Stability of outer planetary systems

The conditions for stability in the Liapunov-Hill sense of outer planetary systems are given in terms of radii of planetary orbits. The outer planets of the solar system are found stable and the possible existence of other than the presently known planets between Jupiter and Pluto are indicated. The existence of other planetary systems with arbitrary mass ratios of the primaries is suggested, and the stability conditions for such systems are derived.Proceedings of the Sixth Conference on Mathematical Methods in Celestial Mechanics held at Oberwolfach (West Germany) from 14 to 19 August, 1978.     

Doppler searches for planetary systems

Despite extensive Doppler searches, no companions of Jupiter, or Brown Dwarf, mass have been found within a few AU of more than 100 late-type stars and, for many, astrometry suggests that there are none in larger orbits either. Terrestrial-mass companions have been found for the millisecond pulsar PSR1257+12. I also consider what improvements in optical spectroscopic techniques would allow us to detect stellar companions of Uranus-mass.     

From boulders to planetary systems

In this chapter, we will give a brief overview on our current theoretical understanding how planets form from the solid material in circumstellar disks in the core accretion-gas capture model. This chapter will not be as concise and complete as a review on this matter, yet will serve as an introductory text to generate interest in the subject. Students are referred to comprehensive text books and some important reviews.This chapter will discuss “dusty storms”, e.g. the dust transport in turbulent protoplanetary disks, followed by the latest model of planetesimal formation, e.g. gravoturbulent planetesimal formation, which deals with particle concentration in turbulence and N-body simulations thereof. We also briefly describe the core accretion-gas capture process and talk about nascent planets, e.g. the observability of planet–disk interaction concluding with the migration of young planets and the final arrangement of planetary systems.     

Peculiar A-stars and planetary systems

A suggestion is put forward that a number of spectral anomalies observed in some A-stars (Am and Ap-stars) may be due to the existence of planetary systems. Terrestrial type planets condense in matter exchanged between components of close binaries. Exchange of matter takes place at the stage of system formation and in later stages of evolution, with both late and early stars. If the outer layers of components in a system do not become renewed by mixing or outflow, then surface anomalies in the chemical composition of stars onto which fall some of the forming planetoids may serve as an evidence of the formation of planets.     

Evolution of planetary ringmoon systems

The last few decades have seen an avalanche of observations of planetary ring systems, both from spacecraft and from Earth. Meanwhile, we have seen steady progress in our understanding of these systems as our intuition (and our computers) catch up with the myriad ways in which gravity, fluid and statistical mechanics, and electromagnetism can combine to shape the distribution of the submicron-to-several-meter size particles which comprise ring systems [1–5]. The now-complete reconnaissance of the gas giant planets by spacecraft has revealed that ring systems are invariably found in association with families of regular satellites, and there is an emerging perspective that they are not only physically but causally linked. There is also mounting evidence that many features or aspects of all planetary ring systems, if not the ring systems themselves, are considerably younger than the solar system.     

Extrasolar planet detection

This paper discusses the concept of extrasolar planet detection using a large-aperture infrared imaging telescope. Coronagraphic stellar apodization techniques are less efficient at infrared wavelengths compared to the visible, as a result of practical limitations on aperture dimensions, thus necessitating additional starlight suppression to make planet detection feasible in this spectral domain. We have been investigating the use of rotational shearing interferometry to provide up to three orders of magnitude of starlight suppression over broad spectral bandwidths. We present a theoretical analysis of the system performance requirements needed to make this a viable instrument for planet detection, including specifications on the interferometer design and telescope aperture characteristics. The concept of using rotational shearing interferometry as a wavefront error detector, thus providing a signal that can be used to adaptively correct the wavefront, will be discussed. We also present the status of laboratory studies of on-axis source suppression using a recently constructed rotational shearing interferometer that currently operates in the visible.Paper presented at the Conference onPlanetary Systems: Formation, Evolution, and Detection held 7–10 December, 1992 at CalTech, Pasadena, California, U.S.A.     

Periodic orbits in three-dimensional planetary systems

Three-dimensional planetary systems are studied, using the model of the restricted three-body problem for Μ =.001. Families of three-dimensional periodic orbits of relatively low multiplicity are numerically computed at the resonances 3/1, 5/3, 3/5 and 1/3 and their stability is determined. The three-dimensional orbits are found by continuation to the third dimension of the vertical critical orbits of the corresponding planar problem     

Formation of planetary and satellite systems

A solar nebula-type theory recently published by the author can explain much more about our planetary system and the satellite systems than all other theories known to date. Here only a few additional and relatively simple aspects are pointed out, especially the formation of the Moon and of the Martian satellites.     

Extrasolar Planetary Systems

The discovery of planetary systems around alien stars is an outstanding achievement of recent years. The idea that the Solar System may be representative of planetary systems in the Galaxy in general develops upon the knowledge, current until the last decade of the 20th century, that it is the only object of its kind. Studies of the known planets gave rise to a certain stereotype in theoretical research. Therefore, the discovery of exoplanets, which are so different from objects of the Solar System, alters our basic notions concerning the physics and very criteria of normal planets. A substantial factor in the history of the Solar System was the formation of Jupiter. Two waves of meteorite bombardment played an important role in that history. Ultimately there arose a stable low-entropy state of the Solar System, in which Jupiter and the other giants in stable orbits protect the inner planets from impacts by dangerous celestial objects, reducing this danger by many orders of magnitude. There are even variants of the anthropic principle maintaining that life on Earth owes its genesis and development to Jupiter. Some 20 companions more or less similar to Jupiter in mass and a few infrared dwarfs, have been found among the 500 solar-type stars belonging to the main sequence. Approximately half of the exoplanets discovered are of the hot-Jupiter type. These are giants, sometimes of a mass several times that of Jupiter, in very low orbits and with periods of 3–14 days. All of their parent stars are enriched with heavy elements, [Fe/H] = 0.1–0.2. This may indicate that the process of exoplanet formation depends on the chemical composition of the protoplanetary disk. The very existence of exoplanets of the hot-Jupiter type considered in the context of new theoretical work comes up against the problem of the formation of Jupiter in its real orbit. All the exoplanets in orbits with a semimajor axis of more than 0.15–0.20 astronomical units (AU) have orbital eccentricities of more than 0.1, in most cases of 0.2–0.5. In conjunction with their possible migration into the inner reaches of the Solar System, this poses a threat to the very existence of the inner planets. Recent observations of gas–dust clouds in very young stars show that hydrogen dissipates rapidly, in several million years, and dissipation is completed earlier than, according to the accretion theory, the gas component of such a planet as Jupiter forms. The mass of the remaining hydrogen is usually small, much smaller than Jupiter's mass. However, the giant planets of the Solar System retain a few percent of the amount of hydrogen that should be contained in the early protoplanetary disk, creating difficulties in understanding their formation. A plausible explanation is that gravitational instabilities in the protoplanetary disk could be the mechanism of their rapid formation.     

On the stability of circumbinary planetary systems

The dynamics of circumbinary planetary systems (the systems in which the planets orbit a central binary) with a small binary mass ratio discovered to date is considered. The domains of chaotic motion have been revealed in the “pericentric distance–eccentricity” plane of initial conditions for the planetary orbits through numerical experiments. Based on an analytical criterion for the chaoticity of planetary orbits in binary star systems, we have constructed theoretical curves that describe the global boundary of the chaotic zone around the central binary for each of the systems. In addition, based on Mardling’s theory describing the separate resonance “teeth” (corresponding to integer resonances between the orbital periods of a planet and the binary), we have constructed the local boundaries of chaos. Both theoretical models are shown to describe adequately the boundaries of chaos on the numerically constructed stability diagrams, suggesting that these theories are efficient in providing analytical criteria for the chaoticity of planetary orbits.     

Planetary nebulae in planetary and binary systems

The problem of the survival of a low-mass secondary orbiting a primary that becomes a planetary nebula is studied. The values of the mass of the primary are 1.0, 1.5, and 2.0M ; the values of the mass of the secondary 0.001M , 0.01M and 0.1M . The orbital decay and mass of the secondary due to accretion and gravitational drag in the common envelope are presented. The possible application of the results to V471 Tau, UU Sge, WZ Sge and the Sun-Jupiter system are discussed.     

Stability of planetary orbits in binary systems

The possible existence of stable orbits is investigated in binary systems using Hill's method. Analytical stability conditions are established for satellites, for inner planets and for outer planets, allowing arbitrary values for the mass-ratio of the binary.Presented at the Symposium Star Catalogues, Positional Astronomy and Celestial Mechanics, held in honor of Paul Herget at the U.S. Naval Observatory, Washington, November 30, 1978.     

On the observability of extrasolar planetary systems

An unresolved companion to a variable star can in principle be detected by taking the apparent autocovariance function of a suitable photometric record of the system.     

Spectro-Polarimetry of Self-Luminous Extrasolar Planets

Planets which are old and close to their parent stars are considered as reflecting planets because their intrinsic temperature is extremely low but they are heated strongly by the impinging stellar radiation and hence radiation of such planets are the reflected star light that is governed by the stellar radiation, orbital distance and albedo of the planet. These planets cannot be resolved from the host stars. The second kind of exoplanets are those which are very young and hence they have high intrinsic temperature. They are far away from their star and so they can be resolved by blocking the star-light. It is now realized that radiation of such planets are linearly polarized due to atmospheric scattering and polarization can determine various physical properties including the mass of such directly detected self-luminous exoplanets. It is suggested that a spectropolarimeter of even low spectral resolution and with a capacity to record linear polarization of 0.5–1% at the thirty-meter telescope would immensely help in understanding the atmosphere, especially the cloud chemistry of the self-luminous and resolvable exoplanets.     

The photometric method of detecting other planetary systems

The photometric method detects planets orbiting other stars by searching for the reduction in the light flux or the change in the color of the stellar flux that occurs when a planet transits a star. A transit by Jupiter or Saturn would reduce the stellar flux by approximately 1% while a transit by Uranus or Neptune would reduce the stellar flux by 0.1%. A highly characteristic color change with an amplitude approximately 0.1 of that for the flux reduction would also accompany the transit and could be used to verify that the source of the flux reduction was a planetary transit rather than some other phenomenon. Although the precision required to detect major planets is already available with state-of-the-art photometers, the detection of terrestrial-sized planets would require a precision substantially greater than the state-of-the-art and a spaceborne platform to avoid the effects of variations in sky transparency and scintillation. Because the probability is so small of observing a planetary transit during a single observation of a randomly chosen star, the search program must be designed to continuously monitor hundreds or thousands of stars. The most promising approach is to search for large planets with a photometric system that has a single-measurement precision of 0.1%. If it is assumed that large planets will have long-period orbits, and that each star has an average of one large planet, then approximately 10⁴ stars must be monitored continuously. To monitor such a large groups of stars simultaneously while maintaining the required photometric precision, a detector array coupled by a fiber-optic bundle to the focal plane of a moderate aperture (≈ 1 m), wide field of view (≈50°) telescope is required. Based on the stated assumptions, a detection rate of one planet per year of observation appears possible.     

A high-precision radial-velocity survey for other planetary systems

The precise measurement of variations in stellar radial velocities provides one of several promising methods of surveying a large sample of nearby solar type stars to detect planetary systems in orbit around them. The McDonald Observatory Planetary Search (MOPS) was started in 1987 September with the goal of detecting other nearby planetary systems. A stabilized I₂ gas absorption cell placed in front of the entrance slit to the McDonald Observatory 2.7 m telescope coudé spectrograph serves as the velocity metric. With this I₂ cell we can achieve radial velocity measurement precision better than 10 m s^–1 in an individual measurement. At this level we can detect a Jupiter-like planet around a solar-type star, and have some hope of detecting Saturn-like planets in a long-term survey. The detectability of planets is ultimately limited by stellar pulsation modes and photospheric motions. Monthly MOPS observing runs allow us to obtain at least 5 independent observations per year of the 33 solar-type (F5-K7) stars on our observing list. We present representative results from the first five years of the survey.Paper presented at the Conference onPlanetary Systems: Formation, Evolution, and Detection held 7–10 December, 1992 at CalTech, Pasadena, California, U.S.A.     

Radiation forces and the formation of planetary systems

We briefly support on some new results about the influence of the rotation and finite size of a stellar radiation source on dust particle orbits, emphasizing the possibility of stable orbits, in the equatorial plane, for dust sizes near the radiation pressure limit.Paper presented at the 11th European Regional Astronomical Meetings of the IAU on New Windows to the Universe, held 3–8 July, 1989, Tenerife, Canary Islands, Spain.     

Stability of planetary systems with respect to masses

The stability in the sense of Lagrange of the Sun–Jupiter–Saturn system and 47 UMa system with respect to masses on a time scale of 10⁶ years was studied using the method of averaging and numerical methods. When the masses of Jupiter and Saturn increase by 20 times (approximately, more accurate value depends on a time-scale of stable motion), these planets can have close approaches. Close approaches appear when analyzing osculating elements; they are absent in the mean elements. A similar situation takes place in the case of 47 UMa and other exoplanetary systems. The study of Lagrange stability with respect to masses allows us to obtain upper limits for masses of extrasolar planets.