30 December 2012
SIZE AND DISTANCE
Back when I was a teacher of science and math, one of my favorite thought experiments was to devise a scale model of the solar system, one which was not only accurate to the relative size of the planets and sun to each other, but also accurate to the distances between them. And therein lies the rub ~ objects in the universe are actually quite tiny compared to the yawning stretches of space which separate them. So one can devise a reasonable scale model that is true to relative size (see image above, click to enlarge), or a scale model that is true to relative distance (see image below). But it requires resources on, well, an astronomical scale to devise a scale model that is true to both, simultaneously.
Perhaps I would have been well served to zoom in on just a portion of the whole. Phil Plait does just that in How Far Away Is The Moon? Plait came across a two-minute video that is making the rounds on the Internet, one which asks "If the Earth were the size of a basketball and the Moon a tennis ball, how far apart would they be?" He decided to check out the math, and discovered that a basketball and a tennis ball are reasonable approximations of the relative sizes of Earth and its moon (7900 miles and 2150 miles in diameter, respectively).
So what about scaling the distance between the two? Well, the moon orbits at a distance of roughly 235,000 miles from Earth. Using the same scale for distance that we used for size, our tennis ball moon would circle our basketball Earth with about 24 feet between them. Which is more than one might expect from looking up into the night sky on a clear night.
To gain an even broader perspective, we introduce the Sun, whose diameter is something like 11,750 Earth diameters. In our scale, the Sun's diameter would be about 93 feet (the size of a very large, very fiery house), and the distance separating mansion Sun from basketball Earth would be .... 1.75 miles !
So there you have a scale model which respects both size and distance. Still a bit ungainly for a school experiment, but not nearly as daunting a challenge as the entire solar system.