than the Antimoon. “There is also a possibility that the Shadow Object is a known celestial body which orbits the sun, and which projects its shadow upon the moon; but more study would be needed to track the positions of Mercury, Venus and the sun’s asteroid satellites and correlate them with the equations for the lunar eclipse before any conclusion could be drawn.”
Here, we happen to agree with the Flat Earth Society. The “shadow object” is a known celestial body – it’s the Earth, dummies! But this waffling is what one expects from an organization that is determined to get the wrong answer, or to introduce ad hoc pseudo-explanations devoid of other motivation for every observable that causes them trouble.
II.5: The Earth’s Rotation
In Flat-Earth theory, the Earth is stationary, which means that it does not revolve around the Sun. Flat-Earthers also deny that the Earth rotates once per day. They spend much time heaping scorn on anyone who believes that the Earth moves.
In particular, they claim that it is not possible that the Earth, together with its bodies of water and the lower atmosphere, are all rotating at the same speed. They present a “demonstration” that they claim proves the Earth could not possibly be rotating. Take a tennis ball and soak it with water. Then spin the tennis ball. The water flies off, as shown in Fig. II.13. Flat-Earthers say “See? The water flies off the tennis ball when it spins. This is exactly what would happen to water on Earth if it was spinning!”
Let’s see why the “wet tennis ball” is a terrible analogy. The tennis ball produces a gravitational acceleration inward on the water. There is also, in the reference frame of the spinning tennis ball, an outward acceleration, the centrifugal acceleration due to the spinning of the ball. (From the viewpoint of an observer on the ground, this just represents the effect of the water’s inertia in the absence of a force that will cause it to spin with the ball.) We can easily calculate those accelerations; given a reasonable rotational speed for the tennis ball, the gravitational acceleration inward is 3.32 x 10-9 m/s2 (or 0.00000000332 meters per second squared), and the centrifugal acceleration will be roughly 376 m/s2. The net acceleration is the difference between those two quantities, or approximately 376 m/s2 outward. So naturally the water flies off the tennis ball.
Next, repeat the same calculation for a drop of water at the Earth’s surface. The gravitational acceleration is 9.82 m/s2 inward, while the centrifugal acceleration is 0.03 m/s2 outward. Thus, the net acceleration is 9.79 m/s2 inward. The net force on the drop of water is inward, and it does not fly off the Earth, as summarized in Fig. II.14. The “tennis ball” analogy is an extremely poor one, because the gravitational force from the Earth is a billion times larger than that for the tennis ball, while the outward centrifugal force from the tennis ball is 10,000 times larger than that of the Earth. The gravitational force from the Earth is much greater than for the tennis ball because of the huge difference in the masses of Earth and tennis ball. The centrifugal acceleration depends on the square of the angular speed ω times the radius of the spinning object. For a tennis ball ω will correspond to about 1-20 complete revolutions/second, while for Earth ω corresponds to one complete revolution/day, 100, 000 or more times smaller than for the tennis ball . The huge difference in the square of ω more than compensates for the much larger radius of the Earth. The tennis ball analogy is relevant only for people who reject the concept of gravity!
Of course, Flat-Earthers could discover this by talking to any physicist; the calculation is trivial. The fact that they continue to push this “analogy” shows that they have no interest in answering their rhetorical question.
Here is a classic demonstration that the Earth is rotating, and that it makes one full (360o) rotation every day. Take a heavy plumb bob (you can purchase one at a hardware store), and attach it to a long wire. Carefully susp