# A man on much faster spinning Earth decides to jump

Imagine that the Earth is spinning much faster than real situation and a man on the Earth's surface feels weightless. Suddenly the man decides to jump vertically with respect to the Earth. What will happen to him and the trajectory ignoring all the frictional forces?

Here's what I think. Since the man feels weightless he is just like a satellite in close circular orbit around the planet. So jumping process is just like giving a radially out impulse to a satellite in which the circular orbit becomes elliptical. More about this: https://physics.stackexchange.com/a/70418/192515

But how does the event happen in the man's frame?

At the moment he jumps he feels a sudden momentary weight, and he gets to the highest altitude and then comes down to the same spot he jumps (ignoring coriolis effect which might be too powerful this time?) and touches the ground with the same feeling of weight which will be momentary again.

I'm especially not sure about the second part of my answer. Please correct me if I have any mistakes.

• How do you know that he comes down to the same spot where he jumped from? – harshit54 Oct 6 '18 at 9:28
• Im not sure about it. Thats why I am asking the question. – physicsguy19 Oct 6 '18 at 9:30
• It would depend on his time of flight and if it matches the time period of the rotation of earth, only then it will land back at the same spot. – harshit54 Oct 6 '18 at 9:32
• Why do you think in the man's frame he should land back on the ground? – Aaron Stevens Oct 6 '18 at 10:48
• Sounds like you are asking this question with the person on the equator, which is a special case. Do you want the general answer for any latitude? – cms Oct 6 '18 at 12:17

Your first question is basically: what is the new orbital? Since the force is radial the angular momentum remains the same. The energy is increased by $$\int \vec F \cdot d\vec{s}$$. It is an elliptical orbital with the same angular momentum as the original circular one but higher energy. Its perigee will be at a nonzero height above the surface. In other words, the man does not land.