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Positions of equilibrium points for dust particles in the circular restricted three-body problem with radiation

For a body with negligible mass moving in the gravitational field of a star and one planet in a circular orbit (the circular restricted three-body problem) five equilibrium points exist and are known as the Lagrangian points. The positions of the Lagrangian points are not valid for dust particles because in the derivation of the Lagrangian points is assumed that no other forces beside the gravitation act on the body with negligible mass. Here we determined positions of the equilibrium points for the dust particles in the circular restricted three-body problem with radiation. The equilibrium points are located on curves connecting the Lagrangian points in the circular restricted three-body problem. The equilibrium points for Jupiter are distributed in large interval of heliocentric distances due to its large mass. The equilibrium points for the Earth explain a cloud of dust particles trailing the Earth observed with the Spitzer Space Telescope. The dust particles moving in the equilibrium points are distributed in interplanetary space according to their properties.