Solar system dynamics
01 Jan 1999-
TL;DR: In this paper, the two-body problem and the restricted three body problem are considered. But the disturbing function is defined as a special case of the two body problem and is not considered in this paper.
Abstract: Preface 1. Structure of the solar system 2. The two-body problem 3. The restricted three-body problem 4. Tides, rotation and shape 5. Spin-orbit coupling 6. The disturbing function 7. Secular perturbations 8. Resonant perturbations 9. Chaos and long-term evolution 10. Planetary rings Appendix A. Solar system data Appendix B. Expansion of the disturbing function Index.
Citations
More filters
TL;DR: Protostars and Planets VI brings together more than 250 contributing authors at the forefront of their field, conveying the latest results in this research area and establishing a new foundation for advancing our understanding of stellar and planetary formation as mentioned in this paper.
4,461 citations
Massachusetts Institute of Technology1, Harvard University2, Princeton University3, University of Chicago4, Las Cumbres Observatory Global Telescope Network5, University of Copenhagen6, Arizona State University7, Carnegie Institution for Science8, Aarhus University9, University of Birmingham10, Goddard Space Flight Center11, University of Maryland, College Park12, Northern Kentucky University13, Vanderbilt University14, Lowell Observatory15, University of Texas at Austin16, University of Florida17, Max Planck Society18, Tokyo Institute of Technology19, University of California, Berkeley20, University of California, Santa Cruz21, Space Telescope Science Institute22, Johns Hopkins University23, Spanish National Research Council24, Lehigh University25, INAF26, Fisk University27
TL;DR: The Transiting Exoplanet Survey Satellite (TESS) as discussed by the authors will search for planets transiting bright and nearby stars using four wide-field optical charge-coupled device cameras to monitor at least 200,000 main-sequence dwarf stars.
Abstract: The Transiting Exoplanet Survey Satellite (TESS) will search for planets transiting bright and nearby stars. TESS has been selected by NASA for launch in 2017 as an Astrophysics Explorer mission. The spacecraft will be placed into a highly elliptical 13.7-day orbit around the Earth. During its 2-year mission, TESS will employ four wide-field optical charge-coupled device cameras to monitor at least 200,000 main-sequence dwarf stars with I C ≈4−13 for temporary drops in brightness caused by planetary transits. Each star will be observed for an interval ranging from 1 month to 1 year, depending mainly on the star’s ecliptic latitude. The longest observing intervals will be for stars near the ecliptic poles, which are the optimal locations for follow-up observations with the James Webb Space Telescope. Brightness measurements of preselected target stars will be recorded every 2 min, and full frame images will be recorded every 30 min. TESS stars will be 10 to 100 times brighter than those surveyed by the pioneering Kepler mission. This will make TESS planets easier to characterize with follow-up observations. TESS is expected to find more than a thousand planets smaller than Neptune, including dozens that are comparable in size to the Earth. Public data releases will occur every 4 months, inviting immediate community-wide efforts to study the new planets. The TESS legacy will be a catalog of the nearest and brightest stars hosting transiting planets, which will endure as highly favorable targets for detailed investigations.
2,604 citations
Cites background from "Solar system dynamics"
...The dynamics of resonant motion has long been studied in celestial mechanics, as it plays a critical role in solar system evolution [10], [11]....
[...]
TL;DR: This model reproduces all the important characteristics of the giant planets' orbits, namely their final semimajor axes, eccentricities and mutual inclinations, provided that Jupiter and Saturn crossed their 1:2 orbital resonance.
Abstract: A collection of three papers in this issue, tackling seemingly unrelated planetary phenomena, marks a notable unification of Solar System dynamics. The three problems covered are the hard-to-explain orbits of giant planets, the evolution of the orbits of Jupiter's Trojan asteroids, and the cause of the ‘Late Heavy Bombardment’ that peppered the Moon with meteors, comets and asteroids some 700 million years after the planets were formed. Key to all these events, on this new model, was a rapid migration of the giant planets (Saturn, Jupiter, Neptune and Uranus) after a long period of stability within the Solar System. Planetary formation theories1,2 suggest that the giant planets formed on circular and coplanar orbits. The eccentricities of Jupiter, Saturn and Uranus, however, reach values of 6 per cent, 9 per cent and 8 per cent, respectively. In addition, the inclinations of the orbital planes of Saturn, Uranus and Neptune take maximum values of ∼2 degrees with respect to the mean orbital plane of Jupiter. Existing models for the excitation of the eccentricity of extrasolar giant planets3,4,5 have not been successfully applied to the Solar System. Here we show that a planetary system with initial quasi-circular, coplanar orbits would have evolved to the current orbital configuration, provided that Jupiter and Saturn crossed their 1:2 orbital resonance. We show that this resonance crossing could have occurred as the giant planets migrated owing to their interaction with a disk of planetesimals6,7. Our model reproduces all the important characteristics of the giant planets' orbits, namely their final semimajor axes, eccentricities and mutual inclinations.
1,493 citations
TL;DR: This model is based on the hypothesis that large movements in stock market activity arise from the trades of large participants, and explains certain striking empirical regularities that describe the relationship between large fluctuations in prices, trading volume and the number of trades.
Abstract: Insights into the dynamics of a complex system are often gained by focusing on large fluctuations. For the financial system, huge databases now exist that facilitate the analysis of large fluctuations and the characterization of their statistical behaviour. Power laws appear to describe histograms of relevant financial fluctuations, such as fluctuations in stock price, trading volume and the number of trades. Surprisingly, the exponents that characterize these power laws are similar for different types and sizes of markets, for different market trends and even for different countries--suggesting that a generic theoretical basis may underlie these phenomena. Here we propose a model, based on a plausible set of assumptions, which provides an explanation for these empirical power laws. Our model is based on the hypothesis that large movements in stock market activity arise from the trades of large participants. Starting from an empirical characterization of the size distribution of those large market participants (mutual funds), we show that the power laws observed in financial data arise when the trading behaviour is performed in an optimal way. Our model additionally explains certain striking empirical regularities that describe the relationship between large fluctuations in prices, trading volume and the number of trades.
1,261 citations
Abstract: This article describes the various experimental bounds on the variation of the fundamental constants of nature. After a discussion of the role of fundamental constants, their definition and link with metrology, it reviews the various constraints on the variation of the fine-structure constant, the gravitational, weak- and strong-interaction couplings and the electron-to-proton mass ratio. The review aims (1) to provide the basics of each measurement, (2) to show as clearly as possible why it constrains a given constant, and (3) to point out the underlying hypotheses. Such an investigation is of importance in comparing the different results and in understanding the recent claims of the detection of a variation of the fine-structure constant and of the electron-to-proton mass ratio in quasar absorption spectra. The theoretical models leading to the prediction of such variation are also reviewed, including Kaluza-Klein theories, string theories, and other alternative theories. Cosmological implications of these results are also discussed. The links with the tests of general relativity are emphasized.
1,051 citations
Cites background from "Solar system dynamics"
...rbital parameters. a and b is the semimajor and semi-minor axis, c = ae the focal distance, p the semi-latus rectum, θ the true anomaly. F is the focus, A and B the periastron and apoastron (see e.g. Murray and Dermott, 2000). It is easy to check that b 2= a (1 −e2) and that p = a(1 −e2) and one defines the frequency or mean motion as n = 2π/P where P is the period. F=1 F=0 1s 1s -m c e α8 2 4 1/2 A h2 / FIG. 4. Hyperfine s...
[...]