  The concept of sphere of influence of a planet is useful in both the context
of impact monitoring of asteroids with the Earth and of the design of
interplanetary trajectories for spacecrafts. After reviewing the classical
results, we propose a new definition for this sphere that depends on the
position and velocity of the small body for given values of the Jacobi constant
$C$. Here we compare the orbit of the small body obtained in the framework of
the circular restricted three-body problem, with orbits obtained by patching
two-body solutions. Our definition is based on an optimisation process,
minimizing a suitable target function with respect to the assumed radius of the
sphere of influence. For different values of $C$ we represent the results in
the planar case: we show the values of the selected radius as a function of two
angles characterising the orbit. In this case, we also produce a database of
radii of the sphere of influence for several initial conditions, allowing an
interpolation.
