Values of the barycentric distance as a function of the velocity parameter 0.5 Myr (black), 1 Myr (violet), 3 Myr (blue), and 5 Myr (green) into the past (left panel) and future (right panel) for 500 control orbits of P/2019 LD₂ (ATLAS). The velocity parameter is the difference between the barycentric and escape velocities at the computed barycentric distance in units of the escape velocity. Positive values of the velocity parameter identify control orbits that could be the result of capture (left panel) or lead to escape (right panel). The thick black line corresponds to the aphelion distance, a (1 + e), limiting casee = 1, that defines the domain of dynamically old comets with a⁻¹ > 2.5 × 10⁻⁵ au⁻¹ (see Królikowska & Dybczyński 2017); the thick red line indicates the radius of the Hill sphere of the solar system (e.g., Chebotarev 1965).