Bode Titius Rule

February 16, 2014

Astronomy, History

Johann Bode and Johann Titius were best buds and they made a rule about planets.
Hubble Bubble Trouble
Okay first of all let’s call it what it is. It’s not really a rule. And it’s not a law. It’s not even a theory. It’s more of a thingy. It’s the Bode Titius Thingy.

It all started in the late 1700’s when pretty much everyone was named Johann. Well, the men anyway. The women were named either Elizabeth or Mary. Maybe most people went by their middle name in order to avoid confusion. Or maybe by surname which might match their family business, like Baker, or Smith. Or by the town they were from. Or maybe a lot of folks had nicknames like Johnny, or John-boy, or John John, or Dickweed.

To fully appreciate the name thing, consider a very old but somewhat well-known Scottish folk song about four Marys. It’s called “Four Marys.” Before I tell you about the Bode Titius story I have to tell the story of Four Marys.

The song claims that Mary Queen of Scots had four hand maids, each named Mary. They each had surnames which I’m pretty sure are towns. The Mary who the song is about, the one whose voice is telling the story in first person style, is Mary Hamilton.

The queen’s husband (a.k.a. the king) calls Mary Hamilton into his bedroom one night and, ummmm, offers her a position on his staff. This puts her in a very dangerous situation. Refusing a direct request from the king pretty much comes with the death penalty. On the other hand, betraying her queen invites the same result. If that isn’t bad enough, Ms Hamilton reveals early in the song that the aforementioned events have led to the secret delivery of a wee baby. Next, the unintended birth announcement propagates throughout the castle. Finally, the new mommy is confronted about it by madam the queen.

The big deal here is not just the slut shaming. That affair was crime enough. But to produce an apparent heir to the throne of Scotland has massive political fall-out. Revolutions frequently result from far less of a premise. To make matters worse, Hamilton explains to the queen that she has placed the brat in a tiny boat (a piner pig in the parlance of the time) and set him to sail out to sea. “To sink or to swim.” Well that was plain crazy. Without physical confirmation of the child’s death, just about any young Scotsman could start a rebellion in a couple of decades hence, and claim to be that kid, survived and all growed up, and ready to rule the land.

And that wasn't chicken.The queen tells Hamilton to come with her as there is going to be a surprise wedding. Ham isn’t stupid. She knows that weddings are well planned in advance and never a surprise. But funerals are often a sudden event. She realizes who the corpse will be at this “wedding.”

Sure enough the wedding turns out to be an execution and Mary Hamilton is the guest of honor, or as it were, the ghost of honor. For some reason when they go to hang her she takes off her gown and makes them string her up in her underwear. Must be a Scottish thing.

A couple of interesting notes here.

  1. There seems to be absolutely no corroborating evidence that these events ever took place, other than the song. Someone may have simply made up the song to justify an attempted rebellion. Who knows?
  2. The song follows a traditional format where the telling of the story is from the voice of a dead person who was wronged, a sad but otherwise benign and friendly ghost.

This format, a story told in first person voice by a friendly ghost, is a recurring theme in Irish and Scottish folklore. To help you fully appreciate the genre, I have to tell this other story.

In California during the early 60’s a couple of folk musicians, who were fans of old Irish and Scottish tunes, were sitting around playing board games and doing lots of drugs and reading books about all kinds of stuff including ghost stories. They realized that the tale of the friendly and benevolent ghost, like Casper, was a common story. By the way, was Casper ever a friendly live boy? Anyway here is an example of the sort of story that the musicians were discovering from their research.

A captain of a ship was in port for a bit and met a fine young chamber maid (ah yes, another maid). They became involved and enamored and entangled and such, and the captain relieved her of her virginity. The maid became forlorn for the captain was soon to ship out. She hung herself to death while wearing nothing but her garters.

What is it with hanging maids and underwear? That in itself is another story and I should be getting back to the Johanns shortly. So with the maid dead and buried, the grieving captain suddenly becomes deathly ill and no doctor or medicine seems to be of any use. He too is dying.

The devil maid me do it.Finally, when he is sufficiently suffering, the ghost of the maid arrives aboard ship in the captain’s cabin. She explains that she is catholic and because she committed suicide the priest refused to give her last rites. Now I’m not a catholic so I don’t fully understand the dogmatic nuance, but apparently this is why she is a ghost, and why the captain is sick. After her explanation of the ecclesiastical details the captain smiles because he is also a catholic, he does understand their dogma, and he immediately sees an obvious solution. He says “Here’s ten bucks on the dresser. For ten bucks the priest will absolve the devil himself.”

The maid goes to heaven, the captain recovers, and the priest, I don’t know, he probably buys a round of pints for the nuns or something.

As you may or may not have guessed. The musicians who were preoccupied by this sort of story found within the literature an official title for this whole “friendly ghost” folk genre. The Grateful Dead. Thus the name for the next and final iteration of their band.

Now then. In the 18th century two dudes named Johann reported a numerical sequence into which the sizes of the planetary orbits seemed to fit, more or less. At the time that the rule was first presented, there were only six known planets; Mercury, Venus, Earth, Mars, Jupiter and Saturn. And the asteroid belt had not yet been discovered. But let’s go ahead and use the rule to examine the whole solar system as we know it today.
1. Numbering the Orbits: From left to right, make ten columns and number them.
2. Mysterious Scaling Factor: Under orbit #1 write 0, under #2 write 3. For the rest, double the previous number (6, 12, 24…).
3. Add 4 to each: In the next row, add 4 to each number above it for each column.
4. Divide by 10: In the next row, divide the number above by 10.

Orbits 1 2 3 4 5 6 7 8 9 10
Scaling 0 3 6 12 24 48 96 192 384 768
Add 4 4 7 10 16 28 52 100 196 388 772
Div by 10 .4 .7 1.0 1.6 2.8 5.2 10.0 19.6 38.8 77.2

5. Now compare the numbers in the last row to the actual known orbital radii of the planets (in Astronomical Units, the Earth-Sun distance). For the asteroid belt put in the average distance to the asteroids, or to your favorite asteroid. It doesn’t matter since this is all witchcraft anyway.

  Merc Venus Earth Mars Aster Jup Sat Ura Nept Pluto
Known AU’s 0.387 0.723 1.000 1.524 2.770 5.203 9.539 19.18 30.06 39.52
Bode Titius 0.400 0.700 1.000 1.600 2.800 5.200 10.00 19.60 38.80 77.20

Textbooks usually remark on the Bode-Titius sequence casually, noting that many astronomers dismiss it as mathematical sleight of hand, a bit of numerical shenanigans, a way of manually stacking the deck. After thorough statistical analysis many astrophysicists insist that it is an anomaly, a coincidence, that nothing universal can be extrapolated or derived from it. Fair enough. But in any event, astronomers also note the following points, which we must keep in mind.

  1. The rule hypothesized a planet between Mars and Jupiter, which turned out to be where the asteroid belt is.
  2. It also hypothesized a planet out from Saturn, which turned out to be where Uranus is.

The inner solar system planets match up with the Bode-Titius sequence reasonably well but the rule gets more and more sloppy as you head outwards so Neptune and Pluto, not so much. Pluto has an especially irregular orbit coming in even closer than Neptune at one point, and it is slightly askew from the plane on which the other orbits closely lie (the ecliptic). Actually Pluto doesn’t fit into the sequence at all and thus probably deserves everlasting condemnation as a rogue and a brute.
Who wants to tell Pluto he is adopted?
Now if you’ll excuse me I have to go check on the maid. She’s been feeling a bit depressed.

Carpe Noctem.

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