Tidal Dissipation in a Homogeneous Spherical Body. 1. Methods

Abstract

A formula for the tidal dissipation rate in a spherical body is derived from first principles to correct some mathematical inaccuracies found in the literature. The development is combined with the Darwin Kaula formalism for tides. Our intermediate results are compared with those by Zschau and Platzman. When restricted to the special case of an incompressible spherical planet spinning synchronously without libration, our final formula can be compared with the commonly used expression from Peale & Cassen. However, the two turn out to differ, as in our expression the contributions from all Fourier modes are positive-definite, which is not the case with the formula from Peale & Cassen. Examples of the application of our expression for the tidal damping rate are provided in the work by Makarov & Efroimsky (Paper II) published back to back with the current paper.

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Document Details

Document Type
Technical Report
Publication Date
Nov 01, 2014
Accession Number
ADA619298

Entities

People

  • Michael Efroimsky
  • Valeri V. Makarov

Organizations

  • United States Naval Observatory

Tags

Communities of Interest

  • Energy and Power Technologies
  • Space

DTIC Thesaurus Topics

  • Boundaries
  • Computational Fluid Dynamics
  • Computational Science
  • Dissipation
  • Employment
  • Equations
  • Fluid Dynamics
  • Fourier Series
  • Frequency
  • Integrals
  • Language
  • Legendre Functions
  • Literature
  • Physical Properties
  • Planetary Sciences
  • Rheology
  • Solar System

Readers

  • Calculus or Mathematical Analysis
  • Space Exploration and Orbital Mechanics.