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The one particle problem in a spherical potential is examined in Classical Mechanics from a group theorical point of view. The constants of motion are classified according to their behaviour under the rotation group $0(3), i.e. according to the irreducible representations D 0 of 80(3) (section 1).The Lie algebras of SO(4) and 80(3) are explicitly built in terms of Poisson brackets for an arbitrary potential, from global considerations. The Kepler and the 3 dimensional oscillator problems are shown to play particular roles with respect to these groups (sections 2 and 3).In the last section, the Kepler problem is analyzed with the aid of the $0(4) group instead of the Lie algebra. It is proved that the transformations generated by the angular momentum and the Runge-Lenz vector form indeed a group of canonical transformations isomorphic to $0(4). Consequences with respect to the quantization problem are examined.

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