On this foundation, Newton derived and generalized the laws of Kepler, showing that orbits could be conic sections other than ellipses. Nonperiodic comets are well-known examples of objects with parabolic or hyperbolic orbits.
The constant in Kepler’s third law, relating the squares of orbital periods to the cubes of semimajor axes, was found to depend on the sum of the masses of the bodies attracting one another. This was basic to determining the masses of numerous stars, in units of the mass of the sun, through observations of binaries. As Cavendish balance experiments provided an independent numerical value for the constant in the law of gravitation, stellar masses in kilograms could be calculated. Later, analysis of observed perturbations in planetary motions led to the prediction of previously unseen planets in our solar system. Studies of the stability of three bodies moving under their mutual gravitational influence led to the discovery of two clusters of asteroids sharing the orbit of Jupiter around the sun.
These successes fostered confidence in the view of one boundless Euclidean space, the preferred inertial frame of reference, as the best arena for the description of all physical activity. Lacking direct evidence to the contrary, theoretical cosmologists at first assumed that the space of the universe was filled, on the largest scales, with matter distributed uniformly and of unchanging density. Analysis soon disclosed that Newtonian mechanics implied instability to gravitational collapse into clumps for an initially homogeneous and static universe. This stimulated the observational quest for knowledge of the present structure of the cosmos outside the solar system.