This paper considers the restricted two-body problem with atmospheric drag. A simple formula is presented that approximates the atmospheric density from raw data, replaces previous models, and is amenable to closed-form solution of the orbit equation for high tangential speeds. A procedure for subdividing an altitude interval and calculating the parameters of the formula over each subinterval leads to highly improved accuracy in the solutions and compares favorably with numerical integration. To validate our model we compare it with the trajectory and flight time of a satellite in an exponential atmosphere starting from a near-circular orbit at 7120 km from the Earth's center.
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