The Adventures of the Rocketeer: Accelerated Motion Under the Influence of Expanding Space

TL;DR

This paper explores how cosmological expansion affects accelerated interstellar travel, highlighting the challenges of navigation over vast distances and the conditions under which motion resembles Newtonian gravity.

Contribution

It provides a detailed analysis of accelerated motion in expanding universes, emphasizing the impact of cosmological parameters on intergalactic navigation and travel duration.

Findings

Expansion increases navigation difficulty over intergalactic distances.

Small uncertainties in cosmological parameters cause large deviations in trajectories.

Accelerated motion can appear Newtonian under small acceleration conditions.

Abstract

It is well known that interstellar travel is bounded by the finite speed of light, but on very large scales any rocketeer would also need to consider the influence of cosmological expansion on their journey. This paper examines accelerated journeys within the framework of Friedmann- Lemaitre-Robertson-Walker universes, illustrating how the duration of a fixed acceleration sharply divides exploration over interstellar and intergalactic distances. Furthermore, we show how the universal expansion increases the difficulty of intergalactic navigation, with small uncertainties in cosmological parameters resulting in significantly large deviations. This paper also shows that, contrary to simplistic ideas, the motion of any rocketeer is indistinguishable from Newtonian gravity if the acceleration is kept small.