THE ROCHE COORDINATES AND THEIR USE IN CELESTIAL MECHANICS OR HYDRODYNAMICS,

Abstract

The air of the report will be to introduce a new system of curvilinear coordinates--hereafter referred to as Roche coordinates--in which spheres of constant radius are replaced by equipotential surfaces of a rotating gravitational dipole (which consists of two discrete points of finite mass, revolving around their common center of gravity); while the remaining coordinates are orthogonal to the equipotentials. It will be shown that the use of such coordinates offers a new method of approach to the solution of certain problems of particle dynamics (such as, for instance, the construction of certain types of trajectories in the restricted problem of three bodies); as well as of the hydrodynamics of gas streams in close binary systems, in which the equipotential surfaces of their components distorted by axial rotation and mutual tidal interaction constitute essential boundary conditions. (Author)

Document Details

Document Type
Technical Report
Publication Date
Apr 01, 1969
Accession Number
AD0688245

Entities

People

  • Zdenek Kopal

Organizations

  • Boeing

Tags

DTIC Thesaurus Topics

  • Boundaries
  • Celestial Mechanics
  • Center Of Gravity
  • Construction
  • Dynamics
  • Gravity
  • Hydrodynamics
  • Mechanics
  • Orbits
  • Particles
  • Physics
  • Rotation
  • Trajectories

Fields of Study

  • Physics

Readers

  • Fluid Dynamics.
  • Graph Algorithms and Convex Optimization.