Orbit projection for an example BH-LC with ﹩{M}_{\mathrm{BH}}=10\,{M}_{\odot }﹩, ﹩{M}_{\mathrm{LC}}=5\,{M}_{\odot }﹩, ﹩{a}_{\mathrm{LC}}=37.28\,\mathrm{au}﹩, and Ecc = 0.6. The solid black line shows the original orbit, with no prescribed orientation. The dashed line shows the projected size of the same orbit with binary orientation given by ﹩i=45\,\deg ﹩, ﹩{\rm{\Omega }}=171.9\,\deg ﹩, and ﹩\omega =257.8\,\deg ﹩. The dotted line shows the projected semimajor axis ﹩{a}_{\mathrm{LC},\mathrm{project}}﹩.