Applications of V-Infinity Leveraging Maneuvers to Endgame Strategies for Planetary Moon Orbiters

Abstract

Delivering an orbiter to a planetary moon such as Europa or Titan requires an excessive amount of fuel if the trajectory is not carefully and cleverly planned. V-infinity leveraging maneuvers are an effective means to reduce total Delta-V requirements to achieve orbit about a planetary satellite. This work characterizes optimal sequences of flybys and leveraging maneuvers with the aid of tools to construct, map, and analyze these sequences and compare them with a theoretical minimum. Numerical results show that the optimal location for performing V-infinity reduction maneuvers is not necessarily at apoapsis, due to targeting constraints. By plotting total Delta-V versus time-of-flight for tens of thousands of generated sequences, a Pareto front is created of the most efficient sequences for each given flight time. An infinite series of flybys and leveraging maneuvers (theoretical minimum) results in a Delta-V savings of over 70% when compared with a direct burn during flyby. While infinite missions are not possible, it is feasible to reduce the total Delta-V by 50% with only a modest increase in flight time. Increasing the mission duration further does not result in significant reductions. NomenclatureEff fb = efficiency of a powered flyby as defined by Eq. (13) Eff LM = efficiency of a leveraging maneuver as defined by Eq. (7) K = number of gravity-assist body orbit revolutions L = number of spacecraft orbit revolutions R = resonance of the spacecraft's orbit to the gravity-assist body, K=L R cb = radius of the central body in normalized units r ga , a ga = radius and semimajor axis of the gravity-assist body, which are equivalent r min = minimum allowable flyby radius of the gravity-assist body r p = radius of closest approach to the gravity-assist body T sc , T ga = period of the spacecraft/gravity-assist body V c = local circular velocity of the gravity-assist body V ga = velocity of the gravity-assist body (circular) V p = spacecraft velocity at periapsis during a flyby V sc = spacecraft velocity with respect to the central body V 1 = hyperbolic excess velocity of the spacecraft with respect to the gravity-assist body = angle between V 1 and V ga , known as the pump angle V DSM = burn applied at or near apoapsis for a V 1 leveraging maneuver = turn angle of the V 1 vector before and after a flyby max = maximum turn angle of a flyby when r min is used = true anomaly of gravity-assist body at reencounter = reduced mass of the system, 2 = 1 2 1 = gravitational parameter of the central body 2 = gravitational parameter of the gravity-assist body = true anomaly of the spacecraft during the V DSM