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}
}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.
Figures from this paper
47 Citations
Mapping the spacetime metric with GNSS: a preliminary study
- Physics
- 2009
In order to do relativistic gravimetry one needs to define a system of null coordinates for a given constellation of satellites. We present here three methods in order to find the null coordinates of…
Post-Newtonian Equations of Motion for Inertial Guided Space APT Systems
- Physics
- 2015
The equations of motion derived in this paper are aimed to determine according to the post-Newtonian framework the relative motion of Earth satellites with respect to inertial guided space…
Relativity of GPS measurement
- Physics, Geology
- 2003
The relativity of Global Positioning System (GPS) pseudorange measurements is explored within the geometrical optics approximation in the curved space-time near Earth. A space-time grid for…
Relativistic location algorithm in curved spacetime
- PhysicsPhysical Review D
- 2022
In this article, we describe and numerically implement a method for relativistic location in slightly curved, but otherwise generic spacetimes. For terrestrial positioning in the context of Global…
GENERALIZED RADAR 4-COORDINATES AND EQUAL-TIME CAUCHY SURFACES FOR ARBITRARY ACCELERATED OBSERVERS
- Physics
- 2007
All existing 4-coordinate systems centered on the world-line of an accelerated observer are only locally defined, as for Fermi coordinates both in special and general relativity. As a consequence, it…
Simultaneity, radar 4 coordinates and the (3+1) point of view about accelerated observers in special relativity
- Physics, Mathematics
- 2003
After a review of the 1+3 point of view on non-inertial observers and of the problems of rotating reference frames, we underline that was is lacking in their treatment is a good global notion of…
Numerical modeling of a Global Navigation Satellite System in a general relativistic framework
- Physics
- 2010
Relativistic positioning: four-dimensional numerical approach in Minkowski space-time
- Physics
- 2012
We simulate the satellite constellations of two Global Navigation Satellite Systems: Galileo (EU) and GPS (USA). Satellite motions are described in the Schwarzschild space-time produced by an…
Relativistic Stereometric Coordinates from Relativistic Localizing Systems and the Projective Geometry of the Spacetime Manifold
- Physics
- 2014
Relativistic stereometric coordinates supplied by relativistic auto-locating positioning systems made up of four satellites supplemented by a fifth one are defined in addition to the well-known…
References
SHOWING 1-10 OF 35 REFERENCES
Fermi Coordinates of an Observer Moving in a Circle in Minkowski Space: Apparent Behavior of Clocks
- Physics
- 2000
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
- Physics
- 1991
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
- Physics
- 1994
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
- Physics
- 1998
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
- Geology, PhysicsPhilosophical 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
- Physics
- 1938
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
- Physics
- 1998
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
- Mathematics
- 1979
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
- Physics
- 1994
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…