Introduction

How could a space craft, tumbling through interstellar space, re-orientate itself? Or how can a spacecraft cruising towards another galaxy, make a mid-course trajectory correction to ensure it arrives accurately at its destination?

Project Breakthrough Starshot (2016)

These questions may seem like distant problems set arbitrarily far into the future, however, interstellar travel has been deemed at least possible by authors like Forward [10] and projects like Breakthrough Starshot aim to send light propelled nanocraft to Alpha Centuri within our lifetime (breakthroughinitiatives.org).

Spacecraft navigation systems of today rely upon precisely timed radio signals sent back and forth between the craft and the earth in order to triangulate the craft’s exact location. However, as humans seek to explore beyond our own solar system, this form of positioning becomes impractical due to the large communication delays and the very weak signals being received due to the vast distances involved. The ability to self localise, therefore, provides a significant benefit for any future interstellar or intergalactic mission.

Gravitational Waves (GW) were first predicted by Albert Einstein as a consequence of his general theory of relativity [1] and have been indirectly observed through the measurements of the orbits of binary pulsar systems. The first of these binary pulsar systems was discovered in 1974 by Hulse and Taylor [2] who were able to show that the orbit of the pulsars degraded precisely as predicted as a result of the energy lost due to relativistic gravitational-wave emission[3]. Direct measurement of gravitational waves occurred for the first time at the Laser Interferometer Gravitational-Wave Observatory (LIGO), on the 14th September 2015. The measured signal (GW150914) was the result of a binary black hole system coalescing to form a single black hole [4] and closely matched the wave function predicted by general relativity with a statistical significance greater than 5.1 Sigma [5] .

While the final stages of the merger event which resulted in the GW150914 measurement was short-lived (occurring over approximately 0.2s) [4] the emission of gravitational waves by this binary system had been occurring for millions of years prior, albeit, at much smaller amplitudes and frequencies. If the continuous emissions of gravitational waves can be detected at these lower amplitudes and frequencies, then their distance from the earth could be studied and their location in the sky determined.

It is therefore likely, that in time, a catalogue of gravitational wave emission sources will be created. If the location of these sources is well known (through years of study) then their signals could be used by spacecraft to determine their position relative to the various sources. This form of localization is advantageous because it can be done without any communication signals having to be sent back to the earth., which will be a requirement on any long-distance voyage. This form of localization is analogous to how vehicles can obtain their position through the trilateration of GPS radio signals here on Earth.