UNIFIED ANALYTICAL SOLUTIONS TO 2-BODY PROBLEMS WITH DRAG

The two-body problem with a generalized Stokes drag is discussed. The drag force is proportional to the product of the velocity vector and t he inverse square of the distance. The generalization consists of allo wing two different proportionality constants for the radial and the tr ansverse components of the force. Under the 'generalized Robertson tra nsformation', the equation of the orbit takes the form of the Lommel e quation and admits solutions in terms of Bessel and Lommel functions. The exact, analytical solutions for this type of drag reveal a paradox ical effect of increasing eccentricity for all trajectories. The Poynt ing-Robertson drag and Poynting-Plummer-Danby problems are discussed a s particular cases of the general solution.