But that's too fast!

A new planet has just entered the solar system with volume one-third and average density half that of the sun. If the distance between the planet and the sun is \(90 \text{ km}\), then find the total time taken by the planet to revolve around the center of mass of the planet-sun system. Submit your answer in milliseconds.

Details and Assumptions:

  • Take the value of \(G\) (universal gravitational constant) as \(6.67 \times {10}^{-11}\) SI units.
  • Take the mass of the sun as \(2 \times {10}^{30}\text{ kg}\).   
  • Neglect the gravitational forces acting on the planet-sun system due to the other planets in the solar system.   
  • Assume the planet to revolve in a circular path around the sun.

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