What is the maximum radius of cold planets?
arXiv:2509.07048
Abstract
Planets have maximum radii close to that of Jupiter. Qualitatively, the reason for this maximum size is that, as one adds mass, the force of gravity becomes sufficiently strong to cause the radius to decrease. We show that this effect can be understood quantitatively using a simple variational principle very similar to that used to compute the size of the hydrogen atom.
Accepted for publication in American Journal of Physics