Closed-Form Approximation of Revisit Rate for Low-Altitude Satellites

Abstract

For many applications of low-altitude spacecraft, it is important to know how often the spacecraft revisits a given target. Average revisits per day can be calculated for a given scenario using astrodynamic software, but that approach can be tedious if a large number of cases are to be compared. This paper develops a closed-form, continuous, and piecewise differentiable function that gives average revisits per day as a function of orbit altitude, orbit inclination, target latitude, and minimum required elevation. The function is compared with the results of astrodynamic simulations and shown to be accurate to within 0.08 passes per day and 1% in almost all cases. It allows instant calculation of an excellent approximation of this important performance parameter and could be used as part of an optimization routine. The convenience and flexibility provided by this function are demonstrated in a series of charts showing passes per day as a function of one, two, and three variables. The function assumes a circular orbit; the sensitivity of the result to eccentricity is explored using astrodynamic simulations and is found to decrease by 5.3% as eccentricity increases to 0.07 for a typical case.