Towards a General Theory of GPS Inter-Satellite Communications Between Moving Satellites on Arbitrary Space Trajectories, Accounting for General Relativity Effects
Abstract
In previous publications it has been shown that it is possible to calculate (in terms of zero and higher order elliptic integrals) the propagation time of a signal, emitted by a satellite, moving along a plane (or space-determined) Kepler orbit. 2. By means of a method of intersecting null cones, the propagation time was found for the case, when the signal is intercepted by a second satellite. The present paper has the purpose to generalize the above approach for satellites, exchanging signals and moving along arbitrary space trajectories. Previously, the important physical notions of space-time distance and geodesic distance (only positive and greater than the Euclidean distance) have been introduced. It will be shown that these notions can be introduced also for the case of general motion of the satellites, and more importantly, they have the same physical meaning. A generalization of the s. c. ranging equation for the case of a curved space-time has been proposed. It has been proved that the geodesic distances of propagation of the signal in the forward and in the backward directions are not equal. The physical reason is hidden in the non-inertial reference systems of motion of the two satellites. Thus, signal propagation in non-inertial systems is an irreversible process, meaning that the propagation times in the two directions is different. A mathematical model has been created for the forward and subsequent backward propagation of the signal between two moving satellites in a gravitational field. Such a general theory of inter-satellite communications is the first step towards constructing a modern theory for optimal propagation of signals in an integrated dense satellite communication network systems, such as the current 6G and future 7G systems.
Related
- Tracing individual knowledge trajectories in a changing field: the case of general relativity and gravitation
- Keep it sparse: neural spiking demodulator in event optical camera communications
- Signal Pre-Equalizer for Fluorescent Antennas in Optical Wireless Communications
- Intelligent intrinsic physical layer security: joint authentication and encryption for data center communications
- An inadequate over-parameterized Mössbauer spectral analysis for the mistaken detection of surface FeIV=O, in Nature Communications 16, 7642 (2025)
BibTeX
@misc{dimitrov2026towards,
title = {{Towards a General Theory of GPS Inter-Satellite Communications Between Moving Satellites on Arbitrary Space Trajectories, Accounting for General Relativity Effects}},
author = {Bogdan G. Dimitrov},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.26879},
eprint = {2610.26879},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.26879},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Towards a General Theory of GPS Inter-Satellite Communications Between Moving Satellites on Arbitrary Space Trajectories, Accounting for General Relativity Effects
AU - Bogdan G. Dimitrov
PY - 2026
DA - 2026/10/08
PB - arXiv
DO - 10.48550/arxiv.2610.26879
UR - https://arxiv.org/abs/2610.26879
AB - In previous publications it has been shown that it is possible to calculate (in terms of zero and higher order elliptic integrals) the propagation time of a signal, emitted by a satellite, moving along a plane (or space-determined) Kepler orbit. 2. By means of a method of intersecting null cones, the propagation time was found for the case, when the signal is intercepted by a second satellite. The present paper has the purpose to generalize the above approach for satellites, exchanging signals and moving along arbitrary space trajectories. Previously, the important physical notions of space-time distance and geodesic distance (only positive and greater than the Euclidean distance) have been introduced. It will be shown that these notions can be introduced also for the case of general motion of the satellites, and more importantly, they have the same physical meaning. A generalization of the s. c. ranging equation for the case of a curved space-time has been proposed. It has been proved that the geodesic distances of propagation of the signal in the forward and in the backward directions are not equal. The physical reason is hidden in the non-inertial reference systems of motion of the two satellites. Thus, signal propagation in non-inertial systems is an irreversible process, meaning that the propagation times in the two directions is different. A mathematical model has been created for the forward and subsequent backward propagation of the signal between two moving satellites in a gravitational field. Such a general theory of inter-satellite communications is the first step towards constructing a modern theory for optimal propagation of signals in an integrated dense satellite communication network systems, such as the current 6G and future 7G systems.
ER -