 In the view of contemporary mechanical philosophers, especially Huygens and Leibniz, Newton’s conception of universal gravitation involved an entirely unintelligible action at a distance across empty space. Gravitation could only be acceptable, on their view, if it were explained, in turn, by vortices of intervening invisible matter whose tiny microscopic particles effected the apparent attraction of bodies via impulse. Although both Leibniz and Huygens accepted Newton’s demonstration that the orbits of the satellites of the major astronomical bodies in the solar system obey the inverse-square law (the planets with respect to the sun, the moons of Jupiter and Saturn with respect to their planets, the earth’s moon with respect to the earth), they rejected Newton’s unrestricted generalization of this law to hold between all bodies (and all parts of bodies) whatsoever. For them, the inverse-square law could be accepted in astronomy only by taking the major bodies of the solar system as each being surrounded by vortices limited to the finite surrounding region of their satellites. The validity of the inverse-square law would thus be restricted to precisely such a finite region, so that it could not be extended arbitrarily far: the moons of Jupiter would accelerate towards Jupiter, for example, but neither Saturn nor the sun, for example, would experience such accelerations towards  Jupiter.[17]