Alternative formulations for the same constant of motion may be defined, typically by scaling the vector with constants, such as the mass m, the force parameter k or the angular momentum L. The most common variant is to divide A by mk, which yields the eccentricity vector, a dimensionless vector along the semi-major axis whose modulus equals the eccentricity of the conic: e = A m k = 1 m k ( p × × L ) − − r ^ ^ . An equivalent formulation multiplies this eccentricity vector by the major semiaxis a, giving the resulting vector the units of length. Yet another formulation divides A by L 2 , yielding an equivalent conserved quantity with units of inverse length, a quantity that appears in the solution of the Kepler problem u ≡ ≡ 1 r = k m L 2 + A L 2 cos ⁡ ⁡ θ θ where θ θ is the angle between A and the position vector r. Further alternative formulations are given below.