Variational Principle for Planetary Interiors

Journal Article · Thu Sep 15 00:00:00 EDT 2016 · The Astrophysical Journal (Online)

DOI:https://doi.org/10.3847/0004-637x/829/1/18· OSTI ID:1788263

Zeng, Li ^[1]; Jacobsen, Stein B. ^[2]

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1. Harvard Univ., Cambridge, MA (United States); Harvard College, President and Fellows of
2. Harvard Univ., Cambridge, MA (United States)

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. The 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 the variational principle to the planetary interior can beautifully summarize the set of differential equations into one, which provides us some insight into the problem. From this principle, a universal mass–radius relation, an estimate of the error propagation from the equation of state to the mass–radius relation, and a form of the virial theorem applicable to planetary interiors are derived in this work.

• Research Organization: Harvard Univ., Cambridge, MA (United States)
• Sponsoring Organization: Simons Foundation; USDOE National Nuclear Security Administration (NNSA)
• Grant/Contract Number: NA0001804; NA0002937
• OSTI ID: 1788263
• Alternate ID(s): OSTI ID: 22667424
• Journal Information: The Astrophysical Journal (Online), Journal Name: The Astrophysical Journal (Online) Journal Issue: 1 Vol. 829; ISSN 1538-4357
• Publisher: Institute of Physics (IOP)
• Country of Publication: United States
• Language: English

Related Subjects

79 ASTRONOMY AND ASTROPHYSICS
planets and satellites: composition
planets and satellites: fundamental parameters
planets and satellites: general
planets and satellites: interiors
planets and satellites: physical evolution
planets and satellites: terrestrial planets