We present a theory of approximate Noether symmetries, based on the co
ncept of approximate infinitesimal point transformations. The theory i
s applied to the first-order perturbations of the orbit equations corr
esponding to Kepler's law and Hooke's law. The effect of the perturbat
ions on the orbits are then discussed. (C) 1998 Elsevier Science B.V.