The most interesting mathematical mistake in the solar system

Johann Elert Bode is the author of Bode's Law, one of the most contentious laws in astronomy. It's a ridiculous idea which juggles numbers, seemingly for no reason, and it ends up revealing the spacing of the planets in the solar system. Or does it?

No matter what you happen to think of Bode's Law, no one can deny that it fulfills one of the most important and long-lasting traditions in physics: It is not named after the person who actually created it. A gentleman (and presumably a scholar) by the name of Johan Titius first came up with it in the mid-1700s. Six years later, in 1772, Johan Bode published it, and it has born his own name since then. Then again, when you look at it, that might be a fitting punishment.


Bode's law is a simple series of calculations. First take a specific sequence of number: 0, 3, 6, 12, 24, . . . and so on. Except for zero and three, each number is double the last. Simple enough. Then add four to each number, getting 4, 7, 10, 16, 28, and upwards. Then divide by ten. The distance between the sun and the various planets is generally measured in Astronomical Units, which are arbitrary but act as a convenient shorthand when you don't always want to say umpteen million miles when describing distance. Each AU is the distance from the sun to the earth. Divide the sequence by ten and you get this:

0.4, 0.7, 1.0, 1.6, 2.8, 5.2, 10.0, 19.6, 38.8, and 77.2

These correspond remarkably with many of the planets (and Pluto) which orbit the sun. Back in the 1700s, when people didn't have so many planets to work with, Bode's Law only raised an eyebrow or two - until 1781, when Uranus was found hovering 19.2 AUs from the sun.

Today, Bode's Law is more a historical curiosity of astronomy than a guide for anyone. The planets are not arbitrarily scattered over the solar system. If they were to orbit at just the right time, or orbit too close to each other, two planets would interact gravitationally, probably destroying both of them, so a random scattering of plot points would not be likely to approximate the lay of the planets in the way Bode's Law does. However, while there are some coincidences, there are a few errant data points. There's no planet at or around 2.8, and Neptune's coordinates aren't on the list. Still, even if it's a fake, it's a little inspiring. Grab a sequence of random numbers and futz around with them a little, and even you can have a law named after you. Well, actually the guy who comes in six years later, can, but it's something to strive for.

Image: NASA

Via The Physics Book.


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