Shadow of Io Theorem


(all (time-voyager-2-c)
     (find (shadow-point-c)
   (exists
   (time-sun sun-spacetime-loc time-io io-spacetime-loc 
     time-jupiter jupiter-spacetime-loc time-voyager-2 
     voyager-2-spacetime-loc shadow-point jupiter-ellipsoid 
     ray-sun-to-io)
   (and
    (= ray-sun-to-io
(two-points-to-ray
 (event-to-position sun-spacetime-loc) 
 (event-to-position io-spacetime-loc))) 
     (= jupiter-ellipsoid
(body-and-time-to-ellipsoid jupiter 
    time-jupiter))
    (= shadow-point
(intersect-ray-ellipsoid ray-sun-to-io jupiter-ellipsoid)) 
     (lightlike? jupiter-spacetime-loc voyager-2-spacetime-loc) 
     (lightlike? io-spacetime-loc jupiter-spacetime-loc) 
     (lightlike? sun-spacetime-loc io-spacetime-loc) 
     (= voyager-2-spacetime-loc
(ephemeris-object-and-time-to-event voyager-2 time-voyager-2)) 
     (= jupiter-spacetime-loc
(ephemeris-object-and-time-to-event jupiter time-jupiter)) 
     (= io-spacetime-loc
(ephemeris-object-and-time-to-event io time-io)) 
     (= sun-spacetime-loc
(ephemeris-object-and-time-to-event sun time-sun))
     (= shadow-point (abs (coords-to-point j2000) shadow-point-c)) 
     (= time-voyager-2
(abs ephemeris-time-to-time time-voyager-2-c))))))

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