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I've had 2 semesters of college-level physics (1 of Mechanics and 1 of E&M) and was wondering after exploring a bit about terminal velocity:

Is it physically possible for a planet to have a terminal velocity greater than its escape velocity?

If so, would it be possible then for a body to escape this planet?

If the answer could be given to a level I can understand, that would be great. But if that is not possible, feel free to use higher-level physics.

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  • $\begingroup$ The terminal velocity of the planet or the body? $\endgroup$ – Qmechanic Sep 27 '19 at 7:31
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No. At most terminal velocity can be the same as escape velocity. And that can only happen if the planet has no atmosphere.

Terminal velocity is the maximum speed you will reach if dropped from a great height. Usually it means the speed at which you lose energy from friction with the atmosphere just as fast as you gain it from dropping.

Without an atmosphere, there would be no friction. So you would gain speed until you hit the ground. Since there is no energy loss from friction, you could launch yourself upward at that speed and reach the same height where you started.

If you started infinitely far away, you would have to launch at the escape velocity to reach the starting point. And the speed you would reach when you dropped all the way to the ground would be the same, escape velocity.

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