Strange Increase in the Total Energy of a Rocket in the Earth-Moon system

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In article , "Greg Neill"
writes:
over time. Interestingly, the behavior of the energies might
be more intuitive if you were to switch to a rotating frame
of reference in which the Earth and Moon are fixed! You
would need to incorporate another potential term associated
with the rotation proportional to the distance from the
origin.

I think you'll find that centrifugal potential goes as the square
of the radius.

force = m omega^2 r
PE = 1/2 m omega^2 r^2

As a sanity check, note that this PE matches the KE of
a "motionless" object viewed from the rotating frame.

Choose an appropriate sign convention, of course.

D'oh! Of course. I was writing faster than I was
thinking. Again.

Cheers.