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