Determination of the velocity of an emitter in spaces with affine connections and metrics

TL;DR

This paper presents a kinematic method to determine the velocity and acceleration of an emitter in space-time with affine connections and metrics by analyzing frequency shifts caused by Doppler and Hubble effects, without relying on dynamic models.

Contribution

It introduces a purely kinematic approach to measure relative velocities and accelerations of astronomical objects using frequency shift variations, independent of dynamic assumptions.

Findings

Velocity and acceleration can be directly determined from frequency shift variations.

Method applies to various space-time models with affine connections and metrics.

Results are obtained without considering dynamic causes of the effects.

Abstract

Doppler effect and Hubble effect in different models of space-time related to the space-time velocity of an observer are considered. The Doppler effect and Doppler shift frequency parameter are connected with the kinematic characteristics of the relative velocity and the relative acceleration of the emitter with respect to the observer (detector). The Hubble effect and Hubble shift frequency parameter are considered in analogous way. It is shown that by the use of the variation of the shift frequency parameter during a time period, considered locally in the proper frame of reference of an observer, one can directly determine the radial (centrifugal, centripetal) relative velocity and acceleration as well as the tangential (Coriolis) relative velocity and acceleration of an astronomical object moving relatively to the observer. All results are obtained on purely kinematic basis without taking into account the dynamic reasons for the considered effect. PACS numbers: 98.80.Jk; 98.62.Py; 04.90.+e; 04.80.Cc