### Various Images from Starts with a Bang re Math and the Environment

Various Images from Starts with a Bangre Math and the Environment

ght now, on Earth, the difference between high and low-tides affects the ocean height by a substantial amount. The Moon (and to a lesser, about 30% effect, the Sun) gravitationally pulls on the Earth slightly more strongly in the direction closest to it, and slightly less strongly in the direction farthest from it.

Image credit: Department of Oceanography, Naval Postgraduate School.

This causes the liquid part of the Earth — the oceans — to form two bulges, which are responsible for the high-and-low tides as the Earth rotates. This is why there are two high tides and two low tides each day; each point on the Earth needs to pass through both high points and both low points to make a complete rotation about its axis.

Image credit: Exploring the Cosmos, via http://exploringthecosmos.tumblr.com/.

With the Moon at our current, 30-Earth-diameter distance, this means that the difference between high tide and low tide can be anywhere from about 5-to-8 feet (1.5 to 2.4 meters), depending on where the Sun, Moon and Earth are relative to one another. (Yes, there are other slight variations to do with latitude etc., but I’m ignoring those.)

Image credit: Wikipedia user NickyMcLean.

But if the Moon were just half-the-distance it is to us now?

You might think that the difference between high and low tide would be twice as large. Or, you might remember that Newton’s Law of Gravitation is an inverse-square-law force, and so you might think the tides would be four times as large.

The way tidal forces work, it turns out, means that the tides would be eight times as large as they are now, or that each day, the difference between high and low tides would be about 52 feet, or 16 meters.

Image credit: user SandyMaiden of allvoices.com.

In other words, every high tide would bring catastrophic worldwide tidal waves to coastal cities everywhere.

And if the Moon were only one-fourth the distance it is right now, those waves would be 400-footers instead of 50-footers.

At that point — just under one-fourth the distance — the Moon would pass through geostationary orbit, and would always appear at the same point in the Earth’s sky.

Image credit: National Space Agency of Japan (NASDA).

Any closer than that, and the Moon would actually appear to rise in the West and set in the East, because it would be orbiting the Earth faster than the Earth itself could spin!