How does an object 200000 miles away cast a shadow that is some 24 times smaller than itself.
Because the object causing it to cast the shadow is much bigger.
It's really not difficult.
Incorrect.
It is ridiculous that you expect people to believe that the Moon which is allegedly 200000 miles away can cast a shadow that is " 24 " times smaller than the moon .
Why the " quote marks " around 24, and why the extra space before the period ?
The moon is roughly 240,000 miles from earth. If you're going to demand people do things to scale, might as well get the dimensions right.
You certainly seem to work extra hard to avoid understanding this even though it's a relatively simple concept.
<description of a poorly-designed experiment>
Does your tennis ball cast a shadow that is 24 times smaller than the tennis ball on your football.
Let's see. According to your recipe:
You will need a light source that ... is the same size as the average house
You will need a child size football (soccer ball for yanks)
You will need a tennis ball
Now, since "the same size as the average house" is kind of vague, and there is more than one definition of a "child size foorball", that leaves us with the tennis ball as a scale. The
diameter of a tennis ball is about 6.7 cm. Since the moon's diameter is about 27% the earth's diameter, to the same scale, earth would need to be just under 25 cm diameter. Now, soccer ball sizes are officially specified by circumference in inches, so, for our scaled earth, circumference is 78 cm, or 30.7 inches. A regulation-size ball for professional play is smaller than that.
The soccer ball used in professional leagues and in the FIFA World Cup is called “size 5”. The following are the specifications of an official size 5 soccer ball:
Circumference: 27 to 28 inches (69 to 71 cm)
...
Kids’ & youth soccer ball circumference
U-6, U-7, & U-8: Size 3 is the official soccer ball for toddlers and young children. It has a circumference of 23-24 inches... Size 3 is the smallest official ball.
U-9, U-10, & U-11: Size 4 is the standard soccer ball for kids aged between nine and 11 years old. It has a circumference of 25-26 inches...
I'm not sure why you specifically call for a child's ball, but that seems to be incorrect if you want to maintain scale.
Anyway, the sun's diameter is approximately 109 times greater than earth's, so your sun should be about 27 meters across (25 cm * 109 = 2700 cm). That's a pretty big house!
Anyway, continuing...
Place your tennis ball 50 m or 60 yards away from your Sun.
Place your child size football 1 m or 1.1 yards away from your tennis ball.
The distance from earth to moon is roughly 30 times the diameter of the earth, so our scaled moon should be 7.5 meters from the earth to match the scale. How did you come up with 1 meter? Similarly, the sun is about 375 times as far from the earth as the moon is, not the 51 times you call for.
Even though your proposal is obviously sloppily designed, let's continue with it, anyway. We will start by solving for the poorly-specified diameter of the sun based on the dimensions of your moon, the distances you provide, and the desired shadow size.
Diameter of the shadow (umbra, I presume) 1m away from our tennis-ball moon is "24 times smaller" than the tennis ball, so 1m is the distance from the tennis ball to 1/24 of the way from the end of its umbra, or 23/24 of the length of the umbra.
This means the umbra ends at a distance:
d = 1m / (23/24)
= 24 * 1m / 23
d = 1.043m
This means that the tennis ball exactly obscures our scaled sun 1.043 meters on the far side of the tennis ball. So how big must the sun be at this scale?
The sun is (50m + 1.043m)/1.043m = 48.9 times times as far away from the end of the umbra as the tennis ball is, so it must be 48.9 times times larger than the tennis ball.
D
sun = 48.9 * 6.7 cm
= 328 cm
D
sun = 3.3m
3.3 meters across is a pretty small house.
Does the shadow on your football move in the opposite direction to your tennis ball you should pay particular attention to the fact that the Sun light source is 50 m directly behind your tennis ball.
That distance isn't really long enough, but the shadow moves in the same direction as the tennis ball. If the linear movements are done to scale and the correct direction, the shadow moves from right to left (ccw about the soccer ball, as viewed from above) faster than a point on the surface of the soccer ball rotates ccw about the center, also from right to left by about a factor of two, so the shadow would move across the surface from west to east, exactly as expected.
I will save you the time in performing this experiment.
Good idea! It terribly flawed and won't work at all as designed.
The conclusion is No No and No your heliocentric model is ridiculous and doesn't match reality.
No, it's much simpler than that. Your understanding doesn't match reality.