Weird gravity question

[Guest tuskir]

If you dig a hole in the earth and jump there, the gravity pulls you down right? This is a hypothetic situation and I know it cant be duplicated but lets assume for a moment that you can dig a hole deep enough to go through the whole earth. You jump in that huge hole and the gravity will continue pulling you until you get to the center of the earth or what? Will you be suspended in the center or just continue falling until you get to the other side and then start falling again or what?

[J.C.MacSwell]

If you dig a hole in the earth and jump there, the gravity pulls you down right? This is a hypothetic situation and I know it cant be duplicated but lets assume for a moment that you can dig a hole deep enough to go through the whole earth. You jump in that huge hole and the gravity will continue pulling you until you get to the center of the earth or what? Will you be suspended in the center or just continue falling until you get to the other side and then start falling again or what?

 

 

If the hole is between the poles and you neglect friction you will accelerate to the center starting at 0 velocity and maximum acceleration until you reach the center at maximum velocity and 0 acceleration. You would then reverse the process (acceleration wise) as you continue to the other pole and come to a stop (for an instant) before heading back.

 

Other "direct routes" would include a corriolis (sp?) like "force" (pseudo force)which will deflect you against the sides of the hole.

[Macroscopic]

If the hole is between the poles and you neglect friction you will accelerate to the center starting at 0 velocity and maximum acceleration until you reach the center at maximum velocity and 0 acceleration. You would then reverse the process (acceleration wise) as you continue to the other pole and come to a stop (for an instant) before heading back.

In simpler terms, you would fall all the way to the center, then your momentum would carry you further until the the gravity wears away your momentum, then you start going back to the center. This would be repeated until all you lost all your momentum, then you would stay at the center. Assuming the heat doesn't kill you.

[J.C.MacSwell]

In simpler terms, you would fall all the way to the center, then your momentum would carry you further until the the gravity wears away your momentum,[/b'] then you start going back to the center. This would be repeated until all you lost all your momentum, then you would stay at the center. Assuming the heat doesn't kill you.

 

Neglecting friction does gravity "wear away Your momentum"? (I think it does in some theories but not in others).

[alext87]

You would surely just keep oscillating between the poles. But if friction was there then you would oscillate but eventually come to rest at the centre of the earth. i also think that the intense heat in the centre of the earth would vapourise your body - or you meant just be very thirsty!!

[swansont]

Neglecting friction does gravity "wear away Your momentum"? (I think it does in some theories but not in others).

 

Yes - in GR accelerating objects emit gravitational radiation. But I suspect friction would be much, much larger.

[[Tycho?]]

Neglecting friction does gravity "wear away Your momentum"? (I think it does in some theories but not in others).

 

The energy would be carried away by gravitational waves in the absense of any friction.

[Guest tuskir]

Thanks for the reply guys.. a lot of smart people on this board

[Martin]

Crash (in New Zealand) asked a broader question yesterday

which has not yet been satisfactorily answered in this thread.

http://www.scienceforums.net/forums/showpost.php?p=143569&postcount=1

 

Crash asked if you jump down the hole

(which I take to be between the N pole and the S pole, so we dont have to worry about corrioloris-type effects of earth's rotation)

then (Crash asked)

"What happens?"

 

which I guess would include wondering about HOW FAST do you get going

and HOW LONG does the trip to the opposite pole take.

 

It would be a total bummer if there were air in the vertical tunnel because

you would be limited to comparatively slow speed so I will assume vacuum

and I guess that the max speed would be

 

sqrt (GM/R) = 7.9 km/second

 

swansont please confirm or let me know if this is wrong

 

===========

I note that tuskir merely asked

"Will you be suspended in the center or just continue falling until you get to the other side and then start falling again or what?"

So his question (which is only about the qualitative result) has been answered.

 

But Crash asked "What happens?" which would include quantitative things like how fast and how long which physicists and physics students normally try to address.

 

So if we want we can respond to Crash broader question as well.

[swansont]

which I guess would include wondering about HOW FAST do you get going

and HOW LONG does the trip to the opposite pole take.

 

It would be a total bummer if there were air in the vertical tunnel because

you would be limited to comparatively slow speed so I will assume vacuum

and I guess that the max speed would be

 

sqrt (GM/R) = 7.9 km/second

 

swansont please confirm or let me know if this is wrong

 

Th force is going to decrease as you fall' date=' since the mass inside r drops as r[sup']3[/sup] and the force explicity depends on r² (assuming constant density)

 

 

Under that assumption I get v = sqrt(Gp(4/3)pi R²) where p is the density, for a speed of ~7.9 km/s (I just noticed that my equation reduces to yours) So we agree.

 

My density ends up being about 5.5 g/cm³ (5500 kg/m³) which is twice as large as the earth's crust, but smaller (of course) than the core. So the initial acceleration would be smaller and the later acceleration larger than I modeled. You'd need p® and get a more complicated integral in figuring the work done by gravity if you wanted to do it more precisely.

[J.C.MacSwell]

If the hole is between the poles and you neglect friction you will accelerate to the center starting at 0 velocity and maximum acceleration until you reach the center at maximum velocity and 0 acceleration. You would then reverse the process (acceleration wise) as you continue to the other pole and come to a stop (for an instant) before heading back.

 

Other "direct routes" would include a corriolis (sp?) like "force" (pseudo force)which will deflect you against the sides of the hole.

 

I forgot about the moon which would be significant. You can almost ignore the sun if you jump "today" or 6 months from now. There must be a path/tunnel that would exit you somewhere (near?) the Earth's surface if you jumped at the right time.