This quantity corresponds to the first integral c0 (“c-sub-zero”) in the double-averaged restricted three-body problem. Approximate solutions to the secular Kozai Hamiltonian are most commonly found by perturbatively expanding it as a function of a ratio of two forms of this quantity. In the Kepler problem, this quantity equals negative standard gravitational parameter over two times specific orbital energy. Averaging orbital distance over the (*) eccentric anomaly yields this quantity. One over this quantity is subtracted from two over distance on the right hand side of the vis-viva equation. This quantity equals the average of apoapsis (10[1])and periapsis. (-5[1])The cube of this quantity is proportional (10[1])to the square of orbital period, according to Kepler’s Third Law. For 10 points, name this quantity equal to half an elliptical orbit’s longest diameter. ■END■ (0[1])