Drops of Jupiter

Classical Mechanics Level pending

This is a continuation of my previous question "Falling Toward a Gas Giant." This time instead of speed you are looking for a time. You can see the solutions to that question for help with this one since the first part of the solutions are identical.

An object is suspended, at rest, ten billion meters (\( 10^{10}\text{ m} \)) from the center of a planet. The planet has a mass of \( 1.9 \cdot 10^{27}\text{ kg} \). At time \(t=0\) the object is released and begins falling in a straight line toward the planet. The planet's gravity is the only force acting on the object. The planet's radius is less than one hundred million meters (\(10^{8}\text{ m}\)).

When will the object be one hundred million meters (\(10^{8}\text{ m}\)) from the center of the planet?

Give answer in days (24 hour Earth days) and rounded to one decimal place.

For the Gravitational Constant use \(G = 6.674 \cdot 10^{-11} \text{ m}^{3} \text{ kg}^{-1} \text{ s}^{-2} \).


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