where β β 2 ≡ ≡ 1 − − J ′ ( u 0 ) is a constant. β β 2 must be non-negative; otherwise, the radius of the orbit would vary exponentially away from its initial radius. (The solution β β = 0 corresponds to a perfectly circular orbit.) If the right side may be neglected (i.e., for small perturbations), the solutions are