ON DETERMINING THE RATIO BETWEEN THE AREA OF AN ELLIPTICAL SECTOR AND ITS TRIANGLE APPROXIMATION

Abstract

A fundamental problem in the estimation of satellite orbit parameters from two position measurements at different times is the computation of the area of an elliptical sector defined by the two observations. Gauss' Method estimates the ratio of the area of the elliptical sector to that of an approximating triangle by an iterative method. The convergence of this procedure is tested empirically by using various examples. In addition, four techniques by which these ratios may be approximated are compared with the method of Gauss and with each other. (Author)

Document Details

Document Type
Technical Report
Publication Date
May 18, 1961
Accession Number
AD0257640

Entities

People

  • E. Dubinsky
  • H.d. Fridman
  • R. Crittenden

Organizations

  • Massachusetts Institute of Technology

Tags

Communities of Interest

  • Space

DTIC Thesaurus Topics

  • Artificial Satellites
  • Computations
  • Convergence
  • Mathematics
  • Measurement
  • Observation
  • Orbits
  • Satellite Orbits
  • Spacecraft
  • Spacecraft Orbits
  • Triangles

Readers

  • Computational Modeling and Simulation
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Space Exploration and Orbital Mechanics.

Technology Areas

  • Space
  • Space - Orbital Debris