Dork Scratchings

Why is it tides are semi-diurnal ? That is, why do they occur every 12 hours when they are caused by the gravitational pull of a moon that we turn to face once a day?  The straightforward answer is that water bulges out on both the side nearest and the side furthest from the moon.  (We'll ignore the Sun for simplicity, but adding it in doesn't change anything.) The Earth rotates while the bulges remain in place, causing tides 12 hours apart.  However, this doesn't explain why there should be two bulges.  The reason becomes clear when you change the frame of reference.  Instead of thinking about a frame in which both the moon and the Earth rotate, set the origin to be the centre of mass of the two objects, and choose a rotating frame in which the moon is stationary.  In this frame there is a "fictional" centrifugal force of $\omega^2 r$ which combines with the gravitational force from the moon, $GM_{\text{moon}}/(r-r_{\text{moon}})^2$ The two forces match at the c

Here's a neat trick for estimating the distance to objects.  Stick out your thumb and look at it with just one eye open, then with just the other eye open.  The distance to the object is the distance it appears to jump multiplied by 10 .  This works because the distance from your eyes to your thumb on your outstretched arm is about 10 times the distance between your eyes.   I thought I'd have a go at using this to measure the distance to the moon