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Saari's homographic conjecture claims that, in the N-body problem under thehomogeneous potential, $U=\alpha^{-1}\sum m_i m_j/r_{ij}^\alpha$ for $\alpha\ne0$, a motion having constant configurational measure $\mu=I^{\alpha/2}U$ ishomographic, where $I$ represents the moment of inertia defined by $I=\sum m_im_j r_{ij}^2/\sum m_k$, $m_i$ the mass, and $r_{ij}$ the distance betweenparticles.  We prove this conjecture for general masses $m_k>0$ in the planar three-bodyproblem under Newton potential ($\alpha=1$) and a strong force potential($\alpha=2$).

Saari's homographic conjecture for general masses in planar three-body problem under Newton potential and a strong force potential