Spin-Orbit Evolution of Mercury Revisited

Abstract

Although it is accepted that the significant eccentricity of Mercury (0.206) favours entrapment into the 3:2 spin orbit resonance, open are the questions of how and when the capture took place. A recent work by Makarov (Makarov, V.V. [2012]. Astrophys. J., 752, 73) has proven that trapping into this state is certain for eccentricities larger than 0.2, provided we use a realistic tidal model based on the Darwin Kaula expansion of the tidal torque. While in Ibid. a Mercury-like planet had its eccentricity fixed, we take into account its evolution. To that end, a family of possible histories of the eccentricity is generated, based on synthetic time evolution consistent with the expected statistics of the distribution of eccentricity. We employ a model of tidal friction, which takes into account both the rheology and self-gravitation of the planet. As opposed to the commonly used constant time lag (CTL) and constant phase lag (CPL) models, the physics-based tidal model changes dramatically the statistics of the possible final spin states. First, we discover that after only one encounter with the spin orbit 3:2 resonance this resonance becomes the most probable end-state. Second, if a capture into this (or any other) resonance takes place, the capture becomes final, several crossings of the same state being forbidden by our model. Third, within our model the trapping of Mercury happens much faster than previously believed: for most histories, 10 20 Myr are sufficient. Fourth, even a weak laminar friction between the solid mantle and a molten core would most likely result in a capture in the 2:1 or even higher resonance, which is confirmed both semi-analytically and by limited numerical simulations.

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Document Details

Document Type
Technical Report
Publication Date
Jun 23, 2014
Accession Number
ADA619297

Entities

People

  • Benoit Noyelles
  • Julien Frouard
  • Michael Efroimsky
  • Valeri V. Makarov

Organizations

  • United States Naval Observatory

Tags

Communities of Interest

  • Advanced Electronics
  • Energy and Power Technologies
  • Space

DTIC Thesaurus Topics

  • Computational Science
  • Differential Equations
  • Equations
  • Frequency
  • Gaussian Distributions
  • Moment Of Inertia
  • Momentum
  • Orbits
  • Personal Information Managers
  • Planets
  • Probability
  • Shape
  • Simulations
  • Solar System
  • Specific Heat
  • Statistical Analysis
  • Statistics

Fields of Study

  • Physics

Readers

  • Quantum spin resonance or Electron Paramagnetic Resonance spectroscopy.
  • Space Exploration and Orbital Mechanics.
  • Systems Analysis and Design

Technology Areas

  • Space
  • Space - Orbital Debris