An empirical method has been developed for onboard guidance within the sphere of influence of a celestial body. For guidance maneuvers made at a relatively large distance from the body, only one preselected measurement from a star to the body is required. Although the method is designed to control the magnitude of the periapsis radius (or entry angle), the periapsis position and velocity automatically remain close to the nominal values. For lunar approach, error analysis with an assumed one-sigma error of 10 seconds of arc in the optical angular measurements and a one-sigma velocity-cutoff error of 0.2 m/sec has shown that perilune radius can be controlled to a one-sigma accuracy of from 7 to 13 km, depending on the time the approach guidance is performed.