At what speed does a shadow (relative to the sun) move?

Question

Suppose we are NOT at the equator but in an American City (New York).

Let's say a ball is placed in a square at 8 AM. The shadow is relatively long to the ball (about 2-3 feet) and points west. 4 hours later is 12 PM. The shadow is now half feet long and points north. 6 hours later (6 PM) the shadow is 4 feet long and points east. 1 hour later the shadow isn't there anymore (which is logical because the sun has set).

Now, my question is : at what speed does a shadow (relative to the sun) move? I am quite sure is way less than a millimeter per second since you can see a millimeter with your eyes alone and realize that no shadow moves at that speed. But we know that every shadow of every object on earth moves; so knowing that the earth rotates at 1000 mph, at what speed do shadows move?

Thanks

Answer 1

It doesn't work like that. The answer to your question depends on the object casting the shadow. Think of it this way. If you have an object like a pencil casting a shadow, at noon in NYC at this time of year, its shadow will be roughly the same length as the pencil itself. The sun moves at roughly 360 degrees per day, wich comes to 15 degrees per hour or a degree every four minutes. The shadow of the pencil will, therefore, also move round by 1 degree in four minutes - which, for a shadow the length of a pencil, is no big deal. As you say, you probably couldn't see that movement with the naked eye.



But now suppose that the object casting the shadow was the Eiffel tower, which is thousands of times longer than a pencil. Its shadow would also be roughly its own length. But as that shadow swung round by even just one degree, the tip of the shadow would move a long way - and you would certainly be able to see the movement with your eye. The only problem with thatm in fact, is that over that sort of distance, the shadow would be rather blurred. If you happen actually to be in NYC, try the experiment not with the Eiffel tower (obviously), but with a big building, like the Chrysler building or the Empire State Building. You'll see what I mean.

Answer 2

The shadow is on earth.

It is moving relative to the thing that casts the shadow,

...

not relative to the earth or the sun.

Answer 3

the shadow does not move