Tossup

Far-field approximations in multipole expansions allow for sub-quadratic complexity in this system, such as in the Barnes–Hut treecode algorithm. Small perturbations in this system lead to large changes in motion in the first-studied “small denominators” problem, which in simulations can be adjusted by applying a “softening parameter” to the potential. The Jacobi integral is an invariant for a form of this system that is “restricted,” (10[1])which produces five equilibrium points named for Lagrange. In the simplest form of this system, (10[1]-5[1])one can fix a reference frame about the center of mass (10[3])and use the reduced mass, allowing one to derive Kepler’s three laws for a form of this system. For 10 points, name this system concerning the orbits of objects in gravitational central force problems. ■END■ (10[1])

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