A mysterious sequence
How an antiquated rule of thumb may identify new Earths
Back in the 1600s telescopes had crude optics that offered very poor views of other planets, so relatively little was known about the nature of our neighbours in the solar system. However one thing that could be accomplished with considerable accuracy was the measurement of planetary position and thus the calculation of orbits. This meant that by the dawn of the 18th century astronomers had an excellent grasp of the relative distance of each planet from the sun.
It wasn’t long before people began to notice that many of those planetary distances fitted into a simple mathematical sequence d = 4 + n, where n doubled with each planet in the sequence 3,6,12,24 etc. There was no theoretical basis for this relation, it just seemed to be something that fit. In the middle of the 18th century, Johann Daniel Titius and Johann Elert Bode formalised what astronomers know today as the Titius Bode law. A rule of thumb that seemed to predict how far each planet would be from the sun.
It wasn’t given that much thought until William Herschel discovered the planet Uranus in 1781 and it fitted almost perfectly into the sequence. This led astronomers to look for a missing planet that the Titius Bode law predicted should exist between Mars and Jupiter. In 1801, the dwarf planet Ceres was discovered right where it was predicted and the Titius Bode law was at the zenith of its credibility.
However in the coming years things became more complicated. Further objects were discovered in what we now know as the asteroid belt and perhaps most damning, the planet Neptune was discovered nowhere near the distance predicted by the Titius Bode law. This coupled with its lack of theoretical basis, saw it lose credibility with professional astronomers.
However in the 21st century, astronomers Tim Bovaird and Charley Lineweaver from Mt Stromlo Observatory have scored another spectacular success for the Titius Bode law. Not in our own solar system, but in a distant system known as KOI-2722. “Even though there’s no current theoretical basis for the Titius Bode law, we were curious to see if it worked as well for other planetary systems as our own.” Tim says, “Until recently this would have been completely impossible because so few exoplanets had been identified. However since the Kepler mission, we have several systems with four or more planets to work with.”
The Kepler satellite launched in 2009, monitors the brightness of more than 100,000 stars watching for the tell-tale dip in intensity when an orbiting planet obscures a small proposition of their light. Earth based telescopes have detected such dips relating to very massive planets transiting but for tiny Earth sized planets that decrease in light is swamped by variations in the light curve caused by our own atmosphere. However from the crystal clear permanent darkness of space, Kepler can monitor the starlight for years on end with absolute precision.
“We looked at the KOI-2722 data and a best fit to the Titius Bode law predicted that there would be an additional smaller planet with a particular orbit. Two months later, the Kepler satellite spotted it! It’s really exciting because this is the first time in over two centuries the Titius Bode law has been successfully used to predict the location of an unknown planet.”
Since then, the scientists have fitted the old empirical law to orbital data in many star systems and incredibly, it fits most of them even better than our own solar system. “We don’t really know why this number sequence should fit planetary systems so well,” Tim says. “But the data fit too well for it to be just coincidence. In fact in 84% of the cases we examined the fit is significantly better than in our own solar system.”
If scientists can predict how far from their parent stars planets should be, they can easily calculate the orbital period for such a planet. Armed with this information they can examine the light curve for even a miniscule dip occurring regularly with that period.
“If we know how bright the star is, in other words how much energy it pours out, we can calculate the average temperature of a planet at any given distance. And we know the size of the planet from how much the light curve dips.” Tim explains. “What’s really exciting to me about this is that it may enable us to identify Earth like planets in the habitable zone of other stars.”
“You can be pretty sure that if and when we make a prediction for such a planet, I’ll be up all night scrutinising the light curve!” Tim says.