Lagrangian orbital oddity

Imagine drawing an equilateral triangle with its base between Earth and the
Moon and its apex at, say, L4. Now rotate the triangle about its base
"north" of the Earth-Moon system, through L5, then "south" back to L4.

This rotation describes a circle that is at right angles to a line between
Earth and Moon, and equidistant from each. As Earth and Moon orbit around
each other, this circle rotates about Earth once per month.

Now, place a spacecraft at L4 and accelerate it along this circle until the
craft reaches an angular velocity (relative to Earth) that is the same as
the Moon's but at 90 degrees to it.

If I am visualizing the resulting orbit correctly, the spacecraft will pass
through L4 and L5 once per orbit, with an orbital period identical to that
of the Moon. Is this correct? Is this orbit stable?

If so, to what uses might it be put? Perhaps three or four satellites
sharing such an orbit might be able to support polar communications for both
Earth and Moon, albeit at a high energy cost for the link, which is
essentially the same as lunar distance.


Jim McCauley