Modified Heliocentric Coordinates for Particle Dynamics

A modified heliocentric coordinate system is found for the dynamics of $n+1\mathrm{}$ particles that is barycentric, diagonalizes the kinetic energy, and is symmetric in $n$ of the particles. The $n$ planetary vectors are based on Radau's canonical point between the center of mass and the heliocenter. These coordinates, described by Radau in 1868 and forgotten, are especially valuable for describing centrosymmetric molecular fragments $A{B}_n$, and useful also for the mass polarization in atoms.