A survey of near-mean-motion resonances between Venus and Earth

It is known since the seminal study of Laskar (1989) that the inner planetary system is chaotic with respect to its orbits and even escapes are not impossible, although in time scales of billions of years. The aim of this investigation is to locate the orbits of Venus and Earth in phase space, respectively, to see how close their orbits are to chaotic motion which would lead to unstable orbits for the inner planets on much shorter time scales. Therefore, we did numerical experiments in different dynamical models with different initial conditions—on one hand the couple Venus–Earth was set close to different mean motion resonances (MMR), and on the other hand Venus’ orbital eccentricity (or inclination) was set to values as large as e = 0.36 (i = 40°). The couple Venus–Earth is almost exactly in the 13:8 mean motion resonance. The stronger acting 8:5 MMR inside, and the 5:3 MMR outside the 13:8 resonance are within a small shift in the Earth’s semimajor axis (only 1.5 percent). Especially Mercury is strongly affected by relatively small changes in initial eccentricity and/or inclination of Venus, and even escapes for the innermost planet are possible which may happen quite rapidly.     

A comparison between Venus and the Earth

By means of the comparison between dynamical figures of Venus and the Earth, we confirmed that the nonhydrostatic moment difference ratios of the two celestial bodies are approximately equal. The hydrostatic flattening of the external equipotential surface of Venus according to the theory of internal field is equal to about 6 × 10^–8, but the observed value of Venusian equatorial flattening is equal to 6.8 × 10^–6. The latter is two orders of magnitude more than the former. These facts indicate that Venus itself is far from hydrostatic equilibrium.     

On the asteroid belt's orbital and size distribution

For absolute magnitudes greater than the current completeness limit of H-magnitude ∼15 the main asteroid belt's size distribution is imperfectly known. We have acquired good-quality orbital and absolute H-magnitude determinations for a sample of small main-belt asteroids in order to study the orbital and size distribution beyond H=15, down to sub-kilometer sizes (H>18). Based on six observing nights over a 11-night baseline we have detected, measured photometry for, and linked observations of 1087 asteroids which have one-week time baselines or more. The linkages allow the computation of full heliocentric orbits (as opposed to statistical distances determined by some past surveys). Judged by known asteroids in the field the typical uncertainty in the (a/e/i) orbital elements is less than 0.03 AU/0.03/0.5°. The distances to the objects are sufficiently well known that photometric uncertainties (of 0.3 magnitudes or better) dominate the error budget of their derived H-magnitudes. The detected asteroids range from HR=12-22 and provide a set of objects down to sizes below 1 km in diameter. We find an on-sky surface density of 210 asteroids per square degree in the ecliptic with opposition magnitudes brighter than mR=23, with the cumulative number of asteroids increasing by a factor of 10^0.27/mag from mR=18 down to the mR?23.5 limit of our survey. In terms of absolute H magnitudes, we find that beyond H=15 the belt exhibits a constant power-law slope with the number increasing proportional to ¹⁰0.30H from H?15 to 18, after which incompleteness begins in the survey. Examining only the subset of detections inside 2.5 AU, we find weak evidence for a mildly shallower slope for H=15-19.5. We provide the information necessary such that anyone wishing to model the main asteroid belt can compare a detailed model to our detected sample.     

The space distribution and orbital resonances of asteroids

We have made a detailed numerical analysis of the various orbital resonances of the asteroids and examined the variation in the distribution of trajectories near the equilibrium points in the phase plane, and hence arrived at a preliminary explanation of the features (gaps and clusters) in their distribution in space.     

The orbital evolution of NEAs and the resonances with Jupiter

two near-earth-asteroids associated with resonances with Jupiter are studied over a time span of 10⁵ yrs. We found that asteroid (887) is temporary trapped in the 3:1 resonance; thus indicating that this resonance could be a source of short-lived NEAs. We also found that asteroid (3552) with a large eccentricity and a high inclination is wandering about the 1:1 resonant region.     

Earth and Venus: A comparative study

The observed density of Venus is about 2% smaller than would be expected if Venus were a twin planet of the Earth, possessing an identical internal composition and structure. In principle, this could be explained by a process of physical segregation of metal particles from silicate particles in the solar nebula prior to accretion, so that Venus accreted from relatively metal-depleted material. However, this model encounters severe difficulties in explaining the nature of the physical segregation process and also the detailed chemical composition of the Earth's mantle. Two alternative hypotheses are examined, both of which attempt to explain the density difference in terms of chemical fractionation processes. Both of these hypotheses assume that the relative abundances of the major elements Fe, Si, Mg, Al, and Ca are similar in both planets. According to the first hypothesis, a larger proportion of the total iron in Venus is present as iron oxide in the mantle, so that the core-to-mantle ratio is smaller than in the Earth. This model implies that Venus is more oxidized than the Earth, with its lower intrinsic density (i.e., corrected to equivalent pressures and temperatures) due to the larger amount of oxygen present. The difference between oxidation states is attributed to differing degrees of accretional heating arising from the relatively smaller mass of Venus. On the other hand, the second hypothesis maintains that Venus is more reduced than the Earth, with its mantle essentially devoid of oxidized iron. The difference intrinsic densities is attributed to the Earth accreting at a lower temperature than Venus as a result of the Earth's greater distance from the center of the nebula. As a result, large amounts of sulfur accreted on the Earth but not on Venus. The sulfur, which entered the core, is believed to have increased the mean density of the Earth because of its relatively high atomic weight. The hypothesis also implies that most of the Earth's potassium, because of its chalcophile properties, entered the core.These hypotheses are evaluated in the light of existing data. The second hypothesis leads to an intrinsic density for Venus which is only 0.4% smaller than that of the Earth. This difference is much smaller than is believed to exist. A wide range of chemical evidence is found to be unfavorable to this second hypothesis, but to be consistent with the interpretation that Venus is more oxidized than the Earth, as required by the first hypothesis.     

The Origin and Evolution of the Atmospheres of Venus, Earth and Mars

The chemical compositions of the primordial atmospheres of Venus, Earth and Mars have long been a topic of debate between the experts. Some believe that the original atmospheres were a product of outgassed volatiles from the newly accreted terrestrial planets and that these atmospheres consisted primarily of carbon dioxide, nitrogen, water vapor and residual hydrogen and helium (e.g., Lewis and Prinn, <it>Planets and their Atmospheres,</it> Academic Press, Orlando, FL, 1984, pp. 62–63, 81–84, 228–231, 383). Still others think the earliest atmospheres were composed of the gas components of the solar nebula from which the solar system formed (i.e., hydrogen, helium, methane, ammonia and water). I consider the latter to be the correct scenario. Presented herein is a proposed mechanism by which the original atmospheres of Venus, Earth and Mars were transformed to atmospheres rich in carbon dioxide and nitrogen. An explanation is proposed for why water is so common on the surface of Earth and so scarce on the surfaces of Venus and Mars. Also presented are the effects the “great impact” (single cataclysmic event that was responsible for producing the Earth–Moon system) had upon the early atmosphere of Earth. The origin, structure and composition of the impacting object are determined through deductive analyses.     

Cassini between Earth and asteroid belt: first in-situ charge measurements of interplanetary grains

Dust particles in interplanetary space are expected to charge up to an electrostatic potential of about +5 V mostly by the solar UV (Horányi, 1996, Annu. Rev. Astrophys. 34, 383). Since the dynamics of charged grains may be quite different from neutral particles, the knowledge of the grain charge Q_d is highly desirable. In the last two decades, several detectors on spacecraft were flown to measure the dust charge in-situ, but the instrumentation was not capable of determining the dust charge unambiguously. The Cosmic Dust Analyser (CDA) on the Cassini spacecraft includes a charge sensitive entrance grid system (QP detector). While entering the instrument, sufficiently charged particles induce a characteristic charge feature onto the grid system, which allows a reliable determination of Q_d as well as of the impact speed v_d. Here we report the first successful in-situ measurement of charged interplanetary dust grains by CDA. Amongst 37 impacts by interplanetary grains registered between November 1999 and January 2000, we identified 6 impacts whose QP signals show a clear feature caused by charged grains, corresponding to Q_d between 1.3 and 5.4 fC. Knowledge of Q_d also allows us to estimate the grain mass m_d. Assuming a potential of φ_d≈+5 V and spheroidal grain morphologies with ratios of the maximum size to the minimum size of less than 2 the masses derived from Q_d were found to be in excess of 10⁻¹³ kg. The dynamics of such particles are dominated by the Sun's gravity. In the framework of the micro-meteoroid models of the Solar System these grains belong to the core population of interplanetary grains (Divine, 1993, J. Geophys. Res. 98, 17029). Furthermore, a rate of 6 impacts of grains with m_d?10⁻¹³ kg during 107 days is in good agreement with the predictions of the interplanetary dust environment model by Staubach et al. (1997, Adv. Space Res. 19, 301). This result demonstrates that charge detectors as the CDA QP system offer a reliable in-situ technique for determining simultaneously both the mass and velocity of big interplanetary grains. The primary CDA subsystem to determine m_d and v_d, however, is an impact ionisation detector. The majority of the 37 recorded dust impacts produced impact charges are well outside the calibrated range. Moreover, these impacts were usually characterised by impact ionisation signals which differ significantly from signals taken in calibration experiments. In this paper we took advantage of the fact that the measurement of Q_d is not affected by the subsequent impact of the grain with the detector. By relating m_d and v_d derived from Q_d of the 6 QP impactors to their corresponding ionisation signals we show that in many cases even for energetic impacts outside the calibrated range meaningful values for the dust mass can be obtained. The observed deviations of the ionisation signals from the calibration measurements are likely due to the large amount of plasma generated by such impacts. We discuss the implications of these findings on a meaningful reduction of impact ionisation signals caused by big particle impacts. A new scheme to identify and to evaluate such signals is presented. These finding are of great importance for future Cassini measurements in the saturnian system.     

Regular black hole motion and stellar orbital resonances

The motion of a black hole about the centre of gravity of its host galaxy induces a strong response from the surrounding stellar population. We treat the case of a harmonic potential analytically and show that half of the stars on circular orbits in that potential shift to an orbit of lower energy, while the other half receive a positive boost and recede to a larger radius. The black hole itself remains on an orbit of fixed amplitude and merely acts as a catalyst for the evolution of the stellar energy distribution function f ( E ). We show that this effect is operative out to a radius of approximately three to four times the hole's influence radius, R _bh. We use numerical integration to explore more fully the response of a stellar distribution to black hole motion. We consider orbits in a logarithmic potential and compare the response of stars on circular orbits, to the situation of a 'warm' and 'hot' (isotropic) stellar velocity field. While features seen in density maps are now wiped out, the kinematic signature of black hole motion still imprints the stellar line-of-sight mean velocity to a magnitude ≃13 per cent the local rms velocity dispersion σ. A study in three dimensions suggests a reduced effect for polar orbits.     

Impact orbits of the asteroid 2009 FJ with the Earth

We show how to calculate the impact orbits of dangerous asteroids using the freely available the OrbFit software, and compare our results with impact orbits calculated using Sitarski??s independent software (Sitarski, 1999; 2000; 2006). The new method is tested on asteroid 2009 FJ. Using the OrbFit package to integrate alternate orbits along the line of variation (Milani et al., 2002; 2005a; 2005b), we identify impact orbits and can plot paths of risk for the Earth or any other body in the Solar System. We present the orbital elements of asteroid 2009 FJ and its ephemerides, along with uncertainties, for the next 100 years. This paper continues a long-term research program on impact solutions for asteroids (Wlodarczyk, 2007; 2008; 2009).     

Topographic comparisons of uplift features on Venus and Earth: Implications for Venus tectonics

Venus and Earth display different hypsography. We use topographic profiles to search for well-understood terrestrial analogs to venusian features. Specifically, by using cross-correlation, we correlate average profiles for terrestrial rifts (slow and fast, “ultra-slow,” incipient and inactive) and also hotspots (oceanic and continental) with those for venusian chasmata and regiones, to draw inferences as to the processes responsible for shaping Venus’ surface. Correlations tend to improve with faster spreading rates; Venus’ correlations rank considerably lower than terrestrial ones, suggesting that if chasmata are analogous to terrestrial spreading centers, then spreading on Venus barely attains ultra-slow rates. Individual features’ normalized average profiles are correlated with profiles of other such features to establish the degree of similarity, which in turn allows for the construction of a covariance matrix. Principal component analysis of this covariance matrix shows that Yellowstone more strongly resembles Atla, Beta and W. Eistla regiones than it does the terrestrial oceanic hotspots, and that venusian chasmata, especially Ganis, most closely resemble the ultra-slow spreading Arctic ridge.     

Effects of impacts on the atmospheric evolution: Comparison between Mars, Earth, and Venus

Classified as a terrestrial planet, Venus, Mars, and Earth are similar in several aspects such as bulk composition and density. Their atmospheres on the other hand have significant differences. Venus has the densest atmosphere, composed of CO₂ mainly, with atmospheric pressure at the planet's surface 92 times that of the Earth, while Mars has the thinnest atmosphere, composed also essentially of CO₂, with only several millibars of atmospheric surface pressure. In the past, both Mars and Venus could have possessed Earth-like climate permitting the presence of surface liquid water reservoirs. Impacts by asteroids and comets could have played a significant role in the evolution of the early atmospheres of the Earth, Mars, and Venus, not only by causing atmospheric erosion but also by delivering material and volatiles to the planets. Here we investigate the atmospheric loss and the delivery of volatiles for the three terrestrial planets using a parameterized model that takes into account the impact simulation results and the flux of impactors given in the literature. We show that the dimensions of the planets, the initial atmospheric surface pressures and the volatiles contents of the impactors are of high importance for the impact delivery and erosion, and that they might be responsible for the differences in the atmospheric evolution of Mars, Earth and Venus.     

Free particle modelling of hypervelocity asteroid collisions with the Earth

This paper presents a time-dependent two-dimensional numerical model of the impact phenomena. The model deals with formation and evolution of a crater, formation of an impact jet, and with global deformation and dynamical parameters of the impacted body. The model is applied to study the problem of deformation of the Earth when impacted by an asteroid. A hydrodynamical code of the free particle numerical method (HEFP) is applied to a silicate asteroid (impactor) and to the multilayered spherical Earth (target) described by the PREM model. The asteroids radii are within a range between 5 and 800 km. The velocity range is 20–30 km s⁻¹. Calculations cover the time intervals up to 2000 s.

Each of the material points of the bodies under consideration (the Earth and an asteroid) is described by its time-dependent position, velocity, specific internal energy, pressure and density. The global results, among others, are as follows: (i) deformation of the Earth's surface; (ii) position of the shock wave within the Earth; (iii) deformation of consecutive layers within the Earth's interior, and (iv) morphology of the crater including behavior of the impact jet and deformation of the impactor.     

Radarclinometry of the Earth and Venus from space-shuttle and Venera-15 imagery

The project to develop a line-integral approach to 2-dimensional radarclinometry and to bring it to the status of producing topographic maps from real radar images has been concluded. The final developments of the theory itself have involved a trial-and-error resolution of the curvature decision process at each integration step over range as follows: (1) Locally Indeterminate Azimuth-Azimuth Curvature is invoked if the range-directed path of integration is within 1 in angle of the tangent to a local characteristic curve of the partial differential equation of radarclinometry (equivalent to a lapse in the necessity for an auxiliary curvature assumption); (2) Local Cylindricity is invoked if the local image isophote has a radius-of-curvature greater than 50 pixels; (3) Least-Squared Local Sphericity is invoked if the characteristic curve trends at greater than 70 to the range direction (the auxiliary curvature assumption is becoming a sufficiently strong influence as to warrant the overconstraint), and (4) the default hypothesis, which is invoked most often, is the localization through the Euler/Lagrange equation from the calculus of variations of the global principle of minimization of the surface area of the terrain. The development of the set of line integrals into a 2-dimensional topographic surface is not practically achieved by branching the line integral at the range threshold, because the radarclinometry equations are too frequently coupled but weakly to the slope component in the direction of radar-azimuth, and under circumstances for which the powerfully influential auxiliary curvature assumption is too unrealistic. In other words, a line integration in radar-azimuth is far more frequently directed orthogonally to the local characteristic curve than is one carried out over range. Such orthogonality results in stepping the strike under the exclusive control of the curvature assumption. Instead, a quasi-surface-integration step is taken by modeling the dependence on initial strike of the gravitational potential energy of the vertical slab of terrain under the range-profile. The adopted starting strike for the range integral is the one which minimizes the gravitational potential energy. This radarclinometric method, in combination with my recently published method for determining an effective radar back-scattering function from one-dimensional slope statistics and image pixel-signal statistics, was applied to three images. First, to separate theoretical difficulties from experimental impediments, an artificial radar image was generated from a topographic map of the Lake Champlain West quadrangle in the Adirondack Mountains. Except for the regional trend in elevation, to which radarclinometry is insensitive by design, the agreement between the original and derived topography appears good. The morphologies agree and the range of relief is the same to within 4%. As an example of data of the highest quality available from space-borne radar at the present time, a SIR-B image of very rugged terrain in the coastal mountains of Oregon was similarly processed. The result, after filtering to redistribute photoclinometric errors about the two-dimensional spatial spectrum, agrees with ground truth almost as well. As an example of the worst possible data, in terms of signal-to-noise ratio and radar incidence angle (no detraction from the praise due the first high resolution space-borne radar-imaging of Venus intended), a Venera-15 image segment in Sedna Planitia just north-east of Sapho was processed, using Venera altimetry and Pioneer roughness data for slope statistics, in spite of the resolution mis-match. Considerably more trial-and-error filtering was required. The result appears plausible, but an error check is, of course, impossible.     

The accuracy of proper orbital elements and the properties of asteroid families: Comparison with the linear theory

The accuracy and reliability of the proper orbital elements used to define asteroid families are investigated by simulating numerically the dynamical evolution of families assumed to arise from the “explosion” of a parent object. The orbits of the simulated family asteroids have then been integrated in the frame of the elliptic restricted three-body problem Sun-Jupiter-asteroid, for times of the order of the circulation periods of perihelia and nodes. By filtering out short-periodic perturbations, we have monitored the behavior of the proper eccentricities and inclinations, computed according to the linear secular perturbation theory. Significant long-period variations have been found especially for families having nonnegligible eccentricities and/or inclinations (like the Eos family), and strong disturbances due to the proximity of mean motion commensurabilities with Jupiter have been evidenced (for instance, in the case of the Themis family). These phenomena can cause a significant “noise” on the proper eccentricities and inclinations, probably affecting in some cases the derived family memberships. They can also give rise to a spurious anisotropy in the fragment ejection velocity fields computed from the dispersion in proper elements observed in each family, and this could explain the puzzling anisotropies of this kind actually found in real families by D. Brouwer (1951, Astron. J. 56, 9–32) and by V. Zappalà, P. Farinella, Z. Knežević, and P. Paolicchi (1984), Icarus 59, 261–285).     

On the possibility of microbiota transfer from Venus to Earth

The possibility of the clouds of Venus providing habitats for extremophilic microorganisms has been discussed for several decades. We show here that the action of the solar wind leads to erosion of parts of the atmosphere laden with aerosols and putative microorganisms, forming a comet-like tail in the antisolar direction. During inferior conjunctions that coincide with transits of the planet Venus this comet-like tail intersects the Earth’s magnetopause and injects aerosol particles. Data from ESA’s Venus Express spacecraft and from SOHO are used to discuss the ingress of bacteria from Venus into the Earth’s atmosphere, which we estimate as ～10¹¹–10¹³ cells for each transit event.     

Secular resonances in the asteroid belt: Theoretical perturbation approach and the problem of their location

In this paper a theoretical perturbation approach to the problem of the dynamics in secular resonance is exposed. This approach avoids any expansion of the main term of the Hamiltonian (linear term in the masses) with respect to the eccentricity or the inclination of the asteroid, in order to achieve results valid for any value of these variables. Moreover suitable action-angle variables are introduced to take properly into account the dynamics related to the motion of the argument of perihelion of the asteroid, which is relevant at high inclination. A class of secular resonances wider than that usually considered is found. An explicit computation of the location of the main secular resonances, estimating also the contribution of the quadratic term in the masses by means of classical series expansion, is reported in the last sections. The accuracy of computations obtained by series expansion is discussed in the paper.     

A note concerning the 2:1 and the 3:2 resonances in the asteroid belt

The dynamical behavior of asteroids inside the 2:1 and 3:2 commensurabilities with Jupiter presents a challenge. Indeed most of the studies, either analytical or numerical, point out that the two resonances have a very similar dynamical behavior. In spite of that, the 3:2 resonance, a little outside the main belt, hosts a family of asteroids, called the Hildas, while the 2:1, inside the main belt, is associated to a gap (the Hecuba gap) in the distribution of asteroids.In his search for a dynamical explanation for the Hecuba gap, Wisdom (1987) pointed out the existence of orbits starting with low eccentricity and inclination inside the 2:1 commensurability and going to high eccentricity, and thus to possible encounters with Mars. It has been shown later (Henrard et al.), that these orbits were following a path from the low eccentric belt of secondary resonances to the high eccentric domain of secular resonances. This path crosses a bridge, at moderate inclination and large amplitude of libration, between the two chaotic domains associated with these resonances.The 3:2 resonance being similar in many respects to the 2:1 resonance, one may wonder whether it contains also such a path. Indeed we have found that it exists and is very similar to the 2:1 one. This is the object of the present paper.     

The P/Halley Stream: Meteor Showers on Earth, Venus and Mars

We have simulated the formation and evolution of comet 1P/Halley’s meteoroid stream by ejecting particles from the nucleus 5000 years ago and propagating them forward to the present. Our aim is to determine the existence and characteristics of associated meteor showers at Mars and Venus and compare them with 1P/Halley’s two known showers at the Earth. We find that one shower should be present at Venus and two at Mars. The number of meteors in those atmospheres would, in general, be less than that at the Earth. The descending node branch of the Halley stream at Mars exhibits a clumpy structure. We identified at least one of these clumps as particles trapped in the 7:1 mean motion resonance with Jupiter, potentially capable of producing meteor ourbursts of ZHR∼1000 roughly once per century.