scholarly journals DYNAMICAL DERIVATION OF BODE'S LAW

2005 ◽  
Vol 14 (01) ◽  
pp. 153-169 ◽  
Author(s):  
R. W. BASS ◽  
A. DEL POPOLO
Keyword(s):  
Angular Momentum ◽  
Total Angular Momentum ◽  
Central Body ◽  
Dynamical Evolution ◽  
Satellite System ◽  
Point Particle ◽  
The Body ◽  
The Sun ◽  
Small Bodies ◽  
Orbital Radius

In a planetary or satellite system, idealized as n small bodies in an initially coplanar with concentric orbits around a large central body obeying the Newtonian point-particle mechanics, resonant perturbations will cause a dynamical evolution of the orbital radii except for cases with highly specific mutual relationships. In particular, the most stable situation can be achieved only when each planetary orbit is roughly twice as far from the Sun as the preceding one. This has been empirically observed by Titius (1766) and Bode (1778). By reformulating the problem as a hierarchical sequence of (unrestricted) 3-body problems and considering only the gravitational interactions among the central body and the body of interest and the adjacent outer body in the orbits, it is proved that the resonant perturbations from the outer body will destabilize the inner body (and vice versa) unless its mean orbital radius is a unique and specific multiple of β, the distal multiplier, of the inner body. In this way a sequence of concentric orbits can each stabilize the adjacent inner orbit, and since the outermost orbit is already tied to the collection of the inner orbits by conservation of total angular momentum, the entire configuration is stabilized.

scholarly journals Calibration of the angular momenta of the minor planets in the solar system

2019 ◽  
Vol 630 ◽  
pp. A68 ◽  
Author(s):  
Jian Li ◽  
Zhihong Jeff Xia ◽  
Liyong Zhou
Keyword(s):  
Angular Momentum ◽  
Solar System ◽  
Total Angular Momentum ◽  
Physical Parameters ◽  
Minor Planets ◽  
The Sun ◽  
Relative Angle ◽  
Angular Momenta ◽  
Dwarf Planets ◽  
Invariable Plane

Aims. We aim to determine the relative angle between the total angular momentum of the minor planets and that of the Sun-planets system, and to improve the orientation of the invariable plane of the solar system. Methods. By utilizing physical parameters available in public domain archives, we assigned reasonable masses to 718 041 minor planets throughout the solar system, including near-Earth objects, main belt asteroids, Jupiter trojans, trans-Neptunian objects, scattered-disk objects, and centaurs. Then we combined the orbital data to calibrate the angular momenta of these small bodies, and evaluated the specific contribution of the massive dwarf planets. The effects of uncertainties on the mass determination and the observational incompleteness were also estimated. Results. We determine the total angular momentum of the known minor planets to be 1.7817 × 1046 g cm2 s−1. The relative angle α between this vector and the total angular momentum of the Sun-planets system is calculated to be about 14.74°. By excluding the dwarf planets Eris, Pluto, and Haumea, which have peculiar angular momentum directions, the angle α drops sharply to 1.76°; a similar result applies to each individual minor planet group (e.g., trans-Neptunian objects). This suggests that, without these three most massive bodies, the plane perpendicular to the total angular momentum of the minor planets would be close to the invariable plane of the solar system. On the other hand, the inclusion of Eris, Haumea, and Makemake can produce a difference of 1254 mas in the inclination of the invariable plane, which is much larger than the difference of 9 mas induced by Ceres, Vesta, and Pallas as found previously. By taking into account the angular momentum contributions from all minor planets, including the unseen ones, the orientation improvement of the invariable plane is larger than 1000 mas in inclination with a 1σ error of ∼50−140 mas.

scholarly journals On the Initial Distance of the Moon Forming in the Circumterrestrial Swarm

1972 ◽  
Vol 47 ◽  
pp. 402-404
Author(s):  
E. L. Ruskol
Keyword(s):  
Angular Momentum ◽  
Total Angular Momentum ◽  
Outer Boundary ◽  
The Sun ◽  
The Moon ◽  
Present Value ◽  
Primitive Earth ◽  
Moon System ◽  
Initial Distance ◽  
The Earth

According to the Radzievskij-Artemjev hypothesis of the ‘locked’ revolution of the circumplanetary swarms around the Sun, the initial Moon-to-Earth distance and the angular momentum acquired by the Earth through the accretion of the inner part of the swarm can be evaluated. Depending on the concentration of the density to the centre of the swarm we obtain the initial distance for a single protomoon in the range 15–26 Earth radii R and for a system of 3-4 protomoons in the range 3–78 R, if the outer boundary of the swarm equals to the radius of the Hill's sphere (235 R). The total angular momentum acquired by the primitive Earth-Moon system through the accretion of the swarm particles is ½–⅔ of its present value. The rest of it should be acquired from the direct accretion of interplanetary particles by the Earth. The contribution of satellite swarms into the rotation of other planets is relatively less.

scholarly journals Orbital features of distant trans-Neptunian objects induced by giant gaseous clumps

2020 ◽  
Vol 642 ◽  
pp. L20
Author(s):  
V. V. Emel’yanenko
Keyword(s):  
Simple Model ◽  
Solar Nebula ◽  
Dynamical Evolution ◽  
Outer Solar System ◽  
The Sun ◽  
High Eccentricity ◽  
Small Bodies ◽  
Dynamical Characteristics ◽  
Gravitational Perturbations ◽  
The Hill

Context. The discovery of distant trans-Neptunian objects has led to heated discussions about the structure of the outer Solar System. Aims. We study the dynamical evolution of small bodies from the Hill regions of migrating giant gaseous clumps that form in the outer solar nebula via gravitational fragmentation. We attempt to determine whether the observed features of the orbital distribution of distant trans-Neptunian objects could be caused by this process. Methods. We consider a simple model that includes the Sun, two point-like giant clumps with masses of ∼10 Jupiter masses, and a set of massless objects initially located in the Hill regions of these clumps. We carry out numerical simulations of the motions of small bodies under gravitational perturbations from two giant clumps that move in elliptical orbits and approach each other. The orbital distribution of these small bodies is compared with the observed distribution of distant trans-Neptunian objects. Results. In addition to the known grouping in longitudes of perihelion, we note new features for observed distant trans-Neptunian objects. The observed orbital distribution points to the existence of two groups of distant trans-Neptunian objects with different dynamical characteristics. We show that the main features of the orbital distribution of distant trans-Neptunian objects can be explained by their origin in the Hill regions of migrating giant gaseous clumps. Small bodies are ejected from the Hill regions when the giant clumps move in high-eccentricity orbits and have a close encounter with each other. Conclusions. The resulting orbital distribution of small bodies in our model and the observed distribution of distant trans-Neptunian objects have similar features.

Analysis of Lead Heavy Metal (Pb) Contamination on Matte Lipstick Preparations for Sale in Banda Aceh City Aceh Market

2020 ◽  
Vol 2 (1) ◽  
Author(s):  
Rizki Andalia ◽  
Mulia Aria Suzanni ◽  
Rini Rini
Keyword(s):  
Heavy Metal ◽  
Atomic Absorption ◽  
Atomic Absorption Spectrophotometry ◽  
The Body ◽  
Permissible Limit ◽  
The Sun ◽  
Absorption Spectrophotometry ◽  
Pb Contamination ◽  
Body Organ ◽  
Banda Aceh

Lipstick or lip dye is a cosmetic dose that serves to coloring, decorative the lips, as a moisturizing material and protect the lips from exposure the sun to provide optimum results. Lipstick should not contain chemicals such as lead (Pb) because the Pb is a heavy metal that is very dangerous when continuously used on the skin, because it will be absorbed into the blood and attack the body organ causing the onset of disease. According to BPOM that the lead rate on the lipstick does not exceed the permissible limit of 20 mg/kg or 20 ppm.This research aims to know the levels contained in the samples are 4 brands of matte lipstick that are sold in the Aceh market in Banda Aceh City with the method of atomic absorption spectrophotometry (AAS). The results showed that on the 4 brands of lipstick matte contain heavy metal lead (Pb) with a rate still qualified allowed by BPOM  is samples A, B, C, and D, respectively at 0.24 ppm; 0.10 ppm; 2.87 ppm and 1.32 ppm, so that the 4 brands of lipstick matte are still used.

scholarly journals III. On the nature and construction of the sun and fixed stars

1795 ◽  
Vol 85 ◽  
pp. 46-72 ◽  
Keyword(s):  
Central Body ◽  
Planetary System ◽  
Considerable Progress ◽  
The Sun ◽  
Great Satisfaction ◽  
The Earth ◽  
The World ◽  
Celestial Bodies ◽  
The Universe ◽  
Made In

Among the celestial bodies the sun is certainly the first which should attract our notice. It is a fountain of light that illuminates the world! it is the cause of that heat which main­tains the productive power of nature, and makes the earth a fit habitation for man! it is the central body of the planetary system; and what renders a knowledge of its nature still more interesting to us is, that the numberless stars which compose the universe, appear, by the strictest analogy, to be similar bodies. Their innate light is so intense, that it reaches the eye of the observer from the remotest regions of space, and forcibly claims his notice. Now, if we are convinced that an inquiry into the nature and properties of the sun is highly worthy of our notice, we may also with great satisfaction reflect on the considerable progress that has already been made in our knowledge of this eminent body. It would require a long detail to enumerate all the various discoveries which have been made on this subject; I shall, therefore, content myself with giving only the most capital of them.

scholarly journals Total Angular Momentum Dichroism of the Terahertz Vortex Beams at the Antiferromagnetic Resonances

2021 ◽  
Vol 126 (15) ◽  
Author(s):  
A. A. Sirenko ◽  
P. Marsik ◽  
L. Bugnon ◽  
M. Soulier ◽  
C. Bernhard ◽  
...  
Keyword(s):  
Angular Momentum ◽  
Total Angular Momentum ◽  
Vortex Beams

scholarly journals Galactic tide and local stellar perturbations on the Oort cloud: creation of interstellar comets

2019 ◽  
Vol 629 ◽  
pp. A139 ◽  
Author(s):  
S. Torres ◽  
M. X. Cai ◽  
A. G. A. Brown ◽  
S. P. Zwart
Keyword(s):  
Dynamical Evolution ◽  
Cumulative Effect ◽  
Oort Cloud ◽  
Radial Velocities ◽  
Current Status ◽  
Interstellar Space ◽  
The Sun ◽  
Semi Major Axis ◽  
Software Environment ◽  
External Perturbations

Comets in the Oort cloud evolve under the influence of internal and external perturbations, such as giant planets, stellar passages, and the Galactic gravitational tidal field. We aim to study the dynamical evolution of the comets in the Oort cloud, accounting for the perturbation of the Galactic tidal field and passing stars. We base our study on three main approaches; analytic, observational, and numerical. We first construct an analytical model of stellar encounters. We find that individual perturbations do not modify the dynamics of the comets in the cloud unless very close (<0.5 pc) encounters occur. Using proper motions, parallaxes, and radial velocities from Gaia DR2 and combining them with the radial velocities from other surveys, we then construct an astrometric catalogue of the 14 659 stars that are within 50 pc of the Sun. For all these stars we calculate the time and distance of closest approach to the Sun. We find that the cumulative effect of relatively distant (≤1 pc) passing stars can perturb the comets in the Oort cloud. Finally, we study the dynamical evolution of the comets in the Oort cloud under the influence of multiple stellar encounters from stars that pass within 2.5 pc of the Sun and the Galactic tidal field over ±10 Myr. We use the Astrophysical Multipurpose Software Environment (AMUSE), and the GPU-accelerated direct N-body code ABIE. We considered two models for the Oort cloud, compact (a ≤ 0.25 pc) and extended (a ≤ 0.5 pc). We find that the cumulative effect of stellar encounters is the major perturber of the Oort cloud for a compact configuration while for the extended configuration the Galactic tidal field is the major perturber. In both cases the cumulative effect of distant stellar encounters together with the Galactic tidal field raises the semi-major axis of ~1.1% of the comets at the edge of the Oort cloud up to interstellar regions (a > 0.5 pc) over the 20 Myr period considered. This leads to the creation of transitional interstellar comets (TICs), which might become interstellar objects due to external perturbations. This raises the question of the formation, evolution, and current status of the Oort cloud as well as the existence of a “cloud” of objects in the interstellar space that might overlap with our Oort cloud, when considering that other planetary systems should undergo similar processes leading to the ejection of comets.

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