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 (10[1])is an invariant (10[1])for a form of this system that is “restricted,” (10[2])which produces five equilibrium points named for Lagrange. (10[4])In the simplest (10[1])form of this system, (10[3]-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 (10[1])three laws for (10[1])a form (-5[1])of this system. For 10 points, name this system concerning the orbits of objects in gravitational central force problems. ■END■ (10[1]0[3])

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