Symmetry and Dynamics: Two Distinct Methodologies from Kepler to Supersymmetry

Barut, A. O.

doi:10.1007/978-1-4757-1472-2_4

Cited by 4 publications

(10 citation statements)

References 7 publications

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“…As illustrated by the figures, the observed data of the planetary motion seem to follow a symmetry-inspired regularity. In particular, they are in line with the transformation rules described by Equations ( 4) and ( 5), obtained from the dynamical group of the Kepler problem [6]. It is hard to believe that this coincidence is completely by chance.…”

Section: Discussionsupporting

confidence: 82%

“…Here, we concentrate on the proposal of Barut [6], which was inspired by the hidden symmetries of the Kepler problem. He found that the logarithms of the planetary velocities, periods, and distances follow straight lines as a function of the natural sequence number of the planets:…”

Section: Transformations Of Planetary Orbitsmentioning

confidence: 99%

“…Here, λ is a constant, but with this single parameter we can predict any planetary orbital, if we know one of them. The dilatation (4) is a transformation, which is suggested by the O(4,2) dynamical group of the Kepler problem [6].…”

Section: Transformations Of Planetary Orbitsmentioning

confidence: 99%

“…The dynamical group of the Kepler problem is O(4,2) [6,14], which leaves invariant the x 2 1 + x 2 2 + x 2 3 + x 2 4 − x 2 5 − x 2 6 quadratic form. This group found its first physical application as a global or external space-time transformation.…”

Section: Symmetries Of the Kepler Problemmentioning

confidence: 99%

“…In the late 20th century, Barut proposed a new relation [6], which was inspired by the hidden symmetries of the Kepler problem. He realized that a space and time dilatation, which corresponds to the O(4,2) dynamical group, transforms the planetary orbits into each other.…”

Section: Introductionmentioning

confidence: 99%

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Planetary Systems and the Hidden Symmetries of the Kepler Problem

Cseh

2020

Symmetry

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The question of whether the solar distances of the planetary system follow a regular sequence was raised by Kepler more than 400 years ago. He could not prove his expectation, inasmuch as the planetary orbits are not transformed into each other by the regular polyhedra. In 1989, Barut proposed another relation, which was inspired by the hidden symmetry of the Kepler problem. It was found to be approximately valid for our Solar System. Here, we investigate if exoplanet systems follow this rule. We find that the symmetry-governed sequence is valid in several systems. It is very unlikely that the observed regularity is by chance; therefore, our findings give support to Kepler’s guess, although with a different transformation rule.

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Section: Discussionsupporting

confidence: 82%

Section: Transformations Of Planetary Orbitsmentioning

confidence: 99%

Section: Transformations Of Planetary Orbitsmentioning

confidence: 99%

Section: Symmetries Of the Kepler Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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