On a paper of Moeckel on central configurations

This paper is devoted to general properties of the central configurations: we do not make any restriction on the number $n \geqslant 3$ of particles nor on the dimension $d \geqslant 1$ of the configuration. Part 7 considers however the particular case $n = d + 2$, of interest because the case $n = 4$, $d = 2$ is the first for which we cannot solve the equations for central configurations. Our main result is Proposition 6, which gives some estimates implying an important estimate due to [23]. Our main tool is Equation (4.5).