Time to fall through a hole in Earth, but not through center

In summary, the conversation discusses the classic physics problem of falling through a hole in the center of the Earth and the time it would take to reach the other side. It also mentions a variation of this problem where the hole is not directly through the center but along a chord from one part of the Earth's surface to another. The question is posed about how to calculate this fall in the chord situation and how to approach problems with non-uniform density distributions, such as considering the Earth to be an oblate spheroid instead of a sphere. The answer is the same regardless of the placement of the hole.
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Kavorka
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It is a classic physics problem to calculate how long it would take to fall through a hole that passes through the center of the Earth to the other side, assuming Earth is a sphere with uniform density. I also remember being posed a problem for if you were falling through a hole that passed not directly through the center of the Earth, but say along a chord from one part of the Earth's surface to another with a distance A from the chord's bisect to the Earth's center.

My question is how to calculate the trip of the fall in the chord situation (I know you'd need calculus to approach the mass distribution).

Also, how would you approach these types of problems using a non-uniform density distribution for the Earth? What if you considered the Earth to be an oblate spheroid and not a sphere? I'm interested in messing around with these problems.
 
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FAQ: Time to fall through a hole in Earth, but not through center

1. How long would it take to fall through a hole in the Earth?

The time it would take to fall through a hole in the Earth would depend on the size and depth of the hole, as well as the Earth's gravitational pull. It would also depend on the speed at which the object or person is falling. Generally, it would take a few minutes to reach the other side of the Earth.

2. Would a person survive falling through a hole in the Earth?

No, a person would not survive falling through a hole in the Earth. The intense heat and pressure near the Earth's core would be fatal. Additionally, the rapid acceleration and deceleration during the fall would most likely cause serious injuries.

3. How does air resistance affect the time it takes to fall through a hole in the Earth?

Air resistance would not have a significant impact on the time it takes to fall through a hole in the Earth. As the person or object approaches the Earth's core, the air density would increase, but the gravitational pull would also increase, making the overall impact of air resistance minimal.

4. Would the time to fall through a hole in the Earth be the same regardless of where the hole is located?

No, the time to fall through a hole in the Earth would not be the same regardless of where the hole is located. This is because the Earth's core is not a perfect sphere, and the distance to the core would vary depending on where the hole is located on the Earth's surface.

5. What factors influence the time it takes to fall through a hole in the Earth?

The time it takes to fall through a hole in the Earth would be influenced by several factors, including the size and depth of the hole, the Earth's gravitational pull, air resistance, and the speed at which the person or object is falling. It would also depend on the density and composition of the Earth's layers, which can vary in different locations.

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