  In the past few years, the number of confirmed planets has grown above 2000.
It is clear that they represent a diversity of structures not seen in our own
solar system. In addition to very detailed interior modeling, it is valuable to
have a simple analytical framework for describing planetary structures.
Variational principle is a fundamental principle in physics, entailing that a
physical system follows the trajectory which minimizes its action. It is
alternative to the differential equation formulation of a physical system.
Applying this principle to planetary interior can beautifully summarize the set
of differential equations into one, which provides us some insight into the
problem. From it, a universal mass-radius relation, an estimate of error
propagation from equation of state to mass-radius relation, and a form of
virial theorem applicable to planetary interiors are derived.
