Circular orbits on a warped spandex fabric

@article{Middleton2014CircularOO,
  title={Circular orbits on a warped spandex fabric},
  author={Chad A. Middleton and M. A. Langston},
  journal={American Journal of Physics},
  year={2014},
  volume={82},
  pages={287-294}
}
We present a theoretical and experimental analysis of circular-like orbits made by a marble rolling on a warped spandex fabric. We show that the mass of the fabric interior to the orbital path influences the motion of the marble in a nontrivial way and can even dominate the orbital characteristics. We also compare a Kepler-like expression for such orbits to similar expressions for orbits about a spherically symmetric massive object in the presence of a constant vacuum energy, as described by… 

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References

SHOWING 1-10 OF 13 REFERENCES

The shape of “the Spandex” and orbits upon its surface

What is the shape that results when a flat rubber sheet is warped by placing a heavy ball upon it? We show that, at distance R far from the center of a ball of mass M, the height h of the surface

The geodesic structure of the Schwarzschild anti-de Sitter black hole

In this work, we find the geodesic structure of an AdS black hole. By means of a detailed analysis of the corresponding effective potentials for particles and photons, we find all possible motions

Geodesic equation in Schwarzschild-(anti-)de Sitter space-times: Analytical solutions and applications

The complete set of analytic solutions of the geodesic equation in a Schwarzschild-(anti-)de Sitter space-time is presented. The solutions are derived from the Jacobi inversion problem restricted to

Spacetime and Geometry: An Introduction to General Relativity

1. Special Relativity and Flat Spacetime. 2. Manifolds. 3. Curvature. 4. Gravitation. 5. The Schwarzchild Solution. 6. More General Black Holes. 7. Perturbation Theory and Gravitational Radiation. 8.

Perfect Form: Variational Principles, Methods, and Applications in Elementary Physics

This short book is concerned with the physical applications of variational principles of the calculus. It is intended for undergraduate students who have taken some introductory lectures on the

Gravity: An Introduction to Einstein's General Relativity

General relativity is one of the cornerstones of modern physics. In spite of this, the teaching of general relativity at undergraduate level remains quite marginal. The reasons for this particular

Trajectories of rolling marbles on various funnels

We investigate the trajectories of a small marble constrained to roll on frictionless surfaces, called funnels, of varying shapes. Actual coin funnels have a hyperbolic surface, and here we disprove

As is the case for the Schwarzschild metric, r < 3GM yields no circular orbits