The geometry of impacts on a synchronous planetary satellite

We consider a satellite in a circular orbit about a planet that, in turn, is in a circular orbit about the Sun; we further assume that the plane of the planetocentric orbit of the satellite is the same as that of the heliocentric orbit of the planet. The pair planet–satellite is encountered by a population of small bodies on planet-crossing, inclined orbits. With this setup, and using the extension of Öpik’s theory by Valsecchi et al. (Astron Astrophys 408:1179–1196, 2003), we analytically compute the velocity, the elongation from the apex and the impact point coordinates of the bodies impacting the satellite, as simple functions of the heliocentric orbital elements of the impactor and of the longitude of the satellite at impact. The relationships so derived are of interest for satellites in synchronous rotation, since they can shed light on the degree of apex–antapex cratering asymmetry that some of these satellites show. We test these relationships on two different subsets of the known population of Near Earth Asteroids.     

Expansion of the perturbing function of a satellite restricted four-body problem

A satellite four-body problem is the problem of motion of an artificial satellite of a planet in a region of the space where perturbations due to the gravitational field of the planet are of the same order as perturbations due to influences of two perturbing bodies. In this paper an expansion of the perturbing function into a Fourier series in terms of angular Keplerian elements ( _j , _j ,M _j :j=0,1,2) (designations are standard) is obtained taking into account a sharp commensurability of the typen/ ₀=(p+q)/p (n is the mean motion of the artificial satellite and ₀ is the angular velocity of rotation of the planet,p andq are integers).The coefficients of the Fourier series are the functions of the positional Keplerian elements (a _j ,e _j ,i _j ;j=0, 1, 2) (designations are standard) and, in particular, are series in terms ofe _j that, generally speaking, can be written out to an accuracy ofe _j ¹⁹ .The expansion obtained can be used for the construction of a semianalytical theory of motion of resonant satellites on the basis of conditionally periodic solutions of the restricted four-body 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.     

Review of planetary and satellite theories

Planetary and satellite theories have been historically and are presently intimately related to the available computing capabilities, the accuracy of observational data, and the requirements of the astronomical community. Thus, the development of computers made it possible to replace planetary and lunar general theories with numerical integrations, or special perturbation methods. In turn, the availability of inexpensive small computers and high-speed computers with inexpensive memory stimulated the requirement to change from numerical integration back to general theories, or representative ephemerides, where the ephemerides could be calculated for a given date rather than using a table look-up process. In parallel with this progression, the observational accuracy has improved such that general theories cannot presently achieve the accuracy of the observations, and, in turn, it appears that in some cases the models and methods of numerical integration also need to be improved for the accuracies of the observations. Planetary and lunar theories were originally developed to be able to predict phenomena, and provide what are now considered low accuracy ephemerides of the bodies. This proceeded to the requirement for high accuracy ephemerides, and the progression of accuracy improvement has led to the discoveries of the variable rotation of the Earth, several planets, and a satellite. By means of mapping techniques, it is now possible to integrate a model of the motion of the entire solar system back for the history of the solar system. The challenges for the future are: Can general planetary and lunar theories with an acceptable number of terms achieve the accuracies of observations? How can numerical integrations more accurately represent the true motions of the solar system? Can regularly available observations be improved in accuracy? What are the meanings and interpretations of stability and chaos with respect to the motions of the bodies of our solar system? There has been a parallel progress and development of problems in dealing with the motions of artificial satellites. The large number of bodies of various sizes in the limited space around the Earth, subject to the additional forces of drag, radiation pressure, and Earth zonal and tesseral forces, require more accurate theories, improved observational accuracies, and improved prediction capabilities, so that potential collisions may be avoided. This must be accomplished by efficient use of computer capabilities.     

Irregular satellite capture during planetary resonance passage

The passage of Jupiter and Saturn through mutual 1:2 mean-motion resonance has recently been put forward as explanation for their relatively high eccentricities [Tsiganis, K., Gomes, R., Morbidelli, A., Levison, H.F., 2005. Nature 435, 459-461] and the origin of Jupiter's Trojans [Morbidelli, A., Levison, H.F., Tsiganis, K., Gomes, R., 2005. Nature 435, 462-465]. Additional constraints on this event based on other small-body populations would be highly desirable. Since some outer satellite orbits are known to be strongly affected by the near-resonance of Jupiter and Saturn (“the Great Inequality”; ?uk, M., Burns, J.A., 2004b. Astron. J. 128, 2518-2541), the irregular satellites are natural candidates for such a connection. In order to explore this scenario, we have integrated 9200 test particles around both Jupiter and Saturn while they went through a resonance-crossing event similar to that described by Tsiganis et al. [Tsiganis, K., Gomes, R., Morbidelli, A., Levison, H.F., 2005. Nature 435, 459-461]. The test particles were positioned on a grid in semimajor axes and inclinations, while their initial pericenters were put at just 0.01 AU from their parent planets. The goal of the experiment was to find out if short-lived bodies, spiraling into the planet due to gas drag (or alternatively on orbits crossing those of the regular satellites), could have their pericenters raised by the resonant perturbations. We found that about 3% of the particles had their pericenters raised above 0.03 AU (i.e. beyond Iapetus) at Saturn, but the same happened for only 0.1% of the particles at Jupiter. The distribution of surviving particles at Saturn has strong similarities to that of the known irregular satellites. If saturnian irregular satellites had their origin during the 1:2 resonance crossing, they present an excellent probe into the early Solar System's evolution. We also explore the applicability of this mechanism for Uranus, and find that only some of the uranian irregular satellites have orbits consistent with resonant pericenter lifting. In particular, the more distant and eccentric satellites like Sycorax could be stabilized by this process, while closer-in moons with lower eccentricity orbits like Caliban probably did not evolve by this process alone.     

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.     

Precession effects on a liquid planetary core

Motivated by the desire to understand the rich dynamics of precessionally driven flow in a liquid planetary core, we investigate, through numerical simulations, the precessing fluid motion in a rotating cylindrical annulus, which simultaneously possesses slow precession. The same problem has been studied extensively in cylinders, where the precessing flow is characterized by three key parameters: the Ekman number E, the Poincar′e number P o and the radius-height aspect ratio Γ. While in an annulus,there is another parameter, the inner-radius-height aspect ratio Υ, which also plays an important role in controlling the structure and evolution of the flow. By decomposing the nonlinear solution into a set of inertial modes, we demonstrate the properties of both weakly and moderately precessing flows. It is found that, when the precessional force is weak, the flow is stable with a constant amplitude of kinetic energy. As the precessional force increases, our simulation suggests that the nonlinear interaction between the boundary effects and the inertial modes can trigger more turbulence, introducing a transitional regime of rich dynamics to disordered flow. The inertial mode u_(111), followed by u_(113) or u_(112), always dominates the precessing flow when 0.001 ≤ Po ≤ 0.05, ranging from weak to moderate precession.Moreover, the precessing flow in an annulus shows more stability than in a cylinder which is likely to be caused by the effect of the inner boundary that restricts the growth of resonant and non-resonant inertial modes. Furthermore, the mechanism of triadic resonance is not found in the transitional regime from a laminar to disordered flow.     

On the effect of the eccentricity of a planetary orbit on the stability of satellite orbits

The effect of the eccentricity of a planet’s orbit on the stability of the orbits of its satellites is studied. The model used is the elliptic Hill case of the planar restricted three-body problem. The linear stability of all the known families of periodic orbits of the problem is computed. No stable orbits are found, the majority of them possessing one or two pairs of real eigenvalues of the monodromy matrix, while a part of a family with complex instability is found. Two families of periodic orbits, bifurcating from the Lagrangian points L₁, L₂ of the corresponding circular case are found analytically. These orbits are very unstable and the determination of their stability coefficients is not accurate, so we compute the largest Liapunov exponent in their vicinity. In all cases these exponents are positive, indicating the existence of chaotic motions     

Satellite capture by scattering of an existing massive planetary satellite

The dynamics of the satellite–planet system under the influence of the Sun is analyzed in the rotating frame of the planet. This system is described by the well-established, restricted three-body potential. In order to break the capture/escape scenario in temporary satellites, a scattering mechanism by an existing planetary satellite is suggested to account for permanent capture of guest bodies.     

A general model of the planetary radiation pressure on a satellite with a complex shape

The purpose of this paper is to present a general model for the acceleration exerted on a spacecraft by the radiation coming from a planet. Both the solar radiation reflected by the planet and the thermal emission associated with its temperature are considered. The planet albedo and the planet emissive power are expanded in spherical harmonics with respect to an equatorial reference frame attached to the planet. The satellite external surface is assumed to consist of a juxtaposition of planar surfaces. A particular choice of variables allows to reduce the surface integrals over the lit portion of the planet visible to the satellite to one-dimension integrals.     

The effects of ablation on the cross section of planetary envelopes at capturing planetesimals

We explore the cross section of giant planet envelopes at capturing planetesimals of different sizes. For this purpose we employ two sets of realistic planetary envelope models (computed assuming for the protoplanetary nebula masses of 10 and 5 times the mass of the minimum mass solar nebula), account for drag and ablation effects and study the trajectories along which planetesimals move. The core accretion of these models has been computed in the oligarchic growth regime [Fortier, A., Benvenuto, O.G., Brunini, A., 2007. Astron. Astrophys. 473, 311-322], which has also been considered for the velocities of the incoming planetesimals. This regime predicts velocities larger that those used in previous studies of this problem. As the rate of ablation is dependent on the third power of velocity, ablation is more important in the oligarchic growth regime. We compute energy and mass deposition, fractional ablated masses and the total cross section of planets for a wide range of values of the critical parameter of ablation. In computing the total cross section of the planet we have included the contributions due to mass deposited by planetesimals moving along unbound orbits. Our results indicate that, for the case of small planetary cores and low velocities for the incoming planetesimals, ablation has a negligible impact on the capture cross section in agreement with the results presented in Inaba and Ikoma [Inaba, S., Ikoma, M., 2003. Astron. Astrophys. 410, 711-723]. However for the case of larger cores and high velocities of the incoming planetesimals as predicted by the oligarchic growth regime, we find that ablation is important in determining the planetary cross section, being several times larger than the value corresponding ignoring ablation. This is so regardless of the size of the incoming planetesimals.     

General presentation of secular part of the perturbing function of mutual attraction in the satellite system of a planet

A special presentation of secular part of the perturbing function of mutual attraction in the satellite system is presented. In contrast to known ones, it is given in general analytical form for any ratio between semimajor axes for perturbed and perturbing satellites.     

The geomagnetic effects on the motion of an electrically charged artificial satellite

The orbital effects of the Lorentz force on the motion of an electrically charged artificial satellite moving in the Earth's magnetic field are determined. The geomagnetic field is considered as a multipole potential field and the satellite electrical charge is supposed to be constant. The relativistic perturbations of the main geomagnetic field are discussed briefly. The results are concentrated on the determination of the secular changes, and numerical values are computed for the case of the LAGEOS satellite. The results are discussed in the context of a possible detection of the Lense-Thirring effect analyzing the orbital perturbations of the LAGEOS and LAGEOS X satellites.     

On the expansion of the secular part of the perturbing function of mutual attraction in the satellite systems of planets

We propose a special representation for the secular part of the perturbing function describing the mutual attraction of satellites. In contrast to the known representations, it has a single analytical form for any ratio between the semimajor axes of the perturbed and perturbing satellites. The resulting expression is a partial sum of a power series with respect to the small eccentricities and planet-equatorial inclinations of the satellites’ orbits. This sum includes terms up to and including the fourth degree with respect to these small parameters. The proposed expansion is compared with one of the known expansions for the secular part of the perturbing function.     

The effects of the satellite position on the spatial occurrence of angular scintillations

Phase interferometry, based on longitudinal (north-south) and transverse (east-west) antenna systems, was used to record scintillations in the angle-of-arrival of satellite beacon transmissions at a frequency of 136.410 MHz. It was found that the enhancement region of angular scintillations was equatorwards of the recording stations, and coincided with small angles (denoted as aspect angles) between the ray-path and magnetic field. Ninety per cent of the night-time passes, recorded at the azimuth angles 170–190°, were associated with the occurrence of scintillations; the number of scintillations decreased for satellite passes removed east or west of the plane of the station's meridian. Horizontal extents of scintillations were considerably larger east or west, than directly south of the station. Finally, no transverse angular scintillations were recorded whenever the aspect angle reached its minimum value for each satellite pass; simultaneously longitudinal scintillations were enhanced. It is suggested that the above effects are associated with a specific satellite position in relation to the recording station.     

Investigation of some of the principal geometric effects on planetary polarization

Three major geometric factors which are likely to influence theoretical interpretation of planetary polarization measurements, viz., observer—planet distance, horizontal inhomogeneity of planetary disk, and deviation from a spherical body, are investigated.The distance effect is examined for regional as well as global polarizations. For convenience of analysis, the expressions for zenith and azimuth angles of incident and emergent light appropriate for a snap-shot observation are derived as explicit functions of distance between observer and planet. Sample computations for Venus indicate that regional polarization near the planetary limb is significantly affected by the observer's distance. This effect should be particularly noticeable when an observation is made at a phase angle around which the single scattering polarization of atmospheric scattering agents exhibits a steep variation. The global polarization at large phase angles (measured at disk-center) is gradually moved toward smaller phase angles, as the observer approaches the planet. Any narrow polarization features such as rainbow and glory at small phase angles are heavily smoothed out.The effects of horizontal inhomogeneity are investigated with a planetary disk having highly polarizing regions at high latitudes. Comparison of theoretical global polarization computed for such a disk with the Pioneer Venus OCPP measurements shows a possible change in cloud-haze stratification approximately at 50° latitude, consistent with other imaging observations. An approximate analytical representation of residual polarization at zero phase angle is then derived to compare to the numerical results for Venus. An attempt is also made to explain the relatively large magnitude of residual polarization observed on Jupiter.Finally, to study the effects of nonsphericity of planetary body, the global polarizations are computed for a spheroidal planet. The global polarization tends to increase as the planet's oblateness increases. However, for Jupiter and Saturn, such effect may be of secondary importance.     

Tesseral resonance effects on satellite orbits

Resonance effects on satellite orbits due to tesseral harmonics in the potential field have been studied by many authors. Most of these studies have been restricted to nearly circular 24-hour orbits and to the deep resonance regime, where there is exact commensurability between earth rotation and orbit period. Resonance effects have also been noted, however, on eccentric synchronous and subsynchronous orbits and on orbits with far from commensurate periods. These have received much less attention; the object of this paper is to study the whole spectrum of orbits with respect to resonance effects.     

Analytical method for the effects of the asteroid belt on planetary orbits

Analytic expressions are derived for the perturbation of planetary orbits due to a thick constant density asteroid belt. The derivations include extensions and adaptations of Plakhov's analytic expressions for the perturbations in five of the orbital elements for closed orbits around Saturn's rings. The equations of Plakhov are modified to include the effect of ring thickness and additional equations are derived for the perturbations in the sixth orbital element, the mean anomaly. The gravitational potential and orbital perturbations are derived for the asteroid belt with and without thickness, and for a hoop approximation to the belt. The procedures are also applicable to Saturn's rings and the newly discovered rings of Uranus.The effects of the asteroid belt thickness on the gravitational potential coefficients and the orbital motions are demonstrated. Comparisons between the Mars orbital perturbations obtained using the analytic expressions and those obtained using numerical integration are discussed. The effects of the asteroid belt on the Earth based ranging to Mars are also demonstrated.     

The transmission of mass and angular momentum from a satellite or planetary system to its primary

In this paper main implication of basic properties detected in the satellite systems of Jupiter, Saturn and Uranus, and presented by the author in an earlier contribution (Barricelli, 1971b) are investigated. The similarity between the primary periods in the three systems, their apparent relation to the axial rotation periods of the three planets and other features suggesting that collisions with the planetary surfaces may have played a role in the evolution of the three satellite systems are interpreted by assuming that in each case a satellite of unusually large size was originally disintegrated at the Roche limit of its primary. The disintegration of large satellites and their fusion with the respective planets is assumed to be a normal feature in the latest stage of planetary growth and the main cause of axial rotation in the respective planets.These assumptions make it possible to give a selfconsistent interpretation of the similarity between the axial rotation periods of the three planets and their relation to the primary periods (as defined by Barricelli, 1971b) in the three systems.Similar assumptions when applied to the Earth-Moon system make it possible to understand why the Moon, in its closest approach to the Earth is found to have been almost exactly at the Roche limit (Gerstenkorn, 1955; MacDonald, 1964), a coincidence which is too good to be accidental. According to this interpretation our Moon is a portion (representing about one third) of our original satellite, which survived its approach to the Roche limit and the ensuing fusion process with the Earth. It can be shown (see text) that under certain conditions this could leave a residual satellite with a stationary distance from the Earth (which in retrospect would be identified as its lowest distance from the Earth) at the Roche limit.The only other case in which we have observational evidence of parts of a satellite surviving its fusion process at the Roche limit is represented by the rings of Saturn and possibly the small innermost satellite Janus which seems to have been feeding on the rings.     

The effects of diffuse solar radiation on the motion of an artificial satellite

Previous analyses of the orbits of spherical balloon satellites have attempted to satisfy residuals in observed perturbations in Keplerian elements, assumed to be caused by diffuse radiation pressure, by introducing small variations ins, the parameter representing the reflection characteristics of the satellite's surface. It is difficult to distinguish, however, between those perturbations caused by diffuse radiation and those caused by reflected radiation, as a result of the deformation of the assumed sphere. Following the derivation by Lucas of exact expressions for both incident and reflected radiation forces on a prolate spheroidal satellite, and the subsequent work of Aksnes pertaining to spherical satellites, the theory is extended to include the effects of diffuse radiation whilst at the same time qualifying the assumption that the radiation force acting along the Sun-satellite line can be taken as parallel to the Sun-Earth line.