1. In the general three-dimensional case the limits of integration come from the solution of a 4thorder equation in cos f [26 pp. 155-162],[27 Sec. 2.5.1]. In the planar case we consider (i.e., the orbit lies in the ecliptic plane), the arguments of true anomaly when the spacecraft enters and leaves the Earth's shadow can be expressed as a closedform function of the orbital elements: ecl,enter Sun