A major unsolved question in astrophysics is how merging binary black holes (BBHs) form. Different formation mechanisms have been proposed, but disentangling them from gravitational wave (GW) observations has proven dificult. In this talk, I propose a novel method of probing BBH formation by studying how the surrounding environment of a BBH directly influences the observed GW signal. Specifically, I will talk about BBHs in star clusters that form through interactions with a third BH. The centre-of-mass motion of the BBH around the third BH induces a phase shift onto the GW signal, which, if observed, would allow us to directly constrain the formation environment of the BBH. I will discuss our model of the phase shift, and its detectability prospects in the Einstein Telescope (ET) era. Will ET be able to observe this phase shift and what could that teach us about the astrophysical formation of BBHs?
