**The New Horizons** mission to Pluto revealed a world of breathtaking complexity, renewing calls for Pluto to be reinstated as a full-blown planet. But a mathematical formula devised by astronomer Jean-Luc Margot of the University of California in Los Angeles is snuffing out Pluto’s chances.

A key criterion to qualify as a planet is whether a body orbiting a star is capable of clearing other bodies out of its neighbourhood. Pluto was demoted to dwarf planet status in 2006 by the International Astronomical Union (IAU) because other bodies in the distant Kuiper Belt, including the dwarf planet Eris, skim its orbit.

A formula devised by Margot that was published on *Arxiv* in October says Pluto should remain a dwarf planet. Running Pluto’s numbers through the formula reveals a “striking” disparity between Pluto and the Solar System’s true planets, he says.

“[The formula] does a nice job of quantifying what that awkward phrase ‘clear your orbit’ means,” says Mike Brown, an astronomer at California Institute of Technology. Brown discovered Eris and has described himself as the man who “killed Pluto”. Margot’s formula demonstrates “the huge dichotomy between planets and dwarf planets,” Brown says.

Margot was motivated to develop the formula by his frustration with the current definition of a planet. According to the IAU a planet must fulfil three criteria: it must orbit a star, be large enough for its gravity to make it nearly round, and have cleared other bodies out of its orbit.

When applied to all exoplanets for which there is the data to do the calculation, Margot’s formula instantly classified 99% of them as planets.

Even for our Solar System that definition is a bit vague. “How round is round?” Margot asked at a November meeting of the American Astronomical Association’s Division of Planetary Sciences, in Maryland, where he presented his new formula. Should, for instance, the Earth’s peaks such as Mount Everest disqualify it?

The definition becomes even more problematic once you leave our Solar System.

With very few exceptions, exoplanets – planets orbiting stars other than our Sun – are too far away to see directly. Instead, most exoplanets are discovered indirectly by decoding signals in starlight – for example, the planet’s orbit around its star might give the star a slight wobble, or cause a periodic dimming as the planet passes in front. Such signals do not reveal the exoplanet’s shape, or whether it has cleared other objects from its neighbourhood.

Margot’s formula centres on a number he calls pi (nothing to do with the circumference of a circle) that describes the relationship between the candidate planet’s mass and the mass it would need to have cleared its neighbourhood of competing bodies. Margot acknowledges that a judgement call is required here — even the Earth’s path is sometimes crossed by comets and asteroids, for example.

Calculating Margot’s pi value takes only three parameters. The proposed planet’s mass, the mass of its star and the time it takes for it to orbit its star once. All three can be worked out from light coming from the exoplanet’s star.

Margot’s mathematical proofs show that if the pi value is 1.0 or more, the contender is big enough to clear all rivals from its path. It will also be big enough for its gravity to have forced it into a roughly spherical shape, says Margot.

When applied to all exoplanets for which there is the data to do the calculation, Margot’s formula instantly classified 99% of them as planets. (We don’t know enough about the remaining ones to be able to calculate their pi value yet.)

One “body” failed to make the grade – Pluto. It wasn’t even close. Pluto’s pi value, 0.028, is at least three orders of magnitude smaller than that of the other eight planets in our Solar system. (Earth's pi value, for example, is 810.)

“Pluto is a fascinating body, but it clearly doesn’t belong with the [other] eight planets,” Margot says. “The sharp distinction suggests there is a fundamental difference in how these bodies formed.”

Margot's formula will be published in *Astronomical Journal*.

Also in *Cosmos*: Pluto, an enigma in close-up

Knocking on Pluto's door