  In this study, we investigate trajectories involving multiple impulses within
the framework of a generic spacecraft dynamics. Revisiting the age-old query of
"How many impulses?", we present novel manipulations heavily leveraging on the
properties ofthe state transition matrix. Surprisingly, we are able to
rediscover classical results leading to the introduction of a primer vector,
albeit not making use of Pontryagin Maximum Principle as in the original
developments by Lawden. Furthermore, our mathematical framework exhibits great
flexibility and enables the introduction of what we term a "surrogate primer
vector" extending a well known concept widely used in mission design. This
enhancement allows to derive new simple optimality conditions that provide
insights into the possibility to add and/or move multiple impulsive manoeuvres
and improve the overall mass budget. This proves especially valuable in
scenarios where a baseline trajectory arc is, for example, limited to a single
impulse-an instance where traditional primer vector developments become
singular and hinder conclusive outcomes. In demonstrating the practical
application of the surrogate primer vector, we examine a specific case
involving the four-body dynamics of a spacecraft within an Earth-Moon-Sun
system. The system is characterized by the high-precision and differentiable
VSOP2013 and ELP2000 ephemerides models. The focal point of our investigation
is a reference trajectory representing a return from Mars, utilizing the weak
stability boundary (WSB) of the Sun-Earth-Moon system. The trajectory
incorporates two consecutive lunar flybys to insert the spacecraft into a lunar
distant retrograde orbit (DRO). Conventionally, this trajectory necessitates a
single maneuver at the DRO injection point.
