Dipartimento di Matematica, Università di Pisa
A dynamical definition of the sphere of influence of the Earth
The concept of sphere of influence of a planet is useful both for the impact monitoring of asteroids with the Earth and for the design of interplanetary trajectories of spacecrafts. Classical definitions of the sphere of influence depend only on the mass-ratio between the Sun and the planet and on the planet’s semi-major axis. We propose a new definition that takes into account also the position and velocity of the small body for given values of the Jacobi constant C. By means of a suitable target function, we compare the orbit of the small body obtained with the circular restricted three-body problem to the one obtained by patching two-body solutions. Our definition is based on an optimisation process that minimizes the target function with respect to the radius of the sphere of influence. For different values of C, we represent the results for 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 values of the radius of the sphere of influence for several initial conditions, allowing an interpolation.
This is a joint work with I. Cavallari, G.F. Gronchi, G. Baù and G.B. Valsecchi.
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A dynamical definition of the sphere of influence of the Earth
