Armitage (2020) defines planets as large bodies around stars not massive enough to have ever derived a substantial fraction of their luminosity from nuclear fusion. This implies a limit on the maximum mass of planets to be at the deuterium burning threshold, which is approximately (which consequently becomes the lower mass limit for brown dwarfs). Lower mass limit is harder to define, and much debate has happened to find an accurate definition. In the end, following three criteria were established at the 2006 IAU summit which killed Pluto’s status as a full-fledged planet:
Must have had enough self-gravity to attain a mostly spherical shape through hydrostatic equilibrium.
Have cleared its neighborhood.
Clearing of the neighborhood
Or dynamical dominance in other words has few formal criteria (discussed below) because the it never ever truly possible for a planetary-mass object to completely clear its orbit.
Stern-Levinson’s
is the measure of a body’s ability to scatter small masses out of its orbital region over a period of time equal to the age of the Universe. In other words, how many strong gravitational encounters should a small body experience with the candidate planet over some long time . To derive this heuristic value, Stern & Levison (2002) develop upon the work of Öpik (1951), who gave the probability of a small body passing sufficiently close to a planet, per orbit as
where
denotes the square of the target radius, is the impact parameter, is the semi-major axis of the planet, is the relative speed between planet and planetesimal when they are far enough apart that the planet’s gravity has not yet strongly bent the trajectory, , is the relative encounter speed expressed in the units of planet’s orbital speed , is the inclination between the planet’s and planetesimal’s orbital planes and is the radial component of the dimensionless relative velocity . For a hyperbolic encounter at deflection angle ,
where is the mass of the clearing body, its semi-major axis, and is a function of the orbital elements of the small body
Soter’s
Margot’s
Footnotes
Rogue planets may exist. But it is more appropriate to refer to them as planetary-mass objects. ↩