Oblate-Earth Effects on the Calculation of Ec During Spacecraft Reentry

The bulge in the Earth at its equator has been shown to lead to a clustering of natural decays biased to occur towards the equator and away from the orbit's extreme latitudes. Such clustering must be considered when predicting the Expectation of Casualty (Ec) during a natural decay because of the clustering of the human population in the same lower latitudes. This study expands upon prior work, and formalizes the correction that must be made to the calculation of the average exposed population density as a result of this effect. Although a generic equation can be derived from this work to approximate the effects of gravitational and atmospheric perturbations on a final decay, such an equation averages certain important subtleties in achieving a best fit over all conditions. The authors recommend that direct simulation be used to calculate the true Ec for any specific entry as a more accurate method. A generic equation is provided, represented as a function of ballistic number and inclination of the entering spacecraft over the credible range of ballistic numbers.