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Does any planet, or Kuiper Belt Object, or exoplanet measured or surmised, orbit its star either fast enough, or slow enough and thus distantly enough to cast a long enough shadow, for a spacecraft to orbit it in permanent umbra? (Earth doesn't.)

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Jupiter's L2 point is 53.94 million km behind it.
The L2 point "orbits" the planet on a 1-Jupiter-year cycle, exactly
(just about by definition)

From there Jupiter is 0°8'55" wide, and the sun is 0°5'45" wide.

Jupiter casts a permanent shadow on its L2 point.

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