The triangle spins as each spacecraft in the constellation travel along their orbits: https://en.wikipedia.org/wiki/File:LISA_motion.gif So the dead zone is constantly moving over the course of a year.
(In fact, it has to: in order to keep each leg the same length, each spacecraft must be the same distance from the Sun. There's no way to do that in a free falling orbit and have the formation flat to the ecliptic-- the craft closer to the Sun would orbit faster and drift away from its brothers.)
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The triangle spins as each spacecraft in the constellation travel along their orbits: https://en.wikipedia.org/wiki/File:LISA_motion.gif So the dead zone is constantly moving over the course of a year.
(In fact, it has to: in order to keep each leg the same length, each spacecraft must be the same distance from the Sun. There's no way to do that in a free falling orbit and have the formation flat to the ecliptic-- the craft closer to the Sun would orbit faster and drift away from its brothers.)