An expression for the nodal period correction introduced by earth oblateness /J2/

To ensure payload compatability on shared Shuttle flights, the launch windows for each of the constituent payloads must be available for long-range planning - when neither the time of day nor the time of year of the Shuttle launch is known. A tool for producing graphs of launch opportunities as a function of time of day and time of year has developed in the Interactive Graphics Orbit Selection (IGOS) program - an interactive graphics program. The nodal period is an essential quantity for the analysis leading to the launch windows. Expressions for the nodal period which were found in the literature differed from results of detailed trajectory calculations by an amount greater than first order in J2. In this paper an expression for the nodal period correct to 1st order in J2 is derived. Expressions correct to 2nd order in J2, to 1st order in J3 through J6, and the correction introduced by atmospheric drag are also presented. All expressions are provided with dependence on argument of perigee and averaged over argument of perigee.