The Sideways Tide

When you have the ball “floating” by your helmet, you and the ball are both in circular orbit around the some point, the centre of gravity of the Earth. You and the ball What it means is that we’re choosing the direction to result in the ball still travelling in an exactly circular orbit, but we’ve changed its “tilt” slightly. Then the formula for the displacement is: When $t$ is 92 minutes the displacement has completed one full cycle, so $\omega\times(92 ~mins)=2\pi$, and Now acceleration is the double derivative of that, so We evaluate that at $t$ equal to 23 minutes, which is where the ball is one metre away, and we get: Note: an earlier version had $1.3\times 10^{-7} ms^{-2}$, but I just did the sums again and got $1.3\times 10^{-6} ms^{-2}$.

Source: www.solipsys.co.uk