Changing Coordinates in the Context of Orbital Mechanics

Abstract

This note works through an example of switching between many coordinate systems using a modern matrix language that lends itself to describing arenas with multiple entities such as found in many Defence scenarios. To this end, it describes an example in planetary orbital theory, whose various Sun- and Earth-centred coordinate systems makes that theory a good test-bed for such an exposition of changing coordinates. In particular, we predict the look direction to Jupiter from a given place on Earth at a given time, highlighting the careful book-keeping that is required along the way. To avoid much of the rather antiquated jargon and notation that pervades orbital theory, we explain the first principles of 2-body orbital motion (Kepler's theory), beginning with Newton's laws and proving all the necessary expressions. The systematic and modern approach to changing coordinates described here can also be applied just as readily in contexts such as a Defence aerospace engagement, which follows the interaction of multiple entities that each carry their own coordinate system.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 2017
Accession Number
AD1027338

Entities

People

  • Don Koks

Organizations

  • Defence Science and Technology Group

Tags

Communities of Interest

  • Air Platforms
  • Cyber
  • Space

DTIC Thesaurus Topics

  • Artificial Satellites
  • Cartesian Coordinates
  • Celestial Mechanics
  • Computational Science
  • Computers
  • Coordinate Systems
  • Differential Equations
  • Electronic Warfare
  • Elliptical Orbits
  • Equations
  • Global Positioning Systems
  • Molecular Mechanics Methods
  • Orbital Elements
  • Orbital Inclination
  • Orbital Mechanics
  • Orbits
  • Perihelions

Readers

  • Computational Linguistics
  • Space Exploration and Orbital Mechanics.
  • Theoretical Analysis.

Technology Areas

  • Space
  • Space - Orbital Debris