- 2018 Univelt Inc. All rights reserved. This paper builds upon a recently introduced concept of switching surfaces and performs an in-depth analysis of such switching surfaces for an interplanetary mission from the Earth to the Mars. Indirect method of optimal control theory along with Lawdens primer vector theory are essential to the method and are used to discuss a unified systematic means to study continuous low-thrust and impulsive trajectories. An interplanetary rendezvous-type maneuver from the Earth to the Mars is considered and its associated switching surface is analyzed. A bifurcation is observed in the switching surface, which in general, trigger the creation of new thrust arcs. In general, switching surfaces topology provide new tools for mission designers and enables insights to perform useful trade-offs for sizing vehicles propulsion systems.