Left: Scaling parameter as a function of hardness. The edges are open to illustrate that any binary with, for example h > 10 has 𝒞 = 6. Right: Scatter plots for the fractional change in separation of binaries (top, panel b) and eccentricity (bottom, panel c), against the distance between the tertiary and binary centre-of-mass in units of the binary apoapsis. Only encounters with with a hardness of 0.01 <h≤ 0.10 are considered in this Figure. Blue (orange) dots correspond to encounters that change the binary separation with ≥ 1% (< 1%), where the black dotted lines show the 1% boundary and the black dash-dotted line the chosen value for the scaling parameter 6.