Googling through the earth.
 

This month's Focus magazine mentioned something. The standard question of what happens if something is dropped through the centre of the earth ignores the rotation of the earth. (And lots of other issues.)

So the object would actually follow (or want to) a curved path as the earth rotates.

Can someone [I]attempt[/I] to get me to understand the maths and draw me a nice picture of the curve? I can't picture it. How should the tunnel be dug so the object won't keep hitting the sides?

Will it pass through the centre to reach its antipode?

Edited for clarity.

:smile:

No dropping from the poles! Assume at equator? Assume earth is a perfect sphere if you want.

Or,

If the tunnel was dug just in time under the falling object to avoid it hitting the sides, what shape would the tunnel be and where would the object arrive?

Maybe that's what I mean!? Lol

Assume vacuum, no heat etc.

Drop at equator at zero longitude.

You might want to drain the oceans.

Edit: I'm wondering if it would get stuck in a loop inside the earth. Or a complex, never repeating path through the earth. If not, then can the earth's rotational speed be adjusted so that it does?

Would need to backfill the path to stop the earth getting lighter.

[QUOTE=Flatlander;315140]You might want to drain the oceans.[/QUOTE]What should be assumed about the positions of the sun and moon?

[QUOTE=Uncwilly;315145]What should be assumed about the positions of the sun and moon?[/QUOTE]

You may put them wherever they give the nicest tan and the best fishing experience.

Earth = perfect sphere with evenly distributed mass.

Other objects ignored!

Edit:
I'm guessing that if the rotation of the planet is sufficiently fast, the object follows a curved path that settles to repeatedly looping the core?

[QUOTE=Flatlander;315152]I'm guessing that if the rotation of the planet is sufficiently fast, the object follows a curved path that settles to repeatedly looping the core?[/QUOTE]

It depends on your frame of reference.

[QUOTE=chalsall;315156]It depends on your frame of reference.[/QUOTE]

Agreed. The object should fall straight down towards the center of the earth if you use the earth as the frame of reference. The velocity of the object would cause it to continue on past the center for a while (similiar to a hit/thrown ball defying gravity for a period of time), stop a little ways towards the other side, and then come back towards the center, passing the center again by a lesser margin, stop, and come back towards the center again, and continuing to repeat this process until it eventually stopped completely (using the earth as a frame of reference) at the exact center of the earth's core.

Of course, all of this is theoretical and retorical because the pressure and heat at the earth's core would crush or burn up most anything before it got to the center of the earth.

[QUOTE=gd_barnes;315169]Of course, all of this is theoretical and retorical because the pressure and heat at the earth's core would crush or burn up most anything before it got to the center of the earth.[/QUOTE]A sufficiently slow WIMP? Might be hard to monitor the progress of the experiment.

A micro-BH might be easier as you could follow its progress more easily from the Hawking radiation and, possibly, by seismology. Just make sure that it is small enough that it radiates more than it collects on its journey.

Homework problem: estimate the mass of such a black hole. You may assume if you wish that the earth is made of constant density material and that radiation from the BH doesn't impede matter falling in to it.

[QUOTE=Flatlander;315130]
Will it pass through the centre to reach its antipode?
[/QUOTE]That's an easy one:
Nope.
Conservation of angular momentum about the centre of the earth.

D

Some previous discussion is here:

[url]http://www.mersenneforum.org/showthread.php?t=5294[/url]

[QUOTE=xilman;315180]A micro-BH might be easier as you could follow its progress more easily from the Hawking radiation ...[/QUOTE]Only when it's near the surface, of course. The earth is rather opaque to most forms of EM radiation.

Hmm, interesting question: would seismology be sensitive enough to track its progress very far? Near the surface it could also be followed by gravitometers.

A perfectly spherical planet with evenly distributed mass. Rotating.

A small object/ball, of minimal/negligible mass (at its surface, so rotating with the planet, at the equator) is dropped and a tunnel is dug and back filled by nano-bots just-in-time to stop the ball touching the sides. It never touches the planet.

Im guessing that, using earth's mass and rotational speed, the ball would produce a curved path that misses the core and doesn't pop out at the antipode, right?
What curve would be produced? Where would the ball reappear?

Could the mass of the planet and/or its rotational speed be changed (restart the experiment) such that the ball (always dropped from the equatorial surface, always rotating with the planet) would never re-appear; following a loop inside the planet. Or even a never-repeating pattern inside the planet.

[I]Has to be interesting[/I]?
Beacause as the ball falls in a curve more of the planet is on one side of the ball than the other so the path starts to bend back ...

"A sufficiently slow WIMP?" I volunteer.

It's purely a though experiment, forget heat etc.
(It's frustrating being mathematically incompetent. Writing a program that plots the path and allows me to change the parameters would keep me amused for months.)