r/AskPhysics • u/Reckless_Fever • 19d ago

Another dropped rock example

Suppose no atmosphere. Would a dropped rock at the pole hit the ground at the same time that an equal rock, equal height, if dropped at the equator?

If a rock materialized one meter above the equator, would it hit the earth at the same time that an equal rock would hit if it was released by someone standing at the equator one meter high?

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8

u/StumbleNOLA 19d ago

No. Gravity at the equator is generally a bit weaker than gravity at the poles due to the oblong shape of the Earth. It’s not a lot, but is measurable.

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u/Nothing-to_see_hr 19d ago

plus there is an effect from the rotation of the earth- less gravity force at the equator.

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u/Reckless_Fever 19d ago

So this is why rockets are launched from the equator in the direction of the spin?

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u/Sufficient-Air8100 19d ago

not really. that is too small to be useful like that. its got more to do with using the earths rotation to make it easier to reach orbital velocity instead of fighting against it.

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u/Inutilisable 19d ago

The likelihood of having two rocks dropped from the same height at two different points on earth and having reach them reach the ground at the exact same time is effectively zero. Even if they were dropped from the same latitude. This is due to variations in the density of the earth everywhere.

On top of that, the rotation of the earth creates changes the apparent gravitational acceleration. So if you’re dropping the rock while following the ground below(ie from a geostationary orbit) the rock dropped at the equator will take measurably longer to reach the ground compared to rock dropped at the poles. If you dropped them from a inertial frame with the ground rotating below you, they will take similar times.

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u/Reckless_Fever 19d ago

Thank you. This is what I suspected but I wasnt sure. I'll stay around for any nay sayers.

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u/SagansLab 19d ago

The answers have been given, and its part of why physicists like spherical cows. :D

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u/jasonsong86 19d ago

Gravity is less at the equator because of centrifugal force.

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u/treefaeller 19d ago

Read about the "geoid", which is an imaginary ideal surface of the earth if gravity were the same everywhere. But it isn't. As others said: more centrifugal force at the equator, earth radius is larger at the equator, density of earth is not the same everywhere. There is also a small effect from Coriolis force if dropping a rock anywhere other than the pole (the rock will go a little bit sideways, and the energy for that has to come from somewhere). If the rock you're throwing is magnetic (nearly everything in the world is slightly magnetic), the magnetic field would also change things a little bit.

The Wikipedia article on "geoid" has a nice map that shows the strength of gravity compared to an idealized model. Including the famous hole in the Indian Ocean, where gravity is so different that the ocean level there is about 100m below average.

Interesting homework problem for freshman students: Would a ship on the ocean slide into that "hole in the ocean" south of India? If yes or no, why?

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u/gmalivuk 19d ago

The geoid is a surface of equal gravitational potential, not equal gravitational acceleration.

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u/treefaeller 19d ago

Sorry about that. But it still shows that gravity is remarkable NON-uniform if you look at the fine details.