Falling Towards A Gas Giant

Classical Mechanics Level 4

An object is suspended ten billion meters from the center of a planet. The object is released and begins falling in a straight line toward the planet, whose gravity is the only force acting on the object.

How fast is the object moving when it is one hundred million meters from the center of the planet?

Details and Assumptions

  • \(G = 6.674 \cdot 10^{-11} \text{ m}^{3} \text{ kg}^{-1} \text{ s}^{-2} \).
  • The planet's radius is much less than one hundred million meters.
  • The planet's mass is \( 1.9 \cdot 10^{27}\text{ kg} \).

Give your answer to 3 decimal places.


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