Coordinate frame adopted for deriving the semi-analytic model of tail I. The frame is centred at the star cluster (magenta circle), and the cluster remains at rest in the frame (the frame orbits the Galaxy). The coordinate x- and y-axes, as indicated by thick black arrows, follow the usual convention where the x-axis points towards the galactic anticentre and the y-axis points in the direction of the orbit. The cluster orbits the Galactic centre at radius R₀, which corresponds to x = 0 (thick blue line). The green arrow represents the initial trajectory of a star escaping the cluster. After escaping the cluster, the star moves on the red epicycle of semi-minor axis X, semi-major axis Y, and with guiding centre orbiting at Galactic radius R_g, which corresponds to x = X sin α in the adopted coordinates (thin blue line). The meaning of the escape angle α is shown by the blue curved arrow.