• Corpus ID: 15502210

Copernicus's epicycles from Newton's gravitational force law via linear perturbation theory in geometric algebra

@article{Sugon2008CopernicussEF,
  title={Copernicus's epicycles from Newton's gravitational force law via linear perturbation theory in geometric algebra},
  author={Quirino Sugon and Sarah Bragais and Daniel J. Mcnamara},
  journal={arXiv: Space Physics},
  year={2008}
}
We derive Copernicus's epicycles from Newton's gravitational force law by assuming that a planet's orbit is a perturbed circular orbit, with the perturbation defined to be co-rotating with the said orbit. We substitute this orbit expression into Newton's gravitation law and showed that the perturbation satisfies the linear part of Hill's oscillator equation for lunar motion. We solve this oscillator equation using an exponential Fourier series and impose the boundary conditions at the aphelion… 

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References

SHOWING 1-10 OF 13 REFERENCES

A visit to the newtonian N-body problem via elementary complex variables

The study of how N celestial bodies move under gravitational forces is an old one. If one is willing to acknowledge the work of the ancient astrologers and shepherds ― two groups that carefully

Quasi periodic motions from Hipparchus to Kolmogorov

Contemporary research on the problem of chaotic motions in dynamical systems finds its roots in the Aristotelian idea, often presented as kind of funny in high schools, that motions can always be

The Mathematical Power of Epicyclical Astronomy

T HIS PAPER has two objectives. The first is to describe more graphically than has yet been done the elegance of the ancient technique of epicycleon-deferent. The second is to expose as erroneous an

Geometric Algebra for Physicists

Geometric algebra is a powerful mathematical language with applications across a range of subjects in physics and engineering. This book is a complete guide to the current state of the subject with

Clifford Algebras and Spinor Operators

This paper begins with a historical survey on Clifford algebras and a model on how to start an undergraduate course on Clifford algebras. The Dirac equation and the bilinear covariants are discussed.

New Foundations for Classical Mechanics

1: Origins of Geometric Algebra.- 1-1. Geometry as Physics.- 1-2. Number and Magnitude.- 1-3. Directed Numbers.- 1-4. The Inner Product.- 1-5. The Outer Product.- 1-6. Synthesis and Simplification.-

The Commentariolus of Copernicus

Some years before COPERNICUS consented to the publication of his large work De Revolutionibus Orbium Caelestium (i), he wrote a brief sketch (Commentariolus) of his astronomical system. The

Researches in the Lunar Theory

Theory of Orbits: The Restricted Problem of Three Bodies