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Name: Nick
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Question:
What would happen if a planets rotation speed at the equator was equal to the escape velocity?



Replies:
Hello Nick,

Did you know a person has less weight at the equator than at the poles?

The short answer is that something "very bad" would happen. Think of it this way. Suppose you had a ball a meter off the ground at the equator. And suppose that in fact the rotation of the earth was fast enough that an object near (1 meter high) the surface of the earth was moving at the escape velocity. In this case the object would float in mid-air. From the point of view of a person stuck to the planet it would appear to float stationary. To a person observing from space it would appear to make one revolution around the earth per day.

If the object was closer than that critical height, then it would slowly curve in towards the earth picking up a little velocity in the direction of the earth's rotation and hitting the surface (were the earth completely smooth or the critical height sufficiently large, then the object could orbit as an ellipse like many of our satellites). If the object was a little further away then it would be ejected, never to return.

Now what would that mean for the planet itself? Well, I would not want to be standing on it. Atmosphere and things with sufficient velocity would be ejected from the planet. However, it would probably be much worse than that. Much of what keeps the earth together as a solid mass is the gravitational attraction. If the orbital velocity was high enough, then much of that force would be missing (canceled to a large extent). Suddenly the high pressures in the earth's interior would be unbalanced and I would expect the planet to more or less fly apart from its current form.

You can apply this line of reasoning to look at other planets and how planets (or stars) form as well.

Now, back to a person's weight at the equator. It is less by a small percentage due to the rotation of the earth. However, it is also a bit less because there is a small bulge in the earth near the equator. Why might there be a bulge near the equator? And why would standing on a bulge at the equator further reduce a person's weight? The total effect is around a 0.3% to 0.4% reduction. Next, ask if there is a market for someone to buy precious metals like gold at the equator and then sell them at the poles.

cheers,

Michael S. Pierce



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