Abstract
The paper gives an exact vectorial solution to the Kepler problem. A vectorial regularization that linearizes the Kepler problem is given using a Sundman transformation. Closed form expressions describing the Keplerian motion are deduced. A unified approach to the classic Kepler problem is offered, by studying both rectilinear and non-rectilinear Keplerian motions with the same instrument. The approach is an elementary one and only simple vectorial computations are involved.
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