Application of the Lambert Problem to Inverse-Square Gravity

Abstract

The Lambert Problem is to determine correlated velocity, v(sub c), given initial position (at release), r(sub 1), to the target position, r(sub 2), in a specified time, t(sub f). Correlated velocity, v(sub c) can be determined by employing an iterative procedure that utilizes the Newton-Raphson method. Three candidates for the iteration variable are considered. Equations for an elliptical trajectory in terms of each of the iteration variables are derived. Equations for hyperbolic and parabolic trajectories are then deduced, and it is demonstrated how the type of trajectory can be determined from the given parameters.

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Document Details

Document Type
Technical Report
Publication Date
Dec 01, 2003
Accession Number
ADA451778

Entities

People

  • Isaac Sofair

Organizations

  • Naval Surface Warfare Center

Tags

Communities of Interest

  • Weapons Technologies

DTIC Thesaurus Topics

  • Abstracts
  • Angular Momentum
  • Ballistic Missiles
  • Computations
  • Coordinate Systems
  • Equations
  • Escape Velocity
  • Flight
  • Flight Paths
  • Gravitational Fields
  • Gravity
  • Iterations
  • Metal Matrix Composites
  • Submarine Launched Ballistic Missiles
  • Surface Warfare
  • Trajectories
  • Weapons

Fields of Study

  • Mathematics
  • Physics

Readers

  • Space Exploration and Orbital Mechanics.
  • Statistical inference.