FAMILIES OF PERIODIC ORBITS CONTINUED IN REGULARIZING COORDINATES. THE HECUBA GAP AND THE HILDA GROUP,

Abstract

The first paper contained in this note documents the numerical method which is the tool used extensively to extract the physical conclusions very concisely reported in the second paper. A predictor-corrector algorithm is proposed for continuing analytically families of periodic orbits beyond collision trajectories in the restricted problem of three bodies. It is based on Hill's equation for normal variations in Thiele's regularizing coordinates. The direct planetary orbits of the first kind and the Hilda family both bifurcate out of the family of retrograde planetary orbits of the first kind by triplication of the same orbit. The branching occurs in the Hecuba gap. The period curve of the Hilda family shows a peak indicative of invariant tori of quasi-periodic motions inside which could be trapped the Hilda group of asteroids. (Author)

Document Details

Document Type
Technical Report
Publication Date
Sep 01, 1968
Accession Number
AD0680810

Entities

People

  • Andre Deprit
  • Julian Palmore

Organizations

  • Boeing

Tags

DTIC Thesaurus Topics

  • Algorithms
  • Asteroids
  • Collisions
  • Differential Equations
  • Equations
  • Intercept Trajectories
  • Mathematics
  • Partial Differential Equations
  • Trajectories

Readers

  • Calculus or Mathematical Analysis
  • Nuclear Civil Defense.
  • Space Exploration and Orbital Mechanics.

Technology Areas

  • Space
  • Space - Orbital Debris