General expansion of time transfer functions in optical spacetime

TL;DR

This paper extends the recursive determination of time transfer functions to Gordon's optical spacetime, enabling precise modeling of light propagation in moving dielectric media, with applications to Earth-based experiments.

Contribution

It provides a method to compute time transfer functions to any order in Gordon's optical spacetime, including integral forms for gravitational and refractive effects.

Findings

Derived exact integral forms of transfer functions in optical spacetime

Identified the light-dragging effect due to Earth's atmosphere as near visibility threshold

Provided post-linear approximation expressions for practical applications

Abstract

When dealing with highly accurate modeling of time and frequency transfers into arbitrarily moving dielectrics medium, it may be convenient to work with Gordon's optical spacetime metric rather than the usual physical spacetime metric. Additionally, an accurate modeling of the geodesic evolution of observable quantities (e.g., the range and the Doppler) requires us to know the reception or the emission time transfer functions. In the physical spacetime, these functions can be derived to any post-Minkowskian orders through a recursive procedure. In this work, we show that the time transfer functions can be determined to any order in Gordon's optical spacetime as well. The exact integral forms of the gravitational, the refractive, and the coupling contributions are recursively derived. The expression of the time transfer function is given within the post-linear approximation assuming a stationary optical spacetime covered with geocentric celestial reference system coordinates. The light-dragging effect due to the steady rotation of the neutral atmosphere of the Earth is found to be at the threshold of visibility in many experiments involving accurate modeling of the time and frequency transfers.