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

  1. Mar 3, 2017 #1
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  2. jcsd
  3. Mar 23, 2017 #2

    QuantumQuest

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    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?
     
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