Orbit determination for next generation space clocks

TL;DR

This paper analyzes the orbit determination requirements for next-generation space clocks, demonstrating that achievable orbit accuracy can meet the stringent needs of advanced relativistic timekeeping applications.

Contribution

It provides a relativistic model for orbitography requirements, showing that modest orbit accuracy suffices for next-generation space clocks, facilitating their use in fundamental physics and geodesy.

Findings

Orbit accuracy requirements are less stringent than naive estimates suggest.

Relativistic modeling enables practical orbit determination for space clocks.

Results are applicable to all future space clocks in similar missions.

Abstract

Over the last decade of the 20th century and the first few years of the 21st, the uncertainty of atomic clocks has decreased by about two orders of magnitude, passing from the low 10^-14 to below 10^-16, in relative frequency . Space applications in fundamental physics, geodesy, time/frequency metrology, navigation etc... are among the most promising for this new generation of clocks. Onboard terrestrial or solar system satellites, their exceptional frequency stability and accuracy makes them a prime tool to test the fundamental laws of nature, and to study gravitational potentials and their evolution. In this paper, we study in more detail the requirements on orbitography compatible with operation of next generation space clocks at the required uncertainty based on a completely relativistic model. Using the ACES (Atomic Clock Ensemble in Space) mission as an example, we show that the required accuracy goal can be reached with relatively modest constraints on the orbitography of the space clock, much less stringent than expected from "naive" estimates. Our results are generic to all space clocks and represent a significant step towards the generalised use of next generation space clocks in fundamental physics, geodesy, and time/frequency metrology.