Help, I can't get out!

You stand on a solid sphere of uniform density with total mass \(2 \times 10^{30}~\mbox{kg}\) (the mass of the sun). The escape velocity from the surface of the sphere is equal to the speed of light, \(3 \times 10^8~\mbox{m/s}\). What is the radius of the sphere in meters?

Details and assumptions

  • Newton's constant is \(6.67 \times 10^{-11}~\mbox{Nm}^2/\mbox{kg}^2\).
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