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OCR: BODY /LAGR ANGE While two body systems fo1low simple elliptical paths three or more body systems fo11o'w more complex often chaotic patterns This because each planet in the sy stem interacts gravitationally with each other planet However when many small bodies orbit very large body like the sun there orbits may approach ellipses Lagr ange Points The 18th century mathematician Joseph-Louis Lagr. ange predicted five orbital locations -- which cma1l particle remain motionless relative A two larger orbiting bodies The three bodies would form rotating frame with all three orbiting their combined center of mass Three of these points ar collineal with the two larger bodies one being in the gravit ational balance poini between them pue two being outside the two large Sasseu The other two points fo ...