Bode’s Law

¡SkyCaramba! Weekly astronomy blog for the week ending January 19, 2013

The planets in our solar system seem to be carefully distributed by distance from the sun. At least some people think so. Not everyone agrees. An astronomer in the 1700s noticed a sort of regularity in how each planet’s distance from the sun increases from the next closest. Another astronomer figured out how to express it mathematically. The first astronomer was Johann Titius. The second was J.E. Bode. The formula is called the Titius-Bode Law or sometimes just Bode’s Law.

Bode’s law starts with a series of numbers. The first is 0. The second is 3. After that, you double a number to find out what the next one is. So we have 0, 3, 6, 12, 24, 48, 96, 192, and 384.

Then you add four to each number. So we have 4, 7, 10, 16, 28, 52, 100, 196, and 388.

Next, you divide each number by ten. Now are series becomes 0.4, 0.7, 1, 1.6, 2.8, 5.2, 10, 19.6, and 38.8.

These numbers represent almost exactly how far away each planet is from the sun in relative distances. Start with Mercury at 0.4, Venus at 0.7, and Earth at 1. Mercury’s distance from the sun actually averages 0.39 times the Earth-Sun distance. Venus actually averages 0.72 Earth-Sun distances. Earth, of course, averages exactly one Earth-Sun distance from the sun. We call that measure the astronomical unit, or A.U. Mars shows a little more variation at 1.52 astronomical units where Bode’s Law predicts 1.6.

Back when Titius and Bode worked on Bode’s Law, astronomers didn’t know about the asteroid belt between Mars and Jupiter. So they couldn’t account for any planets at 2.8 astronomical units. But Jupiter fit nicely at exactly 5.2 A.U. Saturn orbits at 9.54 A.U., slightly less than the predicted 10. And Uranus is at 19.19 A.U., a bit less than the 19.6 figure Bode’s Law predicts. Its discovery just a few years after Bode put his formula on paper served as confirmation of Bode’s Law despite the missing planet between Mars and Jupiter.

In the early 1800s, astronomers further confirmed the apparent validity of Bode’s Law with the discovery of several asteroids about 2.8 A.U. from the sun. So, many of them expected the next planet to be discovered at 38.8 A.U. in keeping with Bode’s Law. However, Neptune proved to be a bit closer. Orbiting at 30.1 Earth-Sun distances, Neptune defied expectations and seemed to prove Bode’s Law to be just a coincidence.

Astronomers who doubted Bode’s Law were even more convinced of its coincidental nature after the discovery of Pluto in the 1900s. Pluto orbits at 39.5 A.U. Bode’s Law says the next planet out should be 77.2 A.U. away. For what it’s worth, Pluto is no longer considered a major planet.

There are still some who believe Bode’s Law is a good approximation of how far planets will orbit from their parent sun. They think Neptune once orbited where Bode’s Law says it should have been and perhaps something big hit or came near Neptune to cause its orbit to move in closer. If they’re correct, we may yet find more planets orbiting very far out at distances that almost double from one to the next.

Whether Bode’s Law is a coincidence or there’s some yet unknown reason for planets settling into orbits at such distances, the Titius-Bode formula is fairly easy to remember. You can impress your friends by quickly calculating how far away the planets orbit. Maybe you can intrigue them more about astronomy by letting them in on the secret. ¡SkyCaramba!