# The gravity tunnel in a non-uniform Earth

@article{Klotz2015TheGT, title={The gravity tunnel in a non-uniform Earth}, author={Alexander R. Klotz}, journal={American Journal of Physics}, year={2015}, volume={83}, pages={231-237} }

This paper examines the gravity tunnel using the internal structure of Earth as ascertained from seismic data. Numerically, it is found that the time taken to fall along the diameter is 38 min, compared to 42 min for a planet with uniform density. The time taken to fall along a straight line between any two points is no longer independent of distance but interpolates between 42 min for short trips and 38 min for long trips. The brachistochrone path (minimizing the time between any two points…

## 17 Citations

A note on a straight gravity tunnel through a rotating body

- Geology
- 2020

It is well-known that the straight gravity tunnel between any two different positions on a nonrotating Earth, which has uniform density, is traversable, i.e., an object initially at rest will reach…

Free Fall Through the Earth

- Physics
- 2016

Free fall through the Earth, considered as a sphere of radially symmetric mass density, along the axis of rotation, is calculated using a general differential equation in newtonian gravity theory.…

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- 2018

The gravity train that takes 42.2 min from any point A to any other point B that is connected by a straight-line tunnel through Earth has captured the imagination more than most other applications in…

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- Physics, GeologyAmerican journal of physics
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The fall-through time of polytropes, models of Earth's interior where the pressure varies as a power of the density, is calculated and it is shown that completely degenerate objects have sizes similar to Earth but their much higher masses mean a much larger gravitational strength and a shorter fall-Through time.

A Guided Tour of Planetary Interiors

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- 2015

We explore the gravitational dynamics of falling through planetary interiors. Two trajectory classes are considered: a straight cord between two surface points, and the brachistochrone path that…

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- 2016

We treat, as an illustrative example of gravitational time dilation in relativity, the observation that the centre of the Earth is younger than the surface by an appreciable amount. Richard Feynman…

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- 2017

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A smooth trip to Alpha Centauri: Comment on “The least uncomfortable journey from A to B” [Am. J. Phys. 84(9) 690–695]

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We consider the relativistic generalization of the problem of the “least uncomfortable” linear trajectory from point A to point B. The traditional problem minimizes the time-integrated squared…

Deep space experiment to measure G

- Physics, Geology
- 2016

Responding to calls from the National Science Foundation for new proposals to measure the gravitational constant G, we offer an interesting experiment in deep space employing the classic gravity…

General Brachistochrone Curve

- Physics, Geology
- 2017

In history, the problem of Johann Bernoulli's Brachistochrone Curve (BBC) was assumed the case that the force of gravity on the falling body is constant, for example, the case of near the surface of…

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