relative to the Sun, the UFO, and the
Earth?

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Request for Question Clarification by hedgie-ga on 10 Oct 2004 22:57 PDT

Salvatore

I would be happy to answer the question, however
it may be a good idea to clarify some terms in the question
to make sure I am answering what yiue are wondering about.

The term 'shadow' is used to describe both Umbra and penumbra,
which are shown e.g. here (using a flash player)
http://www.inconstantmoon.com/cyc_ecl1.htm

and defined here
http://www.schorsch.com/kbase/glossary/penumbra.html

Are you interested in relativity aspect of the question,
such as 'can shadow move faster then c?'

is the speed (.5 c) important? 


By constant velocity, I assume you mean 

 ..moving with constant angular speed in cricular path (orbit)
around the Earth?

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Clarification of Question by salvatore347-ga on 12 Oct 2004 00:01 PDT

hedgie-ga

Thank you for your interest in my conundrum. Please allow me to try
another approach.
A very powerful light source 20? in diameter is placed on the 100th
floor of a skyscraper. The light source is shining straight down onto
the sidewalk below. An observer on a balcony of the 50th floor holds
an object (a bowling ball) in the path of the light beam. The object
will cast a shadow onto the sidewalk below. The size of the shadow
cast onto the sidewalk below, I presume, will be the size of the
object.

Next, the object is tossed horizontally out of the same balcony in a
direction perpendicular to the direction of the light beam. The
velocity of the object is .5c. What is the size of the object?s shadow
that is cast onto the sidewalk below? What is the alignment of the
shadow relative to the light source, the object, and the sidewalk?

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Request for Question Clarification by hedgie-ga on 13 Oct 2004 16:45 PDT

Salvatore

 Thanks for clarification. Some things are more clear now,
 but I am still not sure I understand  what are you after.
 
You say:
 The size of the shadow cast onto the sidewalk below, I presume, will be
will be the size of the object.
Actually, no. (try casting some shadows on the wall - using a table lamp).
That is one difference between your former formulation and the new,
simplified one. Sun is far away - and so its rays are almost parallel
here - and so,
size of shadow and size of object MAY be same. With light source on the 100th
floor that will not happen.
 I need to know if you did look at the links I gave
you and if they did show and make sense. 
If the light source is a point source,
things (umbra vs penumbra issue) are more simple - 
so I need to know if the drawing
http://www.inconstantmoon.com/cyc_ecl1.htm
shows on your browser and  makes sense.
I have asked if you are after 'relativistic aspect', in particular,
a (FAQ) question: can shadow move FTL (faster then light)  -
--  shadows in general do move faster then objects which cast them.

 I assume you do not really care about bunch of formulas 
 and just numbers -- what is the concept you want to undestand? 

Relativistic aspect means that 'size', of the object, of the shadow,
 is different for observer sitting on the object or on the building. 
It is a complication, but it can be calculated. 
Is that what you are wondering about?

Hedgie

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Clarification of Question by salvatore347-ga on 13 Oct 2004 23:00 PDT

Dear hedgie-ga;

Your illustration showing the ?light source,? the ?shadow object,? and
the ?umbra,? is excellent.
1)	If the shadow object is stationary the size of the umbra is a
?particular? size, let us call it (A); the umbra is symmetrically
aligned with the shadow object and the light source.
2)	If the shadow object traverses the path of the light source at a
velocity of .5c, what will be the size of the umbra? How will it be
aligned with the shadow object and the light source?

The goal is to determine if light travels relative to a ?medium,? the
?source,? or the ?observer.? The motive should be obvious by now!

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Request for Question Clarification by hedgie-ga on 14 Oct 2004 19:06 PDT

This question - effect of medium speed on the light travelling was an
important question in the history of relativity:

During this time, Fizeau performed a number of experiments dealing
with light;  one in particular, his water stream experiment.  In this
experiment, light was clocked first upstream and then downstream
through swiftly moving water.  It was assumed that the swiftly moving
water would drag the ether along with it, thus producing a
differential in transit time fore light.  Surprisingly, no
differential was detected, and the draggability of ether was
discarded.
http://zyx.org/ETHER.html

Reading this whole article should answer your question. 
Let me know.
http://zyx.org/ETHER.html

Salvatore,

        I have found for you a site which provides  full answer to
 your question.
The algorithm which determines the actual shape of a shade of the object,
moving at high speed (such as .5c),          is called relativistic ray-tracing.
It is modification of the ordinary (classical) 
ray-tracing which is used in computer graphics.
Serch Term: Ray Tracing

Algorithm is described in the paper
http://www.anu.edu.au/Physics/Searle/paper2.pdf

and Fig.7 shows an object (a tram rather then UFO) moving at .9c.

I believe that even more than algorithm itself, you will appreciate
and enjoy the animations of different situations, which authors generated
and placed on this website. There are quite a few strange effects.
The site is at
 http://www.anu.edu.au/Physics/Searle/

That, above given site,  provides the complete answer.

 I am neverthless adding  reference to few other sites:
http://physics.syr.edu/courses/modules/LIGHTCONE/
http://casa.colorado.edu/~ajsh/sr/paradox.html

These sites provides some terminology, concepts, and visualisations (like this one)
http://physics.syr.edu/courses/modules/LIGHTCONE/lightcone.html

which may help you to appreciate the deep meaning of the word 'relative'
in the name of this theory.

 In conclusion - a warning or perhaps an advice:
Be careful in selection of materials on the Internet, in general,
 but for study this topic in particular.
 Web is full of nonsense on many topics,
and on Theory of Relativity in particular.
 I suggest you stay with the
 .edu domains (like http://physics.syr.edu) in the initial selection
of materials and perhaps look at sites listed here:
http://directory.google.com/Top/Science/Physics/Relativity/Courses_and_Tutorials/
for more material.

It is a complex subject -  it will take time to apreciate the
reasoning and the evidence, but it is worth it - so, do not get
discouraged. Good luck

 hedgie

Duplicate.  See: http://answers.google.com/answers/threadview?id=412702

The UFO will not cast any kind of noticable shadow. The UFO is above
the atmosphere and therefore the shadow will be faded by all kinds of
reflections and refractions. if the shadow wouldnt be shatered by
reflecting light, it would be the size of the ufo itself becouse the
sun is practically an infinite distance from the object.
The place of the shadow would depend on where the sun is at that time,
the shadow wouldnt be on a direct line between the sun and the ufo,
the earths atmosphere will change the direction of the light around
the shadow and with that the shadow itself.

hedgie-ga

Thank you for your interest in my conundrum. Please allow me to try
another approach.
A very powerful light source 20? in diameter is placed on the 100th
floor of a skyscraper. The light source is shining straight down onto
the sidewalk below. An observer on a balcony of the 50th floor holds
an object (a bowling ball) in the path of the light beam. The object
will cast a shadow onto the sidewalk below. The size of the shadow
cast onto the sidewalk below, I presume, will be the size of the
object.

Next, the object is tossed horizontally out of the same balcony in a
direction perpendicular to the direction of the light beam. The
velocity of the object is .5c. What is the size of the object?s shadow
that is cast onto the sidewalk below? What is the alignment of the
shadow relative to the light source and the object?

There wouldn't be any shadow from the bowling ball at ground level. 
Go out on a sunny day and look at a shadow cast on a flat, pale
surface (you could use a sheet of paper).  The edge of the shadow will
be fuzzy because the sun isn't a point source of light - the edge of
the shadow is still getting light from one side of the sun even though
light from another part is being blocked. Seen from the ground, your
bowling ball wouldn't cover more than about 1/25th of the searchlight
(I'm assuming a 2' bowling ball!!) - there'd be so much light "coming
round the side" that the shadow would be washed out.

Ian G.

I think you are interested in relativistice effects on shadow
shape/size.  To allow an answer to focus only on this aspect, you
should remove as much of the geometric optics part of the problem as
possible.  So, instead of a 20' diameter light source on the 100th
floor, make it an infinitesimally small (but bright) one very far
away.  Then don't put the object halfway between the source and the
ground, but just above the ground.

So: the north star inexplicably becomes 100000000000 times as bright
as usual.  A flat, circular polar bear bounds over the north pole 10
feet off the ground at a speed of 0.5c.  Where does an observer fixed
relative to the ground see the shadow relative to the bear, and what
shape is the shadow, according to the observer?

Dear hedgie-ga;

Thank you for providing the information regarding the websites. I have
visited the websites, and have not found anything new. At the risk of
being pretentious, will you please direct your attention to (item 2)
contained in my previous communiqué? I assure you it is not an
exercise in futility. When you have successfully depicted the vector
representation, I will offer you my hypothesis, and you will be
challenged to refute its validity.

Salvatore

Hi Salvatore,

The question 'how will the shadow be aligned with the source and the
object?' can only be answered once you choose a reference frame.  The
way things in relative motion are 'aligned' has to do with their
positions at a particular point in time--that is, what are the
simulataneous positions of the three things?  But as you know, what is
simulataneous in one reference frame is not simultaneous in another. 
The alignment in the reference frame of the object will be different
from that in the reference frame of the earth.