scholarly journals Planetary Systems and the Hidden Symmetries of the Kepler Problem

Symmetry ◽  
2020 ◽  
Vol 12 (12) ◽  
pp. 2109
Author(s):  
József Cseh
Keyword(s):  
Solar System ◽  
Planetary System ◽  
Kepler Problem ◽  
Regular Sequence ◽  
Transformation Rule ◽  
Hidden Symmetries ◽  
Regular Polyhedra ◽  
Hidden Symmetry ◽  
Planetary Orbits ◽  
Exoplanet Systems

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.

scholarly journals Is our Sun a Singleton?

2007 ◽  
Vol 3 (S246) ◽  
pp. 273-274
Author(s):  
D. Malmberg ◽  
M. B. Davies ◽  
J. E. Chambers ◽  
F. De Angeli ◽  
R. P. Church ◽  
...  
Keyword(s):  
Binary System ◽  
Solar System ◽  
Planetary System ◽  
Large Fraction ◽  
Planetary Systems ◽  
Number Density ◽  
Single Star ◽  
Close Encounters ◽  
Eccentric Orbits ◽  
Exoplanet Systems

AbstractMost stars are formed in a cluster or association, where the number density of stars can be high. This means that a large fraction of initially-single stars will undergo close encounters with other stars and/or exchange into binaries. We describe how such close encounters and exchange encounters can affect the properties of a planetary system around a single star. We define a singleton as a single star which has never suffered close encounters with other stars or spent time within a binary system. It may be that planetary systems similar to our own solar system can only survive around singletons. Close encounters or the presence of a stellar companion will perturb the planetary system, often leaving planets on tighter and more eccentric orbits. Thus planetary systems which initially resembled our own solar system may later more closely resemble some of the observed exoplanet systems.

scholarly journals Planetary systems in a star cluster I: the Solar system scenario

2019 ◽  
Vol 489 (2) ◽  
pp. 2280-2297 ◽  
Author(s):  
Francesco Flammini Dotti ◽  
M B N Kouwenhoven ◽  
Maxwell Xu Cai ◽  
Rainer Spurzem
Keyword(s):  
Solar System ◽  
Planetary System ◽  
Survival Rates ◽  
Star Clusters ◽  
Planetary Systems ◽  
Star Cluster ◽  
Habitable Zone ◽  
Escape Process ◽  
Exoplanet Systems ◽  
High Diversity

ABSTRACTYoung stars are mostly found in dense stellar environments, and even our own Solar system may have formed in a star cluster. Here, we numerically explore the evolution of planetary systems similar to our own Solar system in star clusters. We investigate the evolution of planetary systems in star clusters. Most stellar encounters are tidal, hyperbolic, and adiabatic. A small fraction of the planetary systems escape from the star cluster within 50 Myr; those with low escape speeds often remain intact during and after the escape process. While most planetary systems inside the star cluster remain intact, a subset is strongly perturbed during the first 50 Myr. Over the course of time, $0.3\!-\!5.3{{\ \rm per\ cent}}$ of the planets escape, sometimes up to tens of millions of years after a stellar encounter occurred. Survival rates are highest for Jupiter, while Uranus and Neptune have the highest escape rates. Unless directly affected by a stellar encounter itself, Jupiter frequently serves as a barrier that protects the terrestrial planets from perturbations in the outer planetary system. In low-density environments, Jupiter provides protection from perturbations in the outer planetary system, while in high-density environments, direct perturbations of Jupiter by neighbouring stars is disruptive to habitable-zone planets. The diversity amongst planetary systems that is present in the star clusters at 50 Myr, and amongst the escaping planetary systems, is high, which contributes to explaining the high diversity of observed exoplanet systems in star clusters and in the Galactic field.

Drifting Through a Planetary System

2018 ◽  
Author(s):  
Karel Schrijver
Keyword(s):  
Seventeenth Century ◽  
Solar System ◽  
Virtual Worlds ◽  
Planetary System ◽  
System P ◽  
History Of ◽  
Or Team ◽  
Water Contents

This chapter describes how the first found exoplanets presented puzzles: they orbited where they should not have formed or where they could not have survived the death of their stars. The Solar System had its own puzzles to add: Mars is smaller than expected, while Venus, Earth, and Mars had more water—at least at one time—than could be understood. This chapter shows how astronomers worked through the combination of these puzzles: now we appreciate that planets can change their orbits, scatter water-bearing asteroids about, steal material from growing planets, or team up with other planets to stabilize their future. The special history of Jupiter and Saturn as a pair bringing both destruction and water to Earth emerged from the study of seventeenth-century resonant clocks, from the water contents of asteroids, and from experiments with supercomputers imposing the laws of physics on virtual worlds.

On regular polyhedra with hidden symmetries

1987 ◽  
Vol 12 (3-4) ◽  
pp. 450-458
Author(s):  
Jörg M. Wills
Keyword(s):  
Hidden Symmetries ◽  
Regular Polyhedra

scholarly journals CAN GENERAL RELATIVISTIC DESCRIPTION OF GRAVITATION BE CONSIDERED COMPLETE?

1998 ◽  
Vol 13 (17) ◽  
pp. 1393-1400 ◽  
Author(s):  
D. V. AHLUWALIA
Keyword(s):  
Solar System ◽  
Gravitational Potential ◽  
Invariance Properties ◽  
Planetary Orbits ◽  
Galactic Cluster ◽  
General Relativistic ◽  
Relativistic Description ◽  
Flavor Oscillation ◽  
Weak Fields ◽  
Great Attractor

The local galactic cluster, the Great attractor, embeds us in a dimensionless gravitational potential of about -3×10-5. In the solar system, this potential is constant to about 1 part in 1011. Consequently, planetary orbits, which are determined by the gradient in the gravitational potential, remain unaffected. However, this is not so for the recently introduced flavor-oscillation clocks where the new redshift-inducing phases depend on the gravitational potential itself. On these grounds, and by studying the invariance properties of the gravitational phenomenon in the weak fields, we argue that there exists an element of incompleteness in the general relativistic description of gravitation. An incompleteness-establishing inequality is derived and an experiment is outlined to test the thesis presented.

scholarly journals The Principle of Least Interaction Action

1974 ◽  
Vol 3 ◽  
pp. 489-489
Author(s):  
M. W. Ovenden
Keyword(s):  
Solar System ◽  
Planetary System ◽  
Satellite System ◽  
Asteroid Belt ◽  
Correct Prediction ◽  
The Sun ◽  
Approximate Methods ◽  
Satellites Of Jupiter ◽  
History Of ◽  
Minimum Interaction

AbstractThe intuitive notion that a satellite system will change its configuration rapidly when the satellites come close together, and slowly when they are far apart, is generalized to ‘The Principle of Least Interaction Action’, viz. that such a system will most often be found in a configuration for which the time-mean of the action associated with the mutual interaction of the satellites is a minimum. The principle has been confirmed by numerical integration of simulated systems with large relative masses. The principle lead to the correct prediction of the preference, in the solar system, for nearly-commensurable periods. Approximate methods for calculating the evolution of an actual satellite system over periods ˜ 109 yr show that the satellite system of Uranus, the five major satellites of Jupiter, and the five planets of Barnard’s star recently discovered, are all found very close to their respective minimum interaction distributions. Applied to the planetary system of the Sun, the principle requires that there was once a planet of mass ˜ 90 Mθ in the asteroid belt, which ‘disappeared’ relatively recently in the history of the solar system.

Quantum cosmology: From hidden symmetries towards a new (supersymmetric) perspective

2016 ◽  
Vol 25 (03) ◽  
pp. 1630009 ◽  
Author(s):  
S. Jalalzadeh ◽  
T. Rostami ◽  
P. V. Moniz
Keyword(s):  
New York ◽  
Boundary Conditions ◽  
Quantum Cosmology ◽  
Ad Hoc ◽  
Hidden Symmetries ◽  
Shape Invariance ◽  
Hidden Symmetry ◽  
Shape Invariant ◽  
Model Dynamics ◽  
Lecture Notes

We review pedagogically some of the basic essentials regarding recent results intertwining boundary conditions, the algebra of constraints and hidden symmetries in quantum cosmology. They were extensively published in Refs. [S. Jalalzadeh, S. M. M. Rasouli and P. V. Moniz, Phys. Rev. D 90 (2014) 023541, S. Jalalzadeh and P. V. Moniz, Phys. Rev. D 89 (2014), S. Jalalzadeh, T. Rostami and P. V. Moniz, Eur. Phys. J. C 75 (2015) 38, arXiv:gr-qc/1412.6439 and T. Rostami, S. Jalalzadeh and P. V. Moniz, Phys. Rev. D 92 (2015) 023526, arXiv:gr-qc/1507.04212], where complete discussions and full details can be found. More concretely, in Refs. [S. Jalalzadeh, S. M. M. Rasouli and P. V. Moniz, Phys. Rev. D 90 (2014) 023541, S. Jalalzadeh and P. V. Moniz, Phys. Rev. D 89 (2014) and S. Jalalzadeh, T. Rostami and P. V. Moniz, Eur. Phys. J. C 75 (2015) 38, arXiv:gr-qc/1412.6439] it has been shown that specific boundary conditions can be related to the algebra of Dirac observables. Moreover, a process afterwards associated to the algebra of existent hidden symmetries, from which the boundary conditions can be selected, was introduced. On the other hand, in Ref. [T. Rostami, S. Jalalzadeh and P. V. Moniz, Phys. Rev. D 92 (2015) 023526, arXiv:gr-qc/1507.04212] it was subsequently argued that some factor ordering choices can be extracted from the hidden symmetries structure of the minisuperspace model.In Refs. [S. Jalalzadeh, S. M. M. Rasouli and P. V. Moniz, Phys. Rev. D 90 (2014) 023541, S. Jalalzadeh and P. V. Moniz, Phys. Rev. D 89 (2014), S. Jalalzadeh, T. Rostami and P. V. Moniz, Eur. Phys. J. C 75 (2015) 38, arXiv:gr-qc/1412.6439 and T. Rostami, S. Jalalzadeh and P. V. Moniz, Phys. Rev. D 92 (2015) 023526, arXiv:gr-qc/1507.04212], we proceeded gradually towards less simple models, ranging from a FLRW model with a perfect fluid [S. Jalalzadeh, S. M. M. Rasouli and P. V. Moniz, Phys. Rev. D 90 (2014) 023541] up to a conformal scalar field content [T. Rostami, S. Jalalzadeh and P. V. Moniz, Phys. Rev. D 92 (2015) 023526, arXiv:gr-qc/1507.04212]. We envisage that we could extend this framework towards a class of shape invariant potentials, which could include well known analytically solvable cosmological cases. Provided, we identify integrability in terms of the shape invariance conditions, we could eventually consider to import features of supersymmetric quantum mechanics towards quantum cosmology [P. V. Moniz, Quantum Cosmology-the Supersymmetric Perspective-Vol. 1: Fundamentals, Lecture Notes in Physics, Vol. 803 (Springer-Verlag, Berlin, 2010), P. V. Moniz, Quantum Cosmology-the Supersymmetric Perspective-Vol. 2: Advanced Topics, Lecture Notes in Physics, Vol. 804 (Springer, New York, 2010)], which we will also discuss in this review.Another point to emphasize is that by means of a hidden symmetry and then an algebra of Dirac observables, boundary conditions are extracted (and not ad hoc formulated) within a framework intrinsic to each model dynamics. Therefore, meeting DeWitt’s conjecture [B. S. DeWitt, Phys. Rev. 160 (1967) 1113] that “the constraints are everything” and nothing else but the constraints should be needed.

scholarly journals Resilient habitability of nearby exoplanet systems

2019 ◽  
Vol 492 (1) ◽  
pp. 352-368 ◽  
Author(s):  
Giorgi Kokaia ◽  
Melvyn B Davies ◽  
Alexander J Mustill
Keyword(s):  
Giant Planet ◽  
Planetary Systems ◽  
Observational Constraints ◽  
Habitable Zone ◽  
Habitable Zones ◽  
Test Particles ◽  
Planetary Orbits ◽  
Two Systems ◽  
Earth Like Planets ◽  
Exoplanet Systems

ABSTRACT We investigate the possibility of finding Earth-like planets in the habitable zone of 34 nearby FGK-dwarfs, each known to host one giant planet exterior to their habitable zone detected by RV. First we simulate the dynamics of the planetary systems in their present day configurations and determine the fraction of stable planetary orbits within their habitable zones. Then, we postulate that the eccentricity of the giant planet is a result of an instability in their past during which one or more other planets were ejected from the system. We simulate these scenarios and investigate whether planets orbiting in the habitable zone survive the instability. Explicitly we determine the fraction of test particles, originally found in the habitable zone, which remain in the habitable zone today. We label this fraction the resilient habitability of a system. We find that for most systems the probability of planets existing [or surviving] on stable orbits in the habitable zone becomes significantly smaller when we include a phase of instability in their history. We present a list of candidate systems with high resilient habitability for future observations. These are: HD 95872, HD 154345, HD 102843, HD 25015, GJ 328, HD 6718, and HD 150706. The known planets in the last two systems have large observational uncertainties on their eccentricities, which propagate into large uncertainties on their resilient habitability. Further observational constraints of these two eccentricities will allow us to better constrain the survivability of Earth-like planets in these systems.

scholarly journals On the survival of resonant and non-resonant planetary systems in star clusters

2020 ◽  
Vol 497 (2) ◽  
pp. 1807-1825
Author(s):  
Katja Stock ◽  
Maxwell X Cai ◽  
Rainer Spurzem ◽  
M B N Kouwenhoven ◽  
Simon Portegies Zwart
Keyword(s):  
Solar System ◽  
Star Clusters ◽  
Planetary Systems ◽  
Dynamical Evolution ◽  
Giant Planets ◽  
Mean Motion Resonances ◽  
Orbital Parameters ◽  
Eccentric Orbits ◽  
The Individual ◽  
Exoplanet Systems

ABSTRACT Despite the discovery of thousands of exoplanets in recent years, the number of known exoplanets in star clusters remains tiny. This may be a consequence of close stellar encounters perturbing the dynamical evolution of planetary systems in these clusters. Here, we present the results from direct N-body simulations of multiplanetary systems embedded in star clusters containing N = 8k, 16k, 32k, and 64k stars. The planetary systems, which consist of the four Solar system giant planets Jupiter, Saturn, Uranus, and Neptune, are initialized in different orbital configurations, to study the effect of the system architecture on the dynamical evolution of the entire planetary system, and on the escape rate of the individual planets. We find that the current orbital parameters of the Solar system giants (with initially circular orbits, as well as with present-day eccentricities) and a slightly more compact configuration, have a high resilience against stellar perturbations. A configuration with initial mean-motion resonances of 3:2, 3:2, and 5:4 between the planets, which is inspired by the Nice model, and for which the two outermost planets are usually ejected within the first 105 yr, is in many cases stabilized due to the removal of the resonances by external stellar perturbation and by the rapid ejection of at least one planet. Assigning all planets the same mass of 1 MJup almost equalizes the survival fractions. Our simulations reproduce the broad diversity amongst observed exoplanet systems. We find not only many very wide and/or eccentric orbits, but also a significant number of (stable) retrograde orbits.

scholarly journals Turning solar systems into extrasolar planetary systems in stellar clusters

2010 ◽  
Vol 6 (S276) ◽  
pp. 304-307
Author(s):  
Melvyn B. Davies
Keyword(s):  
Solar System ◽  
Planetary System ◽  
Large Fraction ◽  
Planetary Systems ◽  
Single Star ◽  
Solar Systems ◽  
Close Encounters ◽  
Eccentric Orbits ◽  
The Galaxy ◽  
Hostile Environments

AbstractMany stars are formed in some form of cluster or association. These environments can have a much higher number density of stars than the field of the galaxy. Such crowded places are hostile environments: a large fraction of initially single stars will undergo close encounters with other stars or exchange into binaries. We describe how such close encounters and exchange encounters will affect the properties of a planetary system around a single star. We define singletons as single stars which have never suffered close encounters with other stars or spent time within a binary system. It may be that planetary systems similar to our own solar system can only survive around singletons. Close encounters or the presence of a stellar companion will perturb the planetary system, leading to strong planet-planet interactions, often leaving planets on tighter and more eccentric orbits. Thus, planetary systems which initially resembled our own solar system may later more closely resemble the observed extrasolar planetary systems.

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