A Priori Time of Flight Estimation for the Q-law

A computationally cheap estimate of the time of flight for orbital transfers performed using the Q-law is developed. The estimate depends only on the initial orbit of the spacecraft, the targeted orbital parameters, and spacecraft properties. The total Delta-v cost can also be estimated under the assumption of continuously-maintained thrust. The estimate is based on the proximity quotient function used in formulating the Q-law with units of time squared. Applying a scaling factor to the square root of a quantity similar to the proximity quotient evaluated at the initial orbit provides an estimate of the total time to reach the target orbit using a continuous-thrust maneuver, all without needing to compute the trajectory itself. A numerical Monte Carlo campaign with randomly sampled initial and target orbits suggests that the ratios of the estimated time of flight to the exact time of flight follow a log-normal distribution, meaning dispersion increases with longer missions. The error is small for short missions, making it useful for planning multiple-target rendezvous missions in Earth orbit.