Navigation in curved space-time

@article{Bahder2001NavigationIC,
  title={Navigation in curved space-time},
  author={Thomas B. Bahder},
  journal={American Journal of Physics},
  year={2001},
  volume={69},
  pages={315-321}
}
  • T. Bahder
  • Published 18 January 2001
  • Physics
  • American Journal of Physics
A covariant and invariant theory of navigation in curved space–time with respect to electromagnetic beacons is written in terms of J. L. Synge’s two-point invariant world function. Explicit equations are given for navigation in space–time in the vicinity of the Earth in Schwarzschild coordinates and in rotating coordinates. The restricted problem of determining an observer’s coordinate time when his or her spatial position is known is also considered. 

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References

SHOWING 1-10 OF 35 REFERENCES

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

Fermi coordinate transformation under baseline change in relativistic celestial mechanics

A relativistic description for the transformation under a change of baseline between the Fermi coordinates associated to two nonrotating local reference frames is carried out by using techniques

Relativistic theory for picosecond time transfer in the vicinity of Earth

Abstract : The problem of light propagation is treated in a geocentric reference system with the goat of ensuring picosecond accuracy for time transfer techniques using electromagnetic signals in the

General relativistic corrections to the Sagnac effect

The difference in travel time of corotating and counterrotating light waves in the field of a central massive and spinning body is studied. The corrections to the special relativistic formula are

The gravity field of the Earth

  • D. King-hele
  • Geology, Physics
    Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences
  • 1980
In recent years the Earth’s gravitational field has been determined with continually improving accuracy, by using hundreds of thousands of observations of Earth satellites, chiefly optical, laser and

The problem of n bodies in general relativity theory

1. In a recent investigation of the problem of two bodies in general relativity theory, Prof. Levi-Civita (1937 b ) has reached the conclusion that the centre of gravity has a secular acceleration in

GENERAL RELATIVISTIC SATELLITE ASTROMETRY. I. A NON-PERTURBATIVE APPROACH TO DATA REDUCTION

A general relativistic scenario is utilized to build a non-perturbative model, in Schwarzschild metric, for the rep- resentation of observed angles among star pairs. This model is then applied to an

On the world function of the Schwarzschild field

The representation of the world function Ω of the Schwarzschild field as a power series is investigated. Initially we concern ourselves with a neighborhood of the event horizon. The symmetries of the

``Sagnac'' effect: A century of Earth-rotated interferometers

The earliest prediction of the Sagnac effect, and of the possibility of detecting the Earth’s rotation with an interferometer of square kilometer area, is by Lodge (1893, 1897). We illustrate the

Gravity field determination with GOCE and GRACE