The time-dependent Kepler problem and its solution via the time-dependent harmonic oscillator and Ermakov invariants

Abstract We present a method for solving certain time-dependent Kepler problems using the Ermakov-Lewis invariants of the associated time-dependent harmonic oscillator problem. We also show that both the time-dependent harmonic oscillator and the Kepler problems can be further transformed in to time-independent problems. We obtain explicit expressions for the invariants for the time-dependent Kepler system, as well as expressions for the equation of the orbit and the Laplace-Runge-Lenz vector. Finally, we present some examples of time-dependent Kepler problems where the method is used.