Three asteroids, located at points P1, P2, and P3, which are not in a line, and having known masses m1, m2, and m3, interact with one another through their mutual gravitational forces only; they are isolated in space and do not interact with any other bodies. Let σ denote the axis going through the center of mass of the three asteroids, perpendicular to the triangle P1P2P3. What conditions should the angular velocity ω of the system (around the axis σ) and the distances
P1P2=a12, P2P3=a23, P1P3 = a13,
fulfill to allow the shape and size of the triangle P1P2P3 to remain unchanged during the motion of the system? That is, under what conditions does the system rotate around the axis σ as a rigid body?
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