Fermi Coordinates of an Observer Moving in a Circle in Minkowski Space: Apparent Behavior of Clocks

Abstract

Space-time coordinate transformations valid for arbitrarily long coordinate time are derived from global Minkowski coordinates to the Fermi coordinates of an observer moving in a circle in three-dimensional space. The metric for the Fermi coordinates is calculated directly from the tensor transformation rule. The Fermi coordinates are used in an examination (from the observer's reference frame) of the detailed behavior of ideal clocks. A complicated relation exists between Fermi coordinate time and proper time on stationary clocks (in the Fermi frame) and between proper time on satellite clocks that orbit the observer. For portable clocks that orbit the Fermi coordinate origin, an orbital Sagnac-like effect exists. The coordinate speed of light is isotropic but is periodic in time and varies with Fermi coordinate position. In a numerical illustration of the magnitudes of these kinematic effects, this report uses parameters relevant to clocks carried aboard satellites orbiting the Earth.

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Document Details

Document Type
Technical Report
Publication Date
May 01, 2000
Accession Number
ADA379965

Entities

People

  • Thomas B. Bahder

Organizations

  • United States Army Research Laboratory

Tags

Communities of Interest

  • Air Platforms
  • Space

DTIC Thesaurus Topics

  • Abstracts
  • Artificial Satellites
  • Clocks
  • Coordinate Systems
  • Difference Frequency
  • Differential Equations
  • Equations
  • Frequency
  • Military Research
  • Minkowski Space
  • Observers
  • Orbits
  • Power Series
  • Rotation
  • Stationary
  • Three Dimensional
  • Time Intervals

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Fluid Dynamics.
  • Geodesy

Technology Areas

  • Space
  • Space - Orbital Debris