Three planets interact with one another through their mutual gravitational forces only; they are isolated in free space and do not interact with any other bodies. They orbit around an axis going through the center-of-mass of the system and perpendicular to the triangle formed by the planets. What should be the angular velocity ω in rad/s so that the shape and size of the triangle remains unchanged during the rotation?
Details and assumptions
The area of the triangle is 1 (A.U.)^2.
The total mass of the planets is 3×10^26 kg.
G=6.67×10^−11 m^3/kg s^2.
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raiz quadrada de (GM/RS^2)
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