# I Intermediate Challenge of the Week #2 03/26/2017

1. Mar 3, 2017

### Greg Bernhardt

Three point masses $m_1, m_2$ and $m_3$ which are located at the non-collinear points $P_1, P_2$ and $P_3$ respectively can interact only through gravitational attractions. The masses are isolated in space and they have no interaction with other objects. We suppose that an axis $\sigma$ is passing through the center of mass of the system of the three given masses and is perpendicular to the plane of the triangle $P_1P_2P_3$ . Which conditions must angular velocity of the system (regarding given axis) and distances $P_1P_2 = d_{12} , P_2P_3 = d_{23}$ and $P_1P_3 = d_{13}$ must satisfy in order the shape and the size of the triangle $P_1P_2P_3$ stay constant, as the system is rotating?