Sensitivity of Orbit Predictions to Density Variability

This paper summarizes the first stage in a research effort designed to obtain a quantitative knowledge and deeper understanding of how prediction error depends on density variability. Initial numerical simulations are performed to obtain a detailed understanding of the theoretical effects of density variations on satellite orbit predictions. The level of knowledge of density variations needed for various orbit prediction requirements is quantified, and results are compiled focusing on the effects of various horizontal wavelengths in the atmosphere. The information obtained in this analysis lays the foundation for the next step of connecting the simulation results to the prediction of actual satellite ephemerides. Nomenclature A = area, m 2 Ap = average daily planetary geomagnetic index a = acceleration, m=s 2 adrag = acceleration due to drag, m=s 2 ap = 3 h planetary geomagnetic index Cd = drag coefficient F = force, N f = fraction of the nominal density at a specified altitude I = impulse, kg m=s m = mass, kg P = period of the spacecraft computed from the initial conditions without taking drag into account, h tf = final time, s ti = initial time, s V = velocity, m=s Va = velocity magnitude relative to the atmosphere, m=s Va = velocity relative to the atmosphere, m=s _ x = x component of the velocity in the inertial frame, m=s _ y = y component of the velocity in the inertial frame, m=s _ z = z component of the velocity in the inertial frame, m=s � V = change in velocity, m=s _ � = rate of the Earth’s rotation, rad=s � = atmospheric density, kg=m 3 � nom = nominal density at a specified altitude, kg=m 3

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