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.

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.

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 Encounters involving planetary systems in birth environments: the significant role of binaries

2020 ◽  
Vol 499 (1) ◽  
pp. 1212-1225
Author(s):  
Daohai Li ◽  
Alexander J Mustill ◽  
Melvyn B Davies
Keyword(s):  
Solar System ◽  
Significant Role ◽  
Cross Sections ◽  
Binary Stars ◽  
Open Cluster ◽  
Planetary Systems ◽  
The Sun ◽  
Crowded Environments ◽  
Stellar Density

ABSTRACT Most stars form in a clustered environment. Both single and binary stars will sometimes encounter planetary systems in such crowded environments. Encounter rates for binaries may be larger than for single stars, even for binary fractions as low as 10–20 per cent. In this work, we investigate scatterings between a Sun–Jupiter pair and both binary and single stars as in young clusters. We first perform a set of simulations of encounters involving wide ranges of binaries and single stars, finding that wider binaries have larger cross-sections for the planet’s ejection. Secondly, we consider such scatterings in a realistic population, drawing parameters for the binaries and single stars from the observed population. The scattering outcomes are diverse, including ejection, capture/exchange, and collision. The binaries are more effective than single stars by a factor of several or more in causing the planet’s ejection and collision. Hence, in a cluster, as long as the binary fraction is larger than about 10 per cent, the binaries will dominate the scatterings in terms of these two outcomes. For an open cluster of a stellar density 50 pc−3, a lifetime 100 Myr, and a binary fraction 0.5, we estimate that Jupiters of the order of 1 per cent are ejected, 0.1 per cent collide with a star, 0.1 per cent change ownership, and 10 per cent of the Sun–Jupiter pairs acquire a stellar companion during scatterings. These companions are typically thousands of au distant and in half of the cases (so 5 per cent of all Sun–Jupiter pairs), they can excite the planet’s orbit through Kozai–Lidov mechanism before being stripped by later encounters. Our result suggests that the Solar system may have once had a companion in its birth cluster.

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.

scholarly journals Formation and Orbital Evolution of Planets

2011 ◽  
Vol 7 (S282) ◽  
pp. 429-436
Author(s):  
Wilhelm Kley
Keyword(s):  
Solar System ◽  
Gravitational Instability ◽  
Planetary Systems ◽  
Large Mass ◽  
Orbital Evolution ◽  
Protoplanetary Disk ◽  
Dynamical Structure ◽  
High Eccentricity ◽  
Exoplanetary Systems ◽  
Alternative Processes

AbstractThe formation of planetary systems is a natural byproduct of the star formation process. Planets can form inside the protoplanetary disk by two alternative processes. Either through a sequence of sticking collisions, the so-called sequential accretion scenario, or via gravitational instability from an over-dense clump inside the protoplanetary disk. The first process is believed to have occurred in the solar system. The most important steps in this process will be outlined. The observed orbital properties of exoplanetary systems are distinctly different from our own Solar System. In particular, their small distance from the star, their high eccentricity and large mass point to the existence of a phase with strong mutual excitations. These are believed to be a result of early evolution of planets due to planet-disk interaction. The importance of this process in shaping the dynamical structure of planetary systems will be presented.

scholarly journals DIVISION III: PLANETARY SYSTEMS SCIENCES

2008 ◽  
Vol 4 (T27A) ◽  
pp. 149-153
Author(s):  
Edward L. G. Bowell ◽  
Karen J. Meech ◽  
Iwan P. Williams ◽  
Alan P. Boss ◽  
Guy J. Consolmagno ◽  
...  
Keyword(s):  
Solar System ◽  
Extrasolar Planets ◽  
Planetary Systems ◽  
The Sun ◽  
Division Iii ◽  
Astronomical Research ◽  
The Universe

Division III's activities focus on a broad range of astronomical research on bodies in the solar system (excluding the Sun), on extrasolar planets, and on the search for life in the Universe.

General discussion (Origin of the Solar System)

1981 ◽  
Vol 303 (1477) ◽  
pp. 377-377
Keyword(s):  
Angular Momentum ◽  
Solar System ◽  
The Sun ◽  
Early Solar System ◽  
Common System ◽  
Different Sources ◽  
Gaseous Disc

There are several indications that cause one to consider some cataclysmic event having occurred in the early Solar System. First, there is the fact that the Sun is 7° skew to the planetary disc, and this is too large an angle to be accounted for, if the angular momentum of Sun and disc came from a common system. It is too small an angle, though, to attribute Sun and disc to entirely different sources. Some major perturbation has to be invoked, while the gaseous disc was present, and before it had formed the planets. A later perturbation would give different inclinations to the different planets.

The origin of the solar system

1960 ◽  
Vol 256 (1285) ◽  
pp. 245-266 ◽  
Keyword(s):  
Angular Momentum ◽  
Solar System ◽  
Critical Mass ◽  
Initial Density ◽  
Axial Rotation ◽  
Mean Free Path ◽  
The Sun ◽  
Average Mass ◽  
Gravitational Fields ◽  
The Right

The theory here outlined attempts to relate the problem of the origin of the solar system to the general problem of star formation. Reasons are given for concluding that interstellar material in which stars are about to be formed consists of fragments (‘floccules’) moving at random amongst themselves and probably composed mainly of molecular hydrogen, the temperature being about 50 °K and the random velocities about 1 km/s. Many stars would then be formed simultaneously, each by the aggregation of portions of material that happen to be moving together. The process producing condensations that grow into stars would also produce minor condensations in material that becomes trapped in the growing gravitational fields of these stars, i.e. planetary systems associated with the stars. It appears to be consistent with this general picture to suppose that the solar system was formed in a region whose radius was about the initial mean free path of the ‘floccules’, and that it accounts for the amount of material originally within this region and for the amount of angular momentum originally possessed by the material in consequence of its random motions. The hypothesis is made that the mass, size and number-density of ‘floccules’ are such that in this way the total mass, radius and angular momentum of the actual solar system are reproduced, thus leaving no free parameters. The particular region considered is centred upon that particular incipient condensation that is destined to grow into the sun. The process of growth is considered and it is shown that, on account of the randomness in the directions from which the material arrives, the resulting sun would have about the right angular momentum. Therefore there would remain in the region a certain amount of material moving at first in randomly disposed orbits about this sun and still carrying most of the original angular momentum. This system would flatten out towards its invariable plane; in order to retain the angular momentum, its final mass must be about that of the actual planetary system. The production of condensations in the material yields a number of these each not greatly in excess of the critical mass for gravitational contraction This is found to be about the average mass of the actual planets and so this, and about the right number of planets, is accounted for. The Roche limit for the estimated initial density of the planets so formed is at about Jupiter’s orbit; thus the theory requires a differentiation between planets formed outside and inside this distance. It also suggests that when the planets were first formed the sun’s tidal action was for a time sufficient to keep them revolving with ‘the same face’ towards the sun; conservation of angular momentum during subsequent gravitational contraction would ultimately require faster axial rotation. It is shown that this may account for the direct axial rotations of the actual planets. The times for the various stages are roughly estimated and it appears that the duration of the entire process would be some 2 x 10 5 years. Finally, it is pointed out that, if the theory be taken in the first place as no more than suggestive, it would suffice strongly to indicate that the sun’s actual angular momentum is most simply accounted for by supposing it to have been produced by the assembling of portions of material of about the mass considered, while the planets’ actual masses are most simply accounted for by supposing them to have been produced from portions of about the density considered. Thus not only would the quantitative hypotheses be checked, but the essentials of the theory would be recovered.

The evolution of rotation in the early history of the Solar System

1984 ◽  
Vol 313 (1524) ◽  
pp. 5-18 ◽  
Keyword(s):  
Dipole Moment ◽  
Angular Momentum ◽  
Solar System ◽  
Giant Planets ◽  
Slow Rotation ◽  
The Sun ◽  
Early Solar System ◽  
Slowing Down ◽  
T Tauri ◽  
History Of

Theories that require the co-genetic formation of the Sun and planets have difficulty in explaining the slow rotation of the Sun. An analysis is made of various mechanisms for slowing down the core of an evolving nebula. Two of these involve a high magnetic dipole moment for the early Sun. The first envisages magnetic linkage to an external plasma but requires a dipole moment 10 6 times that of the present Sun. The other is based on the co-rotation of m atter leaving the Sun during a T Tauri stage, and requires a dipole moment 10 4 times the present value. A mechanical process for transferring angular momentum outward involving dissipation in a solar-nebula disc is incapable of giving what is required. Two processes of star formation in a turbulent cloud are discussed. Both are capable of giving a slowly rotating Sun. Various models for producing planets are examined in relation to the spin they would produce. Planets formed from floccules would be spinning quickly but could evolve in such a way as to give observed spins for giant planets and also satellite families. Accretion models are very sensitive to assumptions, and parameters and can be adjusted to explain almost any observation. Protoplanets formed in elliptical orbits would acquire spin angular momentum through solar tidal action and would evolve to give reasonable spin rates and regular satellite families. The various tilts of their spin axes could be explained by interactions between protoplanets in the early Solar System.

scholarly journals Normalized angular momentum deficit: a tool for comparing the violence of the dynamical histories of planetary systems

2020 ◽  
Vol 636 ◽  
pp. A53 ◽  
Author(s):  
D. Turrini ◽  
A. Zinzi ◽  
J. A. Belinchon
Keyword(s):  
Angular Momentum ◽  
Solar System ◽  
Population Studies ◽  
Planetary Systems ◽  
Dynamical Evolution ◽  
Planetary Formation ◽  
Orbital Eccentricity ◽  
Host System ◽  
Extrasolar Systems ◽  
Dynamical Instabilities

Context. Population studies of the orbital characteristics of exoplanets in multi-planet systems have highlighted the existence of an anticorrelation between the average orbital eccentricity of planets and the number of planets of their host system, that is, its multiplicity. This effect was proposed to reflect the varying levels of violence in the dynamical evolution of planetary systems. Aims. Previous work suggested that the relative violence of the dynamical evolution of planetary systems with similar orbital architectures can be compared through the computation of their angular momentum deficit (AMD). We investigated the possibility of using a more general metric to perform analogous comparisons between planetary systems with different orbital architectures. Methods. We considered a modified version of the AMD, the normalized angular momentum deficit (NAMD), and used it to study a sample of 99 multi-planet systems containing both the currently best-characterized extrasolar systems and the solar system, that is, planetary systems with both compact and wide orbital architectures. Results. We verified that the NAMD allows us to compare the violence of the dynamical histories of multi-planet systems with different orbital architectures. We identified an anticorrelation between the NAMD and the multiplicity of the planetary systems, of which the previously observed eccentricity–multiplicity anticorrelation is a reflection. Conclusions. Our results seem to indicate that phases of dynamical instabilities and chaotic evolution are not uncommon among planetary systems. They also suggest that the efficiency of the planetary formation process in producing high-multiplicity systems is likely to be higher than that suggested by their currently known population.

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