The False Analogy of a Spinning Tennis Ball

The mass of the Earth exerts the gravitational acceleration of about 9.79 m/s² to everything on Earth’s surface toward the center of the Earth. On the other hand, the rotational motion of the Earth generates the centrifugal acceleration of about 0.03 m/s² away from the Earth. The net acceleration is about 9.79 m/s² toward the center of the Earth. That is why everything on Earth’s surface stays on the surface, not flying away to space.

Flat-Earthers often make a false comparison using a wet spinning ball. Water on the surface of a wet spinning ball does not stick to the ball; but the Earth is also round, wet and spins, yet everything stays on the surface. Then they make the erroneous conclusion that the Earth cannot be a spinning ball.

Water remains on the surface of the Earth because of Earth’s gravitational acceleration is greater than the centrifugal acceleration generated by its rotating motion. The Earth does not rotate nearly fast enough to produce the centrifugal acceleration caused by a spinning tennis ball.

Using Newton’s law of universal gravitation, we can find that the gravitational acceleration exerted by a tennis ball on an object on its surface is about 0.00000000332 m/s². On the other hand, its spinning motion generates a centrifugal acceleration of approximately 376 m/s², assuming the rotational rate of 1000 rpm. For comparison, Roger Federer’s backhand can create a spin of 5300 rpm. The net acceleration is about 376 m/s² away from the ball, causing water to fly away from the spinning ball.

Another consideration is that the spinning tennis ball “experiment” was performed on Earth and was affected by Earth’s gravity which is several magnitudes greater than one from the tennis ball. Any water droplet on the surface of the tennis ball is influenced more by Earth’s gravity than tennis ball’s gravity. Water sticks to the surface of a still tennis ball due to surface tension, not gravity.

Calculations

For the tennis ball:

  • Diameter: 2.7 inch
  • Mass: 58.5 gram
  • Rotational velocity: assumed 1000 rpm (Roger Federer’s backhand can result in 5300 rpm spinning tennis ball).
  • Centrifugal acceleration on the surface of a spinning tennis ball: a = ω²r =  (((1000 / minutes) * (2 * π))^2) * (2.7 inch / 2) = 376.031928 m / s2
  • Gravitational acceleration on the surface of a tennis ball: g = G M / r² = G * 58.5 gram / ( 2.7 inch / 2)^2 = 3.32056743 × 10-9 m / s2

For the Earth:

References