Computer studies of the evolution of planetary and satellite systems

This paper describes two computer experiments carried out with a CDC-Cyber 74 program (Barricelliet al., 1979) for computer simulation of a large number of objects in orbit about a central body or primary. The first experiment was started with 125 planets of which the two largest ones had coplanar orbits and masses comparable to those of Jupiter and Saturn, respectively. Their semimajor axes and eccentricities were, however, much larger. The smaller planets had a distribution promoting the formation of an axial meeting area. The experiment gives information relevant to the question of focusing of planetary orbits into a common plane and to the question of the formation and stability of an axial meeting area. Together with the next experiment, it also gives information about the development of commensurabilities (or resonances) with the largest planets.The second experiment started with 55 planets none of them with a mass greater than about 20% of Jupiter's but several of them with orbits close to a common plane. The aim of the experiment was to investigate whether successive captures followed by planetary fusion (Barricelli, 1972a) could lead to the formation of major planets comparable to Jupiter and Saturn, and in similar orbits. Also this experiment gives information relevant to the commensurability problem.     

Report of the IAU Working Group on Cartographic Coordinates and Rotational Elements: 2009

Every three years the IAU Working Group on Cartographic Coordinates and Rotational Elements revises tables giving the directions of the poles of rotation and the prime meridians of the planets, satellites, minor planets, and comets. This report takes into account the IAU Working Group for Planetary System Nomenclature (WGPSN) and the IAU Committee on Small Body Nomenclature (CSBN) definition of dwarf planets, introduces improved values for the pole and rotation rate of Mercury, returns the rotation rate of Jupiter to a previous value, introduces improved values for the rotation of five satellites of Saturn, and adds the equatorial radius of the Sun for comparison. It also adds or updates size and shape information for the Earth, Mars?? satellites Deimos and Phobos, the four Galilean satellites of Jupiter, and 22 satellites of Saturn. Pole, rotation, and size information has been added for the asteroids (21) Lutetia, (511) Davida, and (2867) ?teins. Pole and rotation information has been added for (2) Pallas and (21) Lutetia. Pole and rotation and mean radius information has been added for (1) Ceres. Pole information has been updated for (4) Vesta. The high precision realization for the pole and rotation rate of the Moon is updated. Alternative orientation models for Mars, Jupiter, and Saturn are noted. The Working Group also reaffirms that once an observable feature at a defined longitude is chosen, a longitude definition origin should not change except under unusual circumstances. It is also noted that alternative coordinate systems may exist for various (e.g. dynamical) purposes, but specific cartographic coordinate system information continues to be recommended for each body. The Working Group elaborates on its purpose, and also announces its plans to occasionally provide limited updates to its recommendations via its website, in order to address community needs for some updates more often than every 3 years. Brief recommendations are also made to the general planetary community regarding the need for controlled products, and improved or consensus rotation models for Mars, Jupiter, and Saturn.     

Satellite aided capture

A two body, patched conic analysis is presented for a planetary capture mode in which a gravity assist by an existing natural satellite of the planet aids in the capture. An analytical condition sufficient for capture is developed and applied for the following planet/satellite systems: Earth/Moon, Jupiter/Ganymede, Jupiter/Callisto, Saturn/Titan and Neptune/Triton. Co-planar, circular planetary orbits are assumed. Three sources of bodies to be captured are considered: spacecraft launched from Earth, bodies entering the solar system from interstellar space, and bodies already in orbit around the Sun. Results show that the Neptune/Triton system has the most capability for satellite aided capture of those studied. It can easily capture bodies entering the Solar System from interstellar space. Its ability to capture spacecraft launched from Earth is marginal and can only be decided with better definition of physical properties. None of the other systems can capture bodies from these two sources, but all can capture bodies already in orbit around the Sun under appropriate conditions.     

Interpretation of grazing impacts on Mars by the axial rotation theory

This paper calls attention to the fact that the distribution of grazing impacts on Mars, as described by Schultz and Lutz-Garihan (1982), agrees with the distribution predictable by the theory of planetary axial rotation based on the transmission of mass and angular momentum from a satellite system to its primary (Barricelli, 1972). A few additional implications of the theory are pointed out.     

Magnetic fields of mars and venus: Solar wind interactions

Recent U.S.S.R. studies of the magnetic field and solar wind flow in the vicinity of Mars and Venus confirm earlier U.S.A. reports of a bow shock wave developed as the solar wind interacts with these planets. Mars 2 and 3 magnetometer experiments report the existence of an intrinsic planetary magnetic field, sufficiently strong to form a magnetopause, deflecting the solar wind around the planet and its ionosphere. This is in contrast to the case for Venus, where it is assumed to be the ionosphere and processes therein which are responsible for the solar wind deflection. An empirical relationship appears to exist between planetary dipole magnetic moments and their angular momentum for Moon, Mars, Venus, Earth and Jupiter. Implications for the magnetic fields of Mercury and Saturn are discussed.Paper presented at the Lunar Science Institute Conference on Geophysical and Geochemical Exploration of the Moon and Planets, January 10–12, 1973     

On the stability of Earth-like planets in multi-planet systems

We present a continuation of our numerical study on planetary systems with similar characteristics to the Solar System. This time we examine the influence of three giant planets on the motion of terrestrial-like planets in the habitable zone (HZ). Using the Jupiter–Saturn–Uranus configuration we create similar fictitious systems by varying Saturn’s semi-major axis from 8 to 11 AU and increasing its mass by factors of 2–30. The analysis of the different systems shows the following interesting results: (i) Using the masses of the Solar System for the three giant planets, our study indicates a maximum eccentricity (max-e) of nearly 0.3 for a test-planet placed at the position of Venus. Such a high eccentricity was already found in our previous study of Jupiter–Saturn systems. Perturbations associated with the secular frequency g ₅ are again responsible for this high eccentricity. (ii) An increase of the Saturn-mass causes stronger perturbations around the position of the Earth and in the outer HZ. The latter is certainly due to gravitational interaction between Saturn and Uranus. (iii) The Saturn-mass increased by a factor 5 or higher indicates high eccentricities for a test-planet placed at the position of Mars. So that a crossing of the Earth’ orbit might occur in some cases. Furthermore, we present the maximum eccentricity of a test-planet placed in the Earth’ orbit for all positions (from 8 to 11 AU) and masses (increased up to a factor of 30) of Saturn. It can be seen that already a double-mass Saturn moving in its actual orbit causes an increase of the eccentricity up to 0.2 of a test-planet placed at Earth’s position. A more massive Saturn orbiting the Sun outside the 5:2 mean motion resonance (a _S  ≥9.7 AU) increases the eccentricity of a test-planet up to 0.4.     

X-rays from solar system objects

During the last few years our knowledge about the X-ray emission from bodies within the solar system has significantly improved. Several new solar system objects are now known to shine in X-rays at energies below 2 keV. Apart from the Sun, the known X-ray emitters now include planets (Venus, Earth, Mars, Jupiter, and Saturn), planetary satellites (Moon, Io, Europa, and Ganymede), all active comets, the Io plasma torus (IPT), the rings of Saturn, the coronae (exospheres) of Earth and Mars, and the heliosphere. The advent of higher-resolution X-ray spectroscopy with the Chandra and XMM-Newton X-ray observatories has been of great benefit in advancing the field of planetary X-ray astronomy. Progress in modeling X-ray emission, laboratory studies of X-ray production, and theoretical calculations of cross-sections, have all contributed to our understanding of processes that produce X-rays from the solar system bodies.At Jupiter and Earth, both auroral and non-auroral disk X-ray emissions have been observed. X-rays have been detected from Saturn's disk, but no convincing evidence of an X-ray aurora has been observed. The first soft (0.1–2 keV) X-ray observation of Earth's aurora by Chandra shows that it is highly variable. The non-auroral X-ray emissions from Jupiter, Saturn, and Earth, those from the disk of Mars, Venus, and Moon, and from the rings of Saturn, are mainly produced by scattering of solar X-rays. The spectral characteristics of X-ray emission from comets, the heliosphere, the geocorona, and the Martian halo are quite similar, but they appear to be quite different from those of Jovian auroral X-rays. X-rays from the Galilean satellites and the IPT are mostly driven by impact of Jovian magnetospheric particles.This paper reviews studies of the soft X-ray emission from the solar system bodies, excluding the Sun. Processes of production of solar system X-rays are discussed and an overview is provided of the main source mechanisms of X-ray production at each object. A brief account on recent development in the area of laboratory studies of X-ray production is also provided.     

Secular love numbers and hydrostatic equilibrium of planets

The secular Love numbers of planets and of the Moon have been computed by use of the recent satellite data. It has been demonstrated that Venus, Mercury, and the Moon are far from the ideal hydrostatic equilibrium; the angular velocities (rotation periods) which correspond to the hydrostatic equilibrium have been computed.     

Planetary and figure-figure effects on the moon's rotational motion

An accurate theory of the rotation of the Moon has been constructed by numerical integration. All direct perturbations on the Moon's rotational motion have been analysed. The requirements of the current observational accuracy are such that some improvements had to be added to the theoretical models. First, the gravitational figure of the Moon has been developed up to the fifth degree harmonics. Second, mutual potential effects between the figure of the Moon and the figure of the Earth have been expanded farther up. The direct action of planets must be taken into account, its effects being very small but not always negligible. The physical librations resulting of planetary effects and Earth-Moon figure-figure interactions are presented in this paper.     

Origin and early evolution of the planetary system

It is shown by linear stability analysis that a preplanetary (presatellite) disk of dust and gas with Keplerian velocity field can become unstable due to the collective self-gravity of the disk. The radial distribution of rings, which may result from this instability, is derived. These rings later on can be the formation sites for planets around the Sun and for satellites around the planets. The derived orbits are shown to be in good agreement with that of the planets and the satellites (of Jupiter, Saturn, and Uranus). Predictions and conclusions seem to be possible for the existence of three yet unknown Uranian satellites, the origin of the early Moon and the possible radial extension of the planetary system.     

The INPOP10a planetary ephemeris and its applications in fundamental physics

Compared to the previous INPOP versions, the INPOP10a planetary and lunar ephemeris has several improvements. For the planets of our Solar System, no big change was brought in the dynamics but improvements were implemented in the fitting process, the data sets used in the fit and in the selection of fitted parameters. We report here the main characteristics of the planetary part of INPOP10a like the fit of the product of the solar mass with the gravitational constant ( GM_\odot{{\rm GM}_{\odot}}) instead of the astronomical unit. Determinations of PPN parameters as well as adjustments of the Sun J2 and of asteroid masses are also presented. New advances of nodes and perihelia of planets were also estimated and are given here. As for INPOP08, INPOP10a provides to the user, positions and velocities of the planets, the Moon, the rotation angles of the Earth and the Moon as well as TT-TDB Chebyshev polynomials at .     

Formation of the regular satellite systems and rings of the major planets

In this paper, we apply the ideas presented by one of us (Prentice, 1978a, b) for the development of the proto-solar cloud into a system of Laplacian rings to the development of the protoplanetary clouds which ultimately led to Jupiter, Saturn and Uranus. We show that if one accepts this scenario — especially the idea of supersonic turbulence in the proto-planetary clouds — one can satisfactorily explain, on the basis of fixing a single adjustable parameter, both the geometric precession of the orbital radii of the regular satellite systems of these three planets and the chemical composition and mass distribution of these satellites. We suggest that thermal stirring in the proto-planetary cloud in the vicinity of the surface of the planet may be responsible for the smaller masses of some of the inner satellites as well as for the formation of the rocky rings of Uranus. The icy rings of Saturn are suggested to be the product of condensation processes in a continuous gaseous disc within the Roche limit of the planet.     

Report of the IAU/IAG Working Group on cartographic coordinates and rotational elements: 2006

Every three years the IAU/IAG Working Group on Cartographic Coordinates and Rotational Elements revises tables giving the directions of the poles of rotation and the prime meridians of the planets, satellites, minor planets, and comets. This report introduces improved values for the pole and rotation rate of Pluto, Charon, and Phoebe, the pole of Jupiter, the sizes and shapes of Saturn satellites and Charon, and the poles, rotation rates, and sizes of some minor planets and comets. A high precision realization for the pole and rotation rate of the Moon is provided. The expression for the Sun’s rotation has been changed to be consistent with the planets and to account for light travel time     

Ways that our Solar System helps us understand the formation of other planetary systems and ways that it doesn't

Models of planetary formation can be tested by comparison of their ability to predict features of our Solar System in a consistent way, and then extrapolated to other hypothetical planetary systems by different choice of parameters. When this is done, it is found that the resulting systems are insensitive to direct effects of the mass of the star, but do strongly depend on the properties of the disk, principally its surface density. Major uncertainty results from lack of an adequate theoretical model that predicts the existence, size, and distribution of analogs of our Solar System, particularly the gas giants Jupiter and Saturn. Nevertheless, reasons can be found for expecting that planetary systems, including those containing biologically habitable planets similar to Earth, may be abundant in the Galaxy and Universe.     

Satellite formation,II

The satellite formation model of Harris and Kaula (Icarus24, 516–524, 1975) is extended to include evolution of planetary ring material and elliptic orbital motion. This model is more satisfactory than the previous one in that the formation of the moon begins at a later time in the growth of the earth, and that a significant fraction of the lunar material is processed through a circumterrestrial debris cloud where volatiles might have been lost. Thus the chemical differences between the earth and moon are more plausibly accounted for. Satellites of the outer planets probably formed in large numbers throughout the growth of those planets. Because of rapid inward evolution of the orbits of small satellites, the present satellite systems represent only satellites formed in the last few percent of the growths of their primaries. The rings of Saturn and Uranus are most plausibly explained as the debris of satellites disrupted within the Roche limit. Because such a ring would collapse onto the planet in the course of any significant further accretion by the planet, the rings must have formed very near or even after the conclusion of accretion.     

Rotation of asteroids and planetary axial rotation theory

A theory (Barricelli, 1972) developed for the interpretation of planetary axial rotations is here applied to an interpretation of the axial rotations of major asteroids. The interpretation is based on the assumption that also asteroids can have satellite-systems, which may influence the axial rotation of the respective primaries. The reason why smaller asteroids tend to have slower axial rotation than the major ones as an average is discussed. Predictions of the theory can be tested by space-craft exploration of asteroids.     

A co-accretional model of satellite formation

Numerical calculation of a simple accretion model including the effects of tidal friction indicate that coformation is tenable only if the planet's Q is less than about 10³. The parameter which most strongly affects the final mass ratio of the pair is the time at which the secondary embryo is introduced. Our model yields the proper Moon-Earth mass ratio if the Moon embryo is introduced when the Earth is only about $\text{1}\text{10}$ of its final mass. The lunar orbit remains at about 10 Earth radii throughout most of the growth.This model of satellite formation overcomes two difficulties of the “circumterrestrial cloud” model of Ruskol (1960, 1963, 1972): (1) The difficulty of accumulating a mass as great as the entire Moon before gravitational instability reduces the cloud to a small number of moonlets is removed. (2) The differences between terrestrial and outer planet satellite systems is easily understood in terms of the differences in Q between these planets. The high Q of the outer planets does not allow a satellite embryo to survive a significant portion of the accretion process, thus only small bodies which formed very late in the accumulation of the planet remain as satellites. The low Q of the terrestrial planets allows satellite embryos of these planets to survive during accretion, thus massive satellites such as the Earth's Moon are expected. The present lack of such satellites of the other terrestrial planets may be the result of tidal evolution, either infall following primary despinning (Burns, 1973) or escape due to increase in orbit eccentricity.     

Generation of equatorial jets by large-scale latent heating on the giant planets

Three-dimensional numerical simulations show that large-scale latent heating resulting from condensation of water vapor can produce multiple zonal jets similar to those on the gas giants (Jupiter and Saturn) and ice giants (Uranus and Neptune). For plausible water abundances (3-5 times solar on Jupiter/Saturn and 30 times solar on Uranus/Neptune), our simulations produce ∼20 zonal jets for Jupiter and Saturn and 3 zonal jets on Uranus and Neptune, similar to the number of jets observed on these planets. Moreover, these Jupiter/Saturn cases produce equatorial superrotation whereas the Uranus/Neptune cases produce equatorial subrotation, consistent with the observed equatorial-jet direction on these planets. Sensitivity tests show that water abundance, planetary rotation rate, and planetary radius are all controlling factors, with water playing the most important role; modest water abundances, large planetary radii, and fast rotation rates favor equatorial superrotation, whereas large water abundances favor equatorial subrotation regardless of the planetary radius and rotation rate. Given the larger radii, faster rotation rates, and probable lower water abundances of Jupiter and Saturn relative to Uranus and Neptune, our simulations therefore provide a possible mechanism for the existence of equatorial superrotation on Jupiter and Saturn and the lack of superrotation on Uranus and Neptune. Nevertheless, Saturn poses a possible difficulty, as our simulations were unable to explain the unusually high speed (∼) of that planet’s superrotating jet. The zonal jets in our simulations exhibit modest violations of the barotropic and Charney-Stern stability criteria. Overall, our simulations, while idealized, support the idea that latent heating plays an important role in generating the jets on the giant planets.     

On constructing the general Earth’s rotation theory

In the present paper the equations of the orbital motion of the major planets and the Moon and the equations of the three–axial rigid Earth’s rotation in Euler parameters are reduced to the secular system describing the evolution of the planetary and lunar orbits (independent of the Earth’s rotation) and the evolution of the Earth’s rotation (depending on the planetary and lunar evolution). Hence, the theory of the Earth’s rotation can be presented by means of the series in powers of the evolutionary variables with quasi-periodic coefficients with respect to the planetary–lunar mean longitudes. This form of the Earth’s rotation problem is compatible with the general planetary theory involving the separation of the short–period and long–period variables and avoiding the appearance of the non–physical secular terms.     

Typical Velocities and Magnetic Field Strengths in Planetary Interiors

Recent studies of convection-driven dynamos in the outer core of the Earth have improved our understanding of the dynamical regime in fluid planetary cores. We consider the possible dynamical regimes in the cores of the Earth, Jupiter, and Saturn, and hence we estimate the typical velocities and magnetic fields expected in their interiors. These estimates are in reasonable agreement with observations of the large-scale internal fields of those planets. We use the fully self-consistent anelastic MHD (magnetohydrodynamics) equations which have been developed for the Earth, while the details of similar systems for Jupiter and Saturn are specified here. The known heat and composition fluxes together with magnetic, Archimedean, and Coriolis force balance give us typical velocity, entropy, and composition strengths independent of the rather poorly known transport coefficients. Those turbulent diffusion and magnetic diffusion coefficients are also estimated from mixing length theory and compared with available numerical models and standard kinematic approaches.