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Suppose you drill a hole through the center of the earth (assume the earth is uniform and no air resistance) and you jump in. Would you be "weightless" throughout the entire fall?

The reason I ask is that if you jump off a cliff, throughout the entire fall you feel weightless (just like when astronauts train for the weightless feeling in orbit, they practice by going in an airplane and having the airplane fall to approximate the experience). Does this same weightless experience happen when you are falling through the center-of-the-earth tube?

I know that if you are stationary at the center of the earth, then you are weightless; but, I'm interested in falling throughout the entire hole.

The reason why I'm confused is that it's well-known that when you fall, you oscillate (simple harmonic motion) up and down the tube and this oscillation seems to imply that you will feel your weight.

Qmechanic
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Curiosity
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  • @PM2Ring It will only be weightless in the equilibrium point which is the center of earth. – Debanjan Biswas Oct 15 '22 at 16:23
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    @Debanjan That's not correct. Consider: if you jump off a cliff, you feel weightless from the instant that your feet leave the ground. Please do not try this experiment at home. ;) – PM 2Ring Oct 15 '22 at 16:30
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    @DebanjanBiswas At the center of the gravitating mass we have the following property: an object released to free motion will not start to move relative to its environment. By contrast: when released at any point away from the center of gravitational acceleration the object will accelarate; towards the center of gravitational acceleration.

    It would appear that you define 'weightless' as 'when released to free motion will not accelerate'.

    However, the standard definition of 'weightless' is: an accelerometer (local sensing) does not register acceleration.

     – Cleonis Oct 15 '22 at 16:35
  • Weight can only be felt if there is a force on your body opposing the motion. When you jump off a cliff there is no force opposing it (ignoring air resistance). But when you oscillate around the center of earth, earth's gravity is opposing your motion attracting you towards the center. – Debanjan Biswas Oct 15 '22 at 16:39
  • @DebanjanBiswas I surmise you believe the following: that in free motion there is a measurable difference in between being accelerated by gravitational acceleration, and being decelerated by gravitational acceleration. That is, you appear to believe there is a difference between descending velocity (relative to the gravity vector) and ascending velocity (relative to the gravity vector). I surmise that you believe that this is something that an accelerometer (local sensing) will register. – Cleonis Oct 15 '22 at 16:56
  • @Debanjan But you can't actually feel the oscillation. It's similar to what happens on a trampoline (ignoring air resistance): you don't feel the change of direction at the top of the jump, you only feel the effects when your feet are in contact with the mat. I admit that freefall in the tube doesn't feel identical to freefall in a perfect circular orbit: the tidal force is different, but those tidal effects aren't easy to notice. – PM 2Ring Oct 15 '22 at 16:57

3 Answers3

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In order to feel your weight something must be present that prevents you from free falling.

In everyday life the ground we are standing on provides the barrier that keeps us from free falling.


You refer to the implication that an object in free fall inside a corridor straight through the center of gravity of a gravitating mass will undergo oscillation. That is: the direction of gravitational acceleration is in opposite direction on opposite sides of the center of gravitational acceleration.

The point is: if you grant that inertial mass and gravitational mass are equivalent then an accelerometer-strapped-to-the-object will not register change of direction of gravitational acceleration, since given inertial-gravitational mass equivalence the accelerometer will not register any acceleration in the first place!

If equivalence of inertial and gravitational mass is granted then you expect that an accelerometer-strapped-to-the-object will register acceleration only if some barrier is preventing free fall.

Cleonis
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You would experience the feeling of weightlessness throughout the entire vibration as you move back and forth through the Earth. You hint at this in your question when you make reference to astronauts training for weightlessness in aircraft. The aircraft in this case is not simply moving down (and horizontally) but rather flying in a parabolic arc. Throughout the entire up and down motion the passengers experience the same sensation of weightlessness. You could think of this as half of an oscillation.

As explained in Cleonis's answer weightlessness will be experienced anytime the force of gravity is the only force acting on a person.

M. Enns
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Suppose you drill a hole through the center of the earth (assume the earth is uniform and no air resistance) and you jump in. Would you be "weightless" throughout the entire fall?

Yes, because you would follow the spacetime geodesics. The case you described has been precise analyzed by Edward Parker in A relativistic gravity train, where he calculates the trajectory of a test particle under the gravitational influence of a ball with uniform mass density as the particle falls through the ball’s diameter.

JanG
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