gravity at the center of earth

[soniccity]

If I could drill a hole through the diameter of the earth to the other side and dropped a ball into that hole, what would happen when the ball reached the dead center? Not a trick question, I have no idea.

[Acme]

If I could drill a hole through the diameter of the earth to the other side and dropped a ball into that hole, what would happen when the ball reached the dead center? Not a trick question, I have no idea.

When at the center it would be at its highest speed. Here's a summary.

 

A Ball Dropped Through The Earth Becomes A Permanent Pendulum

[soniccity]

Thank you for an informative reply. A pendulum makes some sense though I wonder about terminal velocity. Another question

That has crossed my mind is one of air travel. I have asked many pilots about this and have never received a satisfactory answer. If I fly San Francisco to to new York, it takes roughly 4 hours to go 3000 miles west to east. Conversely, the return flight takes the same amount of time, give or take the jet stream. So the rotation of the earth doesn't factor in the travel time. Does that mean that as a plane travels west to east, its still travelling 24000 MPH the other way?

[ydoaPs]

If I could drill a hole through the diameter of the earth to the other side and dropped a ball into that hole, what would happen when the ball reached the dead center? Not a trick question, I have no idea.

Where are you drilling the hole?

[Acme]

Thank you for an informative reply. A pendulum makes some sense though I wonder about terminal velocity.

You're welcome. I don't know the theoretical terminal velocity under the circumstances laid out in the article I gave. I'm sure one of the competent folks here could review those circumstances and help you calculate it. (I would quote those circumstances but the author(s) gave a restrictive copyright notice. Interested readers will have to go to the page.)

 

Another question

That has crossed my mind is one of air travel. I have asked many pilots about this and have never received a satisfactory answer. If I fly San Francisco to to new York, it takes roughly 4 hours to go 3000 miles west to east. Conversely, the return flight takes the same amount of time, give or take the jet stream. So the rotation of the earth doesn't factor in the travel time. Does that mean that as a plane travels west to east, its still travelling 24000 MPH the other way?

That 24000mph is a mistaken speed for a jet aircraft. It would be more like 400 mph for a commercial jet. Neglecting tail-winds or head-winds and presuming a constant speed of 400mph then the East-to-West trip would take less time than the West-to-East trip. The exact difference depends on whether or not the courses are directly East/West and at what latitude(s) the flights are made.

[soniccity]

I guess my question is that it takes the same time to fly SF to NY as it does NY to SF, save the prevailing headwinds. It would seem the rotation of the earth would make the west to east trip shorter duration but it doesn't. Spacecraft circumnavigate the earth based partly on earth rotation, yet aircraft don't. Obviously there is some fundemental principal I don't understand. That was point about 24000 MPH or roughly the speed of earth rotation. In my layman's conceptualization, the plane traveling SF to NY at 400 MPH is at the same time, traveling backwards, relative to space, along with the earth. Maybe I'm over thinking it. I have flown east to west at dusk, and the sunset takes longer than if on land, yet the time for distance travelled remains the same. Thanks for indulging my curious yet woefully ignorant inquiries.

Getting back to the gravity question, isn't the pendulum effectively a perpetual motion engine?

[Acme]

I guess my question is that it takes the same time to fly SF to NY as it does NY to SF, save the prevailing headwinds. It would seem the rotation of the earth would make the west to east trip shorter duration but it doesn't.

Yes the earth rotation does make the West-to-East trip shorter in duration if a constant speed is maintained both ways and disregarding head/tail winds. It is only because of scheduling of flights that the trips take roughly the same time. The planes do not in reality maintain a constant speed or fly the same speed each way.

 

Spacecraft circumnavigate the earth based partly on earth rotation, yet aircraft don't. Obviously there is some fundemental principal I don't understand. That was point about 24000 MPH or roughly the speed of earth rotation. In my layman's conceptualization, the plane traveling SF to NY at 400 MPH is at the same time, traveling backwards, relative to space, along with the earth. Maybe I'm over thinking it. I have flown east to west at dusk, and the sunset takes longer than if on land, yet the time for distance travelled remains the same. Thanks for indulging my curious yet woefully ignorant inquiries.

You have it right except for not understanding that it is the scheduling that makes the flights more or less equal in time taken. I hope that's clear now that I have said it twice. Your 'theoretical' conceptualization is fine.

 

Getting back to the gravity question, isn't the pendulum effectively a perpetual motion engine?

No, not effectively. It is only theoretically perpetual. As the article pointed out you have to be able to actually drill the hole and you can't, you have to stop the Earth spin and you can't, and you have to disregard frictional forces of the atmosphere and you cant.

[Janus]

I guess my question is that it takes the same time to fly SF to NY as it does NY to SF, save the prevailing headwinds. It would seem the rotation of the earth would make the west to east trip shorter duration but it doesn't. Spacecraft circumnavigate the earth based partly on earth rotation, yet aircraft don't.

Think about it. How does an aircraft travel? it effectively pushes itself through the air. Its speed is measured in terms of its speed relative to the air. Since the air rotates with the Earth, and disregarding jet stream/wind, remains stationary with respect to the surface ( in perfectly still air, air speed equals ground speed), flying from East to West or West to East is no different than driving it. And you wouldn't expect to be able drive between NY and SF going one way faster than the other.

[soniccity]

I think I'm getting it. Thanks.

[Ophiolite]

Yes the earth rotation does make the West-to-East trip shorter in duration if a constant speed is maintained both ways and disregarding head/tail winds. It is only because of scheduling of flights that the trips take roughly the same time. The planes do not in reality maintain a constant speed or fly the same speed each way.

I am reasonably sure that you are incorrect for the reason noted by Janus: aircraft velocity is relative to the air and that is rotating with the planet. You would need to show some serious maths or peer reviewed references to convince me otherwise.

 

Also travel times are often not the same each way. Lagos to Paris, roughly north-south , is the same in either direction, but Amsterdam to Houston is almost an hour longer heading west than east on account of the jet stream.

 

And as a minor note, commercial aircraft will typically run with an airspeed of 500 -580 mph, not the 400 you quoted. (On one transatlantic crossing, with the benefit of a 250 mph tailwind we had a groundspeed that was supersonic.)

[Acme]

Yes the earth rotation does make the West-to-East trip shorter in duration if a constant speed is maintained both ways and disregarding head/tail winds. It is only because of scheduling of flights that the trips take roughly the same time. The planes do not in reality maintain a constant speed or fly the same speed each way.

 

I am reasonably sure that you are incorrect for the reason noted by Janus: aircraft velocity is relative to the air and that is rotating with the planet. You would need to show some serious maths or peer reviewed references to convince me otherwise.

I agree. The speed difference I mentioned is only relative to speed through space, not relative to speed over the ground. My bad.

 

And as a minor note, commercial aircraft will typically run with an airspeed of 500 -580 mph, not the 400 you quoted. (On one transatlantic crossing, with the benefit of a 250 mph tailwind we had a groundspeed that was supersonic.)

Agreed again. It's only a minor issue.

 

Here's an article that goes into my error in more detail. >> East-to-West Flight Times @ Aerospaceweb.org

[capada]

If I could drill a hole through the diameter of the earth to the other side and dropped a ball into that hole, what would happen when the ball reached the dead center? Not a trick question, I have no idea.

I am not quite sure of pendulum efect in normal hole through Earth(forgetting Earth rotation or other external forces) but am sure of pendulum efect if the hole would be vacum sealed,as only than we could be sure the ball will reach other end of the hole.

What I am not sure in normal hole is,that the air resitance to the center will slow the ball to the center too much for that ball to reach the other end of the hole.