Sorry, Pluto lovers. A recently published paper by Jean-Luc Margot of UCLA (as a Star Trek Next Generation fan, I had to give the author’s full name) proposes a mathematically rigorous way to define a planet. Pluto, for all its undeniably fascinating appeal—it just doesn’t make the cut.
The official body tasked with naming and defining astronomical objects is the International Astronomical Union (IAU), of which most people had never heard until 2006. That was when the IAU gave official sanction to what astronomers had known for years, that Pluto was qualitatively distinct from what we now think of as “classical” planets: Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, and Neptune. The decision prompted millions of people to mostly good-natured outrage. You mean my fourth-grade teacher lied to me? Why can’t those scientists get their story straight? It didn’t help that the proposed definition was both vague and confusing. Here is the original IAU definition.
“A planet is a celestial body that (a) is in orbit around the Sun, (b) has sufficient mass for its self-gravity to overcome rigid body forces so that it assumes a hydrostatic equilibrium (nearly round) shape, and (c) has cleared the neighborhood around its orbit.”
Well, that first criterion is simple enough and explains why the moon (which orbits Earth) is not considered a planet. It does exclude any possible planets that orbit other stars, but we’ll get back to that.
The second criterion is hard to judge. How “nearly” round does the planet have to be? No one would argue against calling Jupiter a planet, but its fluid composition and rapid rotation flatten it at the poles and bulge it at the equator. It is certainly not perfectly round! The dashed line in the image below is a perfect circle.
The third criterion is even worse. To quote from Margot’s article:
“It must be emphasized at the outset that a planet can never completely clear its orbital zone, because gravitational and radiative forces continually perturb the orbits of asteroids and comets into planet-crossing orbits. What the IAU intended is not the impossible standard of impeccable orbit clearing; rather the standard is analogous to what Soter (2006, 2008) described as a dynamical-dominance criterion. In this article, we use the IAU orbit-clearing language even though the dynamical-dominance language seems less prone to misinterpretation.”
What Margot proposes begins with that third criterion. What does it mean for a planet to clear its orbit, or alternatively, to dynamically dominate its orbit? He looks at how long it would take for planet to clear any smaller bodies to a certain distance away, a distance related to the planet’s Hill radius. This can be thought of as the planet’s sphere of gravitational influence. In this image, Earth orbits within the sun’s Hill sphere, while the moon orbits within the Hill sphere of the Earth.
If the time required for a body orbiting a star to clear out its orbit is less than the lifetime of the star—it’s a planet. The math reduces to a simple ratio of masses.
Π = Mbody/Mclear
where Mbody is the mass of the potential planet, and Mclear is the mass required to clear its orbit. Any value greater than one makes the body a planet. For the solar system, the eight planets are clearly distinguished from dwarf planets Pluto, Ceres, and Eris. The horizontal line is a Π value of one.
When applied to exoplanets (planets orbiting stars other than the sun), the results are even clearer.
Margot notes that planets massive enough to clear their orbits are almost certainly round, and that judging roundness is difficult at best. He leaves that criterion out, and so here is his proposed new definition:
“A planet is a celestial body that (a) is in orbit around one or more stars or stellar remnants, (b) has sufficient mass to clear [or dynamically dominate] the neighborhood around its orbit, i.e., Π ≥ 1, (c) has a mass below 13 Jupiter masses, a nominal value close to the limiting mass for thermonuclear fusion of deuterium.”
That last criterion (c) cuts off at the threshold for a brown dwarf, the lowest mass object we might more properly define as a star. This new definition is certainly more rigorous than the 2006 effort. I hope it catches on!