Ken Fox has raised a point about a real world problem that appears in a
physics teaching example. It deals with what are presumably coasting
data from an Apollo transfer trajectory. Ken applies the concepts of
gravitational potential energy and kinetic energy in a context in which
their meanings are unclear, namely an implicitly rotating frame in which
Earth and Moon are at rest. If this is done then a centrifugal potential
must also be imposed. Is it possible that this has not been done?
The crucial question should be one of how the velocity of the spacecraft
is defined. If it is, indeed, defined as I suggest, then the term I
suggest must be added regardless of religious objections* to doing so.
If instead velocities referred to some inertial frame are used, then the
system energy will also include terms due to many other interactions.
The system is no longer ideally isolated, and energy conservation is no
longer a useful concept. After all, that is why gravity assists help in
saving maneuvering fuel.
*There is a religion which holds that the centrifugal force which is
felt and responded to by every body with respect to a rotating frame of
reference is somehow unreal. The centrifugal potential is, of course,
derived from this force. One only needs to use it to get the correct
answer; it is not necessary that one believe in the force to use it.