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We investigate three-body motion in three dimensions under the interactionpotential proportional to r^alpha (alpha \neq 0) or log r, where r representsthe mutual distance between bodies, with the following conditions: (I) themoment of inertia is non-zero constant, (II) the angular momentum is zero, and(III) one body is on the centre of mass at an instant.  We prove that the motion which satisfies conditions (I)-(III) with equalmasses for alpha \neq -2, 2, 4 is impossible. And motions which satisfy thesame conditions for alpha=2, 4 are solved explicitly. Shapes of these orbitsare not figure-eight and these motions have collision. Thereforenon-conservation of the moment of inertia for figure-eight choreography foralpha \neq -2 is proved.  We also prove that the motion which satisfies conditions (I)-(III) withgeneral masses under the Newtonian potential alpha=-1 is impossible

Evolution of the moment of inertia of three-body figure-eight choreography