A Numerical Model of the Moon's Rotation.

Abstract

The differential equations for the Moon's rotation are derived in terms of Euler angles referenced to an inertial coordinate system. Also, the variational equations of the rotation with respect to six Euler angle initial conditions, the lunar J sub 2, the moment-of-inertia ratios Beta and Gamma, and the coefficients of the third and higher-degree gravity harmonics, are presented in detail. The equations of motion were integrated numerically within the framework of MIT's Planetary Ephemeris Program, and the initial conditions were adjusted to fit the libration angles given by the numerical LLB-5 model of J.G. Williams and others at JPL. The postfit rms orientation difference, after removal of a three-axis rotation to correct for lunar orbital ephemeris differences, was about 0.03 arcsec (selenocentric) over a six-year span. Neglected effects and anticipated improvements in our model are also discussed.

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Document Details

Document Type
Technical Report
Publication Date
Jul 25, 1977
Accession Number
ADA045591

Entities

People

  • Charles C. Counselman Iii
  • Irwin I. Shapiro
  • Robert W. King
  • Roger Cappallo

Organizations

  • Massachusetts Institute of Technology

Tags

Communities of Interest

  • Materials and Manufacturing Processes
  • Space

DTIC Thesaurus Topics

  • Accuracy
  • Air Force
  • Computational Science
  • Coordinate Systems
  • Differential Equations
  • Ephemerides
  • Equations
  • Equations Of Motion
  • Euler Angles
  • Jet Propulsion
  • Massachusetts
  • Molecular Mechanics Methods
  • Moment Of Inertia
  • Numerical Integration
  • Solar System
  • United States
  • Variational Equations

Fields of Study

  • Physics

Readers

  • Control Systems Engineering.
  • Space Exploration and Orbital Mechanics.

Technology Areas

  • Space
  • Space - Orbital Debris