Then, since the transfer must occur where the orbits intersect, the radial coordinate at the transfer point is \(r_p\). This will give the minimum \(\Delta v\) requirement, since it is the point where the velocity is highest on the capture orbit, and therefore the place where the velocity on the capture orbit is closest to the hyperbolic velocity. Usually we will assume that the transfer occurs at the periapsis of the capture orbit. Where in the capture orbit, relative to the capture orbit’s periapsis, will the transfer occur To determine the capture orbit, we need to decide on two factors: Review of Vectors, Kinematics, and Newtonian Mechanics Planetary Departure for Interplanetary Transfer Interplanetary Trajectories and Maneuvers Non-Hohmann Transfers: Apse Line Rotation Example Non-Hohmann Transfers: Common Apse Line Example Non-Hohmann Transfers with a Common Apse Line Orbit Independent Solution: The Universal AnomalyĮxample: Comparison of Bi-elliptic and Two-Impulse Hohmann Transfers Time Since Periapsis, Mean Anomaly, and Eccentric Anomaly Right Ascension and Declination CoordinatesĬlassical Orbital Elements and the State Vector Two-Body Numerical Solution in an Inertial FrameĪpplication of the CR3BP: Lagrange PointsĪngular Momentum Is Conserved In Orbital Motion Two-Body Equations of Motion in an Inertial Frame Mass, Force, and Newton’s Law of Gravitation