Australasian Science: Australia's authority on science since 1938

Law Bodes Well for Planetary Discovery

By Stephen Luntz

A famous but generally discredited law is making a comeback and could help the search for Earth-like planets in the habitable zone around other stars.

Bode’s Law, also known as the Titius–Bode relationship, noted a geometric pattern to the distance from the Sun to each planet in our solar system. At first considered a curiosity, it became taken more seriously when Uranus was discovered and fit the pattern.

The spacing required a planet between Mars and Jupiter, leading to the search for Uranus. The orbit of the asteroid Ceres fitted perfectly, and for a while the law was all the rage, but Ceres’ diminutive size, even in conjunction with other asteroids, undermined the rule and Neptune’s orbit is unsuitably close. At least one astronomical journal now refuses to publish papers relating to the topic.

However Tim Bovaird, a PhD student at the Australian National University’s Planetary Science Institute, has investigated all the star systems known to have four or more planets and found in most cases there does indeed seem to be a geometric pattern to their locations, similar to Bode’s Law. The discovery was published in Monthly Notices of the Royal Astronomical Society.

“There are 68 known star systems with at least four planets, 60 from the Kepler Space Telescope,” Bovaird says. “Kepler’s planets are not included unless we have seen them pass in front of the star at least three times, so all have periods of less than 100 days.”

The light curves of stars become more complex with additional planets, making it increasingly difficult to identify smaller planets. However, Bovaird says that if we know where we should be looking it can be easier to pick a signal out of the noise.

“We published a preliminary version of the paper in April and predicted one star would have a planet with an orbit of 16.8 days and a size of less than 1.6 Earth masses,” Bovaird says. “Someone has rechecked the data and found something with 1.2 Earth masses orbiting in 16.53 days.” Bovaird predicts this would be the maximum size on the basis that larger objects would have been identified already.

A US PhD student has claimed in unpublished work to have found five planets in gaps Bovaird identified.

Star systems with very close planets appear to follow the relationship most closely. Bovaird has sought a basis for the location of the innermost planet, saying: “We tested the size and temperature of the star, but didn’t find anything conclusive.”

Several of Bovaird’s predictions for missing planets would locate them at a distance from their star where liquid water could exist.