Abstract In this report we study the symmetries that correspond to the conservation of the Runge-Lenz vector in the Kepler problem.In section 2 we use Noether's theorem to define a Runge-Lenz vector as a consequence of an invariance of the action integral.It's shown that such a vector exists for all central potentials. In section 3 we describe the Kepler problem in space-time.By choosing a nice parametrization we show that the equations of motion and the conservation of energy describe a harmonic oscillator with an extra derivative in four dimensions and a four dimensional sphere,respectively.From this we define a conserved tensor.The components of this tensor correspond to the Runge-Lenz vector and angular momentum. 1Abstract In this report we study the symmetries that correspond to the conservation of the Runge-Lenz vector in the Kepler problem. In section 2 we use Noether’s theorem to define a Runge-Lenz vector as a consequence of an invariance of the action integral. It’s shown that such a vector exists for all central potentials. In section 3 we describe the Kepler problem in space-time. By choosing a nice parametrization we show that the equations of motion and the conservation of energy describe a harmonic oscillator with an extra derivative in four dimensions and a four dimensional sphere, respectively. From this we define a conserved tensor. The components of this tensor correspond to the Runge-Lenz vector and angular momentum. 1