Solar System Geometry, Modern Understandings Of | Research & Encyclopedia Articles

If bound, then one body will orbit the central mass on an elliptical path, as Kepler had stated in his second law of motion; however, if unbound, the relative orbit will be hyperbolic; and if steady-state, the relative orbit will be parabolic. The two-body problem was applicable not only to planets of the solar system, but to the paths of asteroids and comets as well. Of course, the reality of the solar system is that forces beyond just the two bodies in question influence gravitation and orbital paths. Newton noted in his influential book Principia that he believed the solution to a three-body problem would exceed the capacity of the human mind.

From the 1700s onward, mathematical contributions to our understanding of the solar system came from individuals who, unlike before, were not necessarily astronomers. Lagrange, Euler and Laplace—all considered eminent mathematicians—provided new tools for more accurately describing the complexities of the universe. Joseph-Louis Lagrange (1736–1813) studied perturbations of planetary orbits. He lent his name to what has come to be called "Lagrangian points," which are equally spaced locations in front and behind a planet in its orbit, containing bodies (such as asteroids) that obey the principles of the three-body problem.

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