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.

3. Beautiful theories, ugly facts

2021 ◽  
pp. 31-46
Author(s):  
Raymond T. Pierrehumbert
Keyword(s):  
Angular Momentum ◽  
Solar System ◽  
Planetary Systems ◽  
Protoplanetary Disk ◽  
Newtonian Gravity ◽  
The Sun ◽  
French Mathematician ◽  
Modern Form

‘Beautiful theories, ugly facts’ evaluates the theories on planetary systems, particularly the Solar System. In 1734, the Swedish polymath Emmanuel Swedenborg proposed that the Sun and all the planets condensed out of the same ball of gas, in what is probably the earliest statement of the nebular hypothesis. The nebular hypothesis entered something close to its modern form in the hands of the French mathematician Pierre-Simon Laplace, who in 1796 made the clear connection to Newtonian gravity. The angular momentum problem and the structure of a protoplanetary disk, the formation of rocky cores, and the gravitational accretion of gas in the disk also come under this topic.

The early Solar System and the rotation of the Sun

1984 ◽  
Vol 313 (1524) ◽  
pp. 39-45 ◽  
Keyword(s):  
Angular Momentum ◽  
Solar System ◽  
Magnetic Coupling ◽  
Central Star ◽  
The Sun ◽  
Early Solar System ◽  
Low Mass Stars ◽  
Hydrogen Burning ◽  
Low Mass ◽  
Solid Bodies

In most discussions of the formation of the Solar System, the early Sun is assumed to have possessed the bulk of the angular momentum of the system, and a closely surrounding disc of gas was spun out, which, through magnetic coupling, acquired a progressively larger proportion of the total angular momentum. There are difficulties with this model in accounting for the inclined axis of the Sun, the magnitude of the magnetic coupling required, and the nucleogenetic variations recently observed in the Solar System. Another possibility exists, namely that of a slowly contracting disc of interstellar material, leading to the formation of both a central star and a protoplanetary disc. In this model one can better account for the tilt of the Sun’s axis and the lack of mixing necessary to account for the nucleogenetic evidence. The low angular momentum of the Sun and of other low mass stars is then seen as resulting from a slow build-up as a degenerate dwarf, acquiring orbital material at a low specific angular momentum. When the internal temperature reaches the threshold for hydrogen burning, the star expands to the Main Sequence and is now a slow rotator. More massive stars would spin quickly because they had to acquire orbiting material after the expansion, and therefore at a high specific angular momentum. A process of gradual inward spiralling may also allow materials derived from different sources to accumulate into solid bodies, and be placed on a great variety of orbits in the outer reaches of the system, setting up the cometary cloud of uneven nucleogenetic composition.

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 Microscopic analysis of homogeneous electron gas by considering dipole–dipole interaction

2017 ◽  
Vol 31 (35) ◽  
pp. 1750334 ◽  
Author(s):  
G. H. Bordbar ◽  
F. Pouresmaeeli
Keyword(s):  
Angular Momentum ◽  
Total Angular Momentum ◽  
Electron Gas ◽  
Microscopic Analysis ◽  
Dipole Interaction ◽  
Angular Momenta ◽  
State Dependent ◽  
Analytic Expressions ◽  
Quantization Formalism ◽  
The Impact

Implying perturbation theory, the impact of the dipole–dipole interaction (DDI) on the thermodynamic properties of a homogeneous electron gas at zero temperature is investigated. Through the second quantization formalism, the analytic expressions for the ground state energy and the DDI energy are obtained. In this paper, the DDI energy has similarities with the previous works done by others. We show that its general behavior depends on density and the total angular momentum. Especially, it is found that the DDI energy has a highly state-dependent behavior. With the growth of density, the magnitude of DDI energy, which is found to be the summation of all energy contributions of the states with even and odd total angular momenta, grows linearly. It is also found that for the states with even and odd total angular momenta, the DDI energy contributions are corresponding to the positive and negative values, respectively. In particular, an increase of total angular momentum leads to decline in the magnitude of energy contribution. Therefore, the dipole–dipole interaction reveals distinct characteristics in comparison with central-like interactions.

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.

Takeoff Mechanics of the Double Backward Somersault

1990 ◽  
Vol 6 (2) ◽  
pp. 177-186 ◽  
Author(s):  
Inseong Hwang ◽  
Gukung Seo ◽  
Zhi Cheng Liu
Keyword(s):  
Angular Momentum ◽  
Total Angular Momentum ◽  
Dominant Role ◽  
Center Of Mass ◽  
Velocity Curve ◽  
The Other ◽  
Transverse Axis ◽  
Angular Momenta ◽  
Total Body ◽  
Direction Opposite

This study examined the biomechanical profiles of the takeoff phase of double backward somersaults in three flight positions: seven layout double backward somersaults (L), seven twisting double backward somersaults (TW), and seven tucked double backward somersaults (TDB). Selected kinematic variables and angular momenta were calculated in order to compare the differences resulting from different aerial maneuvers. The amount of total body angular momentum about the transverse axis through the gymnasts' center of mass progressively increased from TDB to TW to L. The gymnasts performing the skill in the layout position tried to minimize the angle of block in a direction opposite the intended motion by maximizing the angle of touchdown and takeoff. In so doing, the horizontal velocity center-of-mass curve of the L showed a slowly decreasing curve compared with those of the other two somersaults while the vertical velocity curve of the L increased more slowly than the other curves during the takeoff phase. In all cases the legs played the dominant role in contributing to total angular momentum during takeoff.

scholarly journals I. Inferences and suggestions in cosmical and geological philosophy

1865 ◽  
Vol 14 ◽  
pp. 119-129 ◽  
Keyword(s):  
Solar System ◽  
Minor Planets ◽  
Philosophical Investigation ◽  
The Sun ◽  
Zodiacal Light ◽  
Primary Induction

Theory of the Sun—Synthesis of Ponderable Matter in the Sun—Cause of the Solar Spots—Production of the Zodiacal Light—Origin of Meteorites—Original Formation of the Planets—Discrimination of the Views in Cosmical Philosophy advanced from those of Mayer and his School—Theory of the Minor Planets—Projectile Power of the Sun. This paper commences with the “ Theory of the Sun ,” embracing the subjects of the source of its energies, and the synthesis of ponderable matter. The position, powers, and functions of the Sun, as the physical centre of the solar system, are peculiar, and in fact unique. The “Primary Induction” from them, indicating, in the author’s opinion, “the principle of philosophical investigation.” which should be applied to the Sun, is conceived to be “That they imply a corresponding uniqueness and peculiarity in its constitution, characterizing also the nature as well as the disposition of the substances of which it essentially consists. But the particular density of the Sun indicates that it actually consists both of ponderable and imponderable matter.

scholarly journals Angular Momentum Growth around Local Density Maxima

1988 ◽  
Vol 130 ◽  
pp. 552-552
Author(s):  
A. F. Heavens ◽  
J. A. Peacock
Keyword(s):  
Dark Matter ◽  
Angular Momentum ◽  
Power Spectrum ◽  
Total Angular Momentum ◽  
Cold Dark Matter ◽  
Local Density ◽  
Probability Distributions ◽  
Power Spectra ◽  
Elliptical Galaxies ◽  
Angular Momenta

We have calculated the growth of angular momentum about local density maxima at early epochs. We find that high peaks experience higher torques than low peaks, counteracting the short collapse time during which the high peaks can acquire angular momentum. Which effect is dominant depends on the perturbation power spectrum: for power spectra characteristic of both cold dark matter and hot dark matter, the effects nearly cancel, and the total angular momentum acquired by a collapsing object is almost independent of the height of the peak. Furthermore, the distributions of angular momenta acquired by collapsing protosystems are extremely broad, for all power spectra, far exceeding any modest differences between peaks of different height.These results indicate that it is not possible to account for the systematic differences in angular momentum properties of disk and elliptical galaxies simply by postulating that the latter arise from fluctuations of greater overdensity, contrary to some recent suggestions. The figure shows the probability distributions for the final angular momentum acquired by peaks of dimensionless height 1–4, for a power spectrum similar to cold dark matter. A fuller account of this work has been submitted to MNRAS.

ASTROD–AN OVERVIEW

2002 ◽  
Vol 11 (07) ◽  
pp. 947-962 ◽  
Author(s):  
WEI-TOU NI
Keyword(s):  
Angular Momentum ◽  
Solar System ◽  
Gravitational Wave ◽  
Reference System ◽  
Precise Determination ◽  
The Sun ◽  
Gravitational Wave Detection ◽  
Wave Detection ◽  
The Earth

The objectives of the Astrodynamical Space Test of Relativity using Optical Devices (ASTROD) Mission concept are threefold. The first objective is to discover and explore fundamental physical laws governing matter, space and time via testing relativistic gravity with 3-6 orders of magnitude improvement. Relativistic gravity is an important cornerstone of physics, astronomy and cosmology. Its improved test is crucial to cosmology and modern theories of gravitation including superstring theories. Included in this objective is the precise determination of the relativistic parameters β and γ, the improved measurement of Ġ and a precise determination of an anomalous, constant acceleration directed towards the Sun. The second objective of the ASTROD mission is the high-precision measurement of the solar-system parameter. This includes: (i) a measurements of solar angular momentum via Lense-Thirring effect and the detection of solar g-mode oscillations via their changing gravity field, thus, providing a new eye to see inside the Sun; (ii) precise determination of the planetary orbit elements and masses; (iii) better determination of the orbits and masses of major asteroids. These measurements give better solar dynamics and probe the origin of our solar system. The third objective is to detect and observe gravitational waves from massive black holes and galactic binary stars in the frequency range 50 μHz to 5 mHz. Background gravitational -waves will also be explored. A desirable implementation is to have two spacecraft in separate solar orbit carrying a payload of a proof mass, two telescopes, two 1-2 W lasers, a clock and a drag-free system, together with an Earth reference system. the two spacecraft range coherently with the Earth reference system using lasers. When they are near, they range coherently to each other. The Earth reference system could be ground stations, Earth satellites and/or spacecraft near Earth-Sun Lagrange points. In this overview, we discuss the payload concept, the technological requirements, technological developments, orbit design, orbit simulation, the measurement of solar angular momentum, the gravitational-wave detection sensitivity, and the solar g-mode detection possibility for this mission concept. A simplified mission, Mini-ASTROD with one spacecraft ranging optically with ground stations, together with Super-ASTROD with four spacecraft of 5 AU (Jupiter-like) orbits, will be mentioned in the end. Super-ASTROD is a dedicated low-frequency gravitational-wave detection concept. For Mini-ASTROD, the first objective of ASTROD will be largely achieved; the second objective will be partially achieved; for gravitational wave detection, the sensitivity will be better than the present-day sensitivity using Doppler tracking by radio waves.

Photometric observations of the main-belt asteroid 665 Sabine and Minor Planet Bulletin

2021 ◽  
Author(s):  
Nick Sioulas
Keyword(s):  
Solar System ◽  
Rotation Period ◽  
Space Mission ◽  
Minor Planet ◽  
Minor Planets ◽  
Official Publication ◽  
Main Belt ◽  
Dwarf Planets ◽  
Photometric Observations ◽  
The Town

<p><strong>Photometric observations of the main-belt asteroid 665 Sabine and Minor Planet Bulletin</strong></p> <p> </p> <p>Nick Sioulas</p> <p>NOAK Observatory, Stavraki (IAU code L02) Ioannina, Greece ([email protected])</p> <p><strong>Introduction</strong></p> <p>In this work, the photometric observations of the main-belt asteroid 665 Sabine were conducted from the NOAK Observatory, in Greece in order to determine its synodic rotation period. The results were submitted to Asteroid Lightcurve Photometry Database (ALCDEF) and Minor Planet Bulletin.</p> <p><strong>Abstract</strong></p> <p>The Minor Planet Bulletin is the official publication of the Minor Planets Section of the Association of Lunar and Planetary Observers (ALPO). All amateurs and professionals can publish their asteroid photometry results, including lightcurves, H-G parameters, color indexes, and shape/spin axis models. It is also the refereed journal by the SAO/NASA ADS. All MPB papers are indexed in the ADS.</p> <p> </p> <p>The lightcurve of an asteroid can be used to determine the period, the shape and its size. We can also understand its composition (if it is a solid body or something else) and the orientation of the spin axes. Due to the high number of the asteroids the need of measuring them is important and all available telescopes are necessary to track them.</p> <p> </p> <p>My amateur observatory participates in the effort to record all these objects in the Solar System. It also conducts observations of various objects and other phenomena such as exoplanet transits, contributing to the Ariel Space Mission with the Exoclock Project, asteroid occultations and comet photometry.</p> <p>The observatory is registered in IAU as L02, «NOAK Observatory, Stavraki», in the town of Ioannina, Greece.</p> <p> </p> <p><strong>References</strong></p> <p>[1] Roger Dymock: Asteroids and Dwarf Planets</p> <p>[2] Brian D. Warner: A Practical Guide to Lightcurve Photometry and Analysis</p> <p>[3] http://alcdef.org/index.php</p> <p>[4] http://www.minorplanet.info/MPB/</p>

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