scholarly journals Scaling, Mirror Symmetries and Musical Consonances Among the Distances of the Planets of the Solar System

Author(s):  
Michael J. Bank ◽  
Nicola Scafetta

Orbital systems are often self-organized and/or characterized by harmonic relations. Inspired by music theory, we rewrite the Geddes and King-Hele (QJRAS, 24, 10–13, 1983) equations for mirror symmetries among the distances of the planets of the Solar System in an elegant and compact form by using the 2/3rd power of the ratios of the semi-major axis lengths of two neighboring planets (eight pairs, including the belt of the asteroids). This metric suggests that the Solar System could be characterized by a scaling and mirror-like structure relative to the asteroid belt that relates together the terrestrial and Jovian planets. These relations are based on a 9/8 ratio multiplied by powers of 2, which correspond musically to the interval of the Pythagorean epogdoon (a Major Second) and its addition with one or more octaves. Extensions of the same model are discussed and found compatible also with the still hypothetical vulcanoid asteroids versus the transneptunian objects. The found relation also suggests that the planetary self-organization of our system could be generated by the 3:1 and 7:3 resonances of Jupiter, which are already known to have shaped the asteroid belt. The proposed model predicts the main Kirkwood asteroid gaps and the ratio among the planetary orbital parameters with a 99% accuracy, which is three times better than an alternative, recently proposed harmonic-resonance model for the Solar System. Furthermore, the ratios of neighboring planetary pairs correspond to four musical “consonances” having frequency ratios of 5/4 (Major Third), 4/3 (Perfect Fourth), 3/2 (Perfect Fifth) and 8/5 (Minor Sixth); the probability of obtaining this result randomly has a p < 0.001. Musical consonances are “pleasing” tones that harmoniously interrelate when sounded together, which suggests that the orbits of the planets of our Solar System could form some kind of gravitationally optimized and coordinated structure. Physical modeling indicates that energy non-conserving perturbations could drive a planetary system into a self-organized periodic state with characteristics vaguely similar of those found in our Solar System. However, our specific finding suggests that the planetary organization of our Solar System could be rather peculiar and based on more complex and unknown dynamical structures.

Author(s):  
Gloria Guilluy ◽  
Alessandro Sozzetti ◽  
Paolo Giacobbe ◽  
Aldo S. Bonomo ◽  
Giuseppina Micela

AbstractSince the first discovery of an extra-solar planet around a main-sequence star, in 1995, the number of detected exoplanets has increased enormously. Over the past two decades, observational instruments (both onboard and on ground-based facilities) have revealed an astonishing diversity in planetary physical features (i. e. mass and radius), and orbital parameters (e.g. period, semi-major axis, inclination). Exoplanetary atmospheres provide direct clues to understand the origin of these differences through their observable spectral imprints. In the near future, upcoming ground and space-based telescopes will shift the focus of exoplanetary science from an era of “species discovery” to one of “atmospheric characterization”. In this context, the Atmospheric Remote-sensing Infrared Exoplanet Large (Ariel) survey, will play a key role. As it is designed to observe and characterize a large and diverse sample of exoplanets, Ariel will provide constraints on a wide gamut of atmospheric properties allowing us to extract much more information than has been possible so far (e.g. insights into the planetary formation and evolution processes). The low resolution spectra obtained with Ariel will probe layers different from those observed by ground-based high resolution spectroscopy, therefore the synergy between these two techniques offers a unique opportunity to understanding the physics of planetary atmospheres. In this paper, we set the basis for building up a framework to effectively utilise, at near-infrared wavelengths, high-resolution datasets (analyzed via the cross-correlation technique) with spectral retrieval analyses based on Ariel low-resolution spectroscopy. We show preliminary results, using a benchmark object, namely HD 209458 b, addressing the possibility of providing improved constraints on the temperature structure and molecular/atomic abundances.


1968 ◽  
Vol 33 ◽  
pp. 217-235 ◽  
Author(s):  
Ľ. Kresák

The relation of physical characteristics of meteors to their orbital elements is investigated using Harvard Super-Schmidt data. A set of characteristic indices is defined, allowing for the effects of geocentric velocity, angle of incidence, magnitude and mass, wherever a correction appears appropriate according to the correlations found by Jacchia et al. (1967). The medians for representative meteor samples are plotted in the semi-major axis/eccentricity diagram and the distribution of each parameter is derived. Although the differences are moderate compared to the measuring errors, six regions of different nature can be distinguished.The existence of two families of asteroidal meteors is indicated, one of them brought to crossing with the Earth's orbit by drag effects and the other by collision effects in the main asteroid belt. These meteors are characterized by low and uniform beginning heights, high fragmentation, low ablation, low deceleration, and bright wakes. A direct counterpart to this is represented by meteors moving in short-period orbits of higher eccentricity and shorter perihelion distance, which bear resemblance to the long-period and retrograde cometary meteors. Meteors with perihelion distances of less than 0·15 AU tend to resemble the bona fide asteroidal meteors by a progressive increase of fragmentation and decrease of reduced beginning heights and decelerations as the perihelion approaches the Sun. This is attributed to the selective destruction effects of solar radiation.With the exception of the Draconids, the mean characteristics of meteor showers agree well with those of sporadic meteors moving in similar orbits. It is suggested that the Draconid stream includes a broad variety of meteoric material and that the two peculiar Super-Schmidt meteors on record represent only the less resistive, short-lived component which has already been eliminated from the other showers.


2020 ◽  
Vol 24 (1) ◽  
pp. 56-60
Author(s):  
Mohamed R. Amin

AbstractThe focus of this paper is the design of a self-maintenance orbit using two natural forces against each other. The effect of perturbations due to Earth's oblateness up to the third order on both the semi-major axis and eccentricity for a low Earth orbit satellite together with the perturbation due to air drag on the same orbital parameters were used, in order to create self-maintenance orbits. Numerical results were simulated for a low earth orbit satellite, which substantiates the applicability of the results.


1996 ◽  
Vol 160 ◽  
pp. 525-530 ◽  
Author(s):  
Z. Arzoumanian ◽  
K. Joshi ◽  
F. A. Rasio ◽  
S. E. Thorsett

AbstractPrevious timing data for PSR B1620–26 were consistent with a second companion mass m2anywhere in the range ∼ 10−3– 1M⊙, i.e., from a Jupiter-type planet to a star. We present the latest timing parameters for the system, including a significant change in the projected semi-major axis of the inner binary, a marginal detection of the fourth time derivative of the pulse frequency, and the pulsar proper motion (which is in agreement with published values for the proper motion of M4), and use them to further constrain the mass m2and the orbital parameters. Using the observed value of, we obtain a one-parameter family of solutions, all with m2≲ 10−2M⊙, i.e., excluding stellar masses. Varyingwithin its formal 1σ error bar does not affect the mass range significantly. However, if we varywithin a 4σ error bar, we find that stellar-mass solutions are still possible. We also calculate the predicted rate of change of the projected semi-major axis of the inner binary and show that it agrees with the measured value.


1980 ◽  
Vol 88 ◽  
pp. 511-515
Author(s):  
Kyoji Nariai

When there is mass loss from a binary system, the lost mass carries energy and angular momentum out of the system. Therefore, the remaining system must adjust its orbital parameters to the changing values of the total kinematic energy E and the total angular momentum N as the total mass M decreases. The parameters concerned here are : the fractional mass μ, the semi-major axis a, and the eccentricity e.


2004 ◽  
Vol 218 ◽  
pp. 429-430
Author(s):  
N. Wang ◽  
S. Johnston ◽  
R. N. Manchester

This paper summarizes the results of 13 years of timing observations of a unique binary pulsar, B1259–63, which has a massive B2e star companion. A small glitch in the pulsar period apparently occurred in 1997 Aug, not long after the 1997 periastron. We found that spin-orbit coupling with secular changes in periastron longitude and projected semi-major axis cannot account for the observed period variations. A model in which step changes in pulsar orbital parameters occur at each periastron accounts best for the observed timing behavior.


1985 ◽  
Vol 85 ◽  
pp. 417-420
Author(s):  
P. Barge ◽  
R. Pellat ◽  
J. Millet

AbstractThe scattering of dust grains orbits due to recurrent sectors of the interplanetary magnetic field is reinvestigated with a better formalism. Our method reveals the resonant character of the diffusion and is well suited for the problem. The spreads in the orbital parameters are found less important than believed untill now and to vary rapidly with eccentricity and semi-major axis. Only the small dielectric grains with size less than 0.5 μm may be scattered by the Lorentz force fluctuations; the main diffusion occurs in inclination and near the sun (20-60 R⊙).


2012 ◽  
Vol 27 (12) ◽  
pp. 1250071 ◽  
Author(s):  
L. IORIO

We work out the impact that the recently determined time-dependent component of the Pioneer Anomaly (PA), if interpreted as an additional exotic acceleration of gravitational origin with respect to the well-known PA-like constant one, may have on the orbital motions of some planets of the solar system. By assuming that it points towards the Sun, it turns out that both the semi-major axis a and the eccentricity e of the orbit of a test particle would experience secular variations. For Saturn and Uranus, for which modern data records cover at least one full orbital revolution, such predicted anomalies are up to 2–3 orders of magnitude larger than the present-day accuracies in empirical determinations of their orbital parameters from the usual orbit determination procedures in which the PA was not modeled. Given the predicted huge sizes of such hypothetical signatures, it is unlikely that their absence from the presently available processed data can be attributable to an "absorption" for them in the estimated parameters caused by the fact that they were not explicitly modeled. The magnitude of a constant PA-type acceleration at 9.5 au cannot be larger than 9×10-15 m s-2 according to the latest observational results for the perihelion precession of Saturn.


2009 ◽  
Vol 5 (S264) ◽  
pp. 440-442 ◽  
Author(s):  
Adriana Silva-Válio

AbstractAs a planet eclipses its parent star, dark spots on the surface of the star may be occulted, causing a detectable variation in the transit light curve. There are basically two effects caused by the presence of spots on the surface of the star which can alter the shape of the light curve during transits and thus preclude the correct determination of the planet physical and orbital parameters. The first one is that the presence of many spots within the latitude band occulted by the planet will cause the depth of the transit in the light curve to be shallower. This will erroneously result in a smaller radius for the planet. The other effect is that generated by spots located close to the limb of the star. In this case, the spots will interfere in the light curve during the times of ingress or egress of the planet, causing a decrease in the transit duration. This in turn will provide a larger value for the semi-major axis of the planetary orbit. Qualitative estimates of both effects are discussed and an example provided for a very active star, such as CoRoTo-2.


2021 ◽  
Vol 922 (1) ◽  
pp. 35
Author(s):  
G. Y. Agazie ◽  
M. G. Mingyar ◽  
M. A. McLaughlin ◽  
J. K. Swiggum ◽  
D. L. Kaplan ◽  
...  

Abstract The Green Bank North Celestial Cap survey is a 350 MHz all-sky survey for pulsars and fast radio transients using the Robert C. Byrd Green Bank Telescope. To date, the survey has discovered over 190 pulsars, including 33 millisecond pulsars and 24 rotating radio transients. Several exotic pulsars have been discovered in the survey, including PSR J1759+5036, a binary pulsar with a 176 ms spin period in an orbit with a period of 2.04 days, an eccentricity of 0.3, and a projected semi-major axis of 6.8 light seconds. Using seven years of timing data, we are able to measure one post–Keplerian parameter, advance of periastron, which has allowed us to constrain the total system mass to 2.62 ± 0.03 M ⊙. This constraint, along with the spin period and orbital parameters, suggests that this is a double neutron star system, although we cannot entirely rule out a pulsar-white dwarf binary. This pulsar is only detectable in roughly 45% of observations, most likely due to scintillation. However, additional observations are required to determine whether there may be other contributing effects.


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