Navigation in Curved Space-Time

TL;DR

This paper develops a covariant, invariant framework for navigation in curved space-time using Synge's world function, providing explicit equations near Earth and addressing observer coordinate time determination.

Contribution

It introduces a novel covariant navigation theory in curved space-time utilizing Synge's invariant world function, with explicit equations for Earth-based scenarios.

Findings

Derived explicit navigation equations near Earth in Schwarzschild coordinates.

Formulated methods for determining observer coordinate time from known spatial positions.

Established a covariant, invariant approach applicable in curved space-time environments.

Abstract

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 their spatial position is known is also considered.