Survival of yeast spores in hypervelocity impact events up to velocities of 7.4 km s−1

We report on the survivability in hypervelocity impacts of yeast in spore form, and as mature cultures, at impact velocities from 1 to 7.4 km s^?1, corresponding to an estimated peak shock pressure of ～43 GPa. Spores from a yeast strain (BY4743), deficient in an enzyme required for uracil production, were fired into water (to simulate oceanic impact from space) using a light gas gun. The water was then retrieved and filtered and the resulting retentate and filtrate cultured to determine viability and survival rates of remnant spores. Yeast growth (confirmed as coming from the original sample as it had the same enzyme deficiency) was found in recovered samples at all impact speeds, albeit in smaller quantities at the higher speeds. The survival probabilities were measured as ～50% at 1 km s^?1, falling to ～10^?3% at 7.4 km s^?1. This follows the pattern observed in previous work on survival of microbial life and spores exposed to extreme shock loading, where there is reasonable survival at low peak shock pressures with more severe lethality above a critical shock pressure at the GPa scale (here between 2 and 10 GPa). These results are explained in the context of a general model for survival against extreme shock and are relevant to the hypotheses of panspermia and litho-panspermia, showing that extreme shocks during transfer across space are not necessarily sterilising.     

The Gao‐Guenie impact melt breccia—Sampling a rapidly cooled impact melt dike on an H chondrite asteroid?

The Gao‐Guenie H5 chondrite that fell on Burkina Faso (March 1960) has portions that were impact‐melted on an H chondrite asteroid at ~300 Ma and, through later impact events in space, sent into an Earth‐crossing orbit. This article presents a petrographic and electron microprobe analysis of a representative sample of the Gao‐Guenie impact melt breccia consisting of a chondritic clast domain, quenched melt in contact with chondritic clasts, and an igneous‐textured impact melt domain. Olivine is predominantly Fo_80–82. The clast domain contains low‐Ca pyroxene. Impact melt‐grown pyroxene is commonly zoned from low‐Ca pyroxene in cores to pigeonite and augite in rims. Metal–troilite orbs in the impact melt domain measure up to ~2 mm across. The cores of metal orbs in the impact melt domain contain ~7.9 wt% of Ni and are typically surrounded by taenite and Ni‐rich troilite. The metallography of metal–troilite droplets suggest a stage I cooling rate of order 10 °C s^?1 for the superheated impact melt. The subsolidus stage II cooling rate for the impact melt breccia could not be determined directly, but was presumably fast. An analogy between the Ni rim gradients in metal of the Gao‐Guenie impact melt breccia and the impact‐melted H6 chondrite Orvinio suggests similar cooling rates, probably on the order of ~5000–40,000 °C yr^?1. A simple model of conductive heat transfer shows that the Gao‐Guenie impact melt breccia may have formed in a melt injection dike ~0.5–5 m in width, generated during a sizeable impact event on the H chondrite parent asteroid.     

Can observations inside the Solar System reveal the gravitational properties of the quantum vacuum?

The understanding of the gravitational properties of the quantum vacuum might be the next scientific revolution. It was recently proposed that the quantum vacuum contains the virtual gravitational dipoles; we argue that this hypothesis might be tested within the Solar System. The key point is that the quantum vacuum (“enriched” with the gravitational dipoles) induces a retrograde precession of the perihelion. It is obvious that this phenomenon might eventually be revealed by more accurate studies of orbits of planets and orbits of the artificial Earth satellites. However, we suggest that potentially the best “laboratory” for the study of the gravitational properties of the quantum vacuum is the recently discovered dwarf planet Eris with its satellite named Dysnomia; the distance of nearly 100 AU from the Sun makes it the unique system in which the precession of the perihelion of Dysnomia (around Eris) is strongly dominated by the quantum vacuum.     

Changes in the Sun’s mass and gravitational constant estimated using modern observations of planets and spacecraft

More than 635 thousand positional observations of planets and spacecraft of various types (mostly radiotechnical ones, 1961–2010) were used to estimate possible changes in the gravitational constant, Sun’s mass, and semi-major axes of planetary orbits, as well as the associated value of the astronomical unit. The observations were analyzed based on the EPM2010 ephemerides constructed at the Institute of Applied Astronomy (Russian Academy of Sciences) in a post-Newtonian approximation as a result of simultanious numerical integration of the equations of motion of nine major planets, the Sun, the Moon, asteroids, and trans-Neptunian objects. The heliocentric gravitational constant GM _⊙ was found to vary with a rate of (GṀ _⊙/GM _⊙ = (−5.0 ± 4.1)) × 10⁻¹⁴ per year (at the 3σ level). The positive secular changes in the semimajor axes ȧ _i /a _i were found for Mercury, Venus, Mars, Jupiter, and Saturn provided by high-precision observations. These changes also correspond to the decrease in the heliocentric gravitational constant. The changing of GM _⊙, itself is probably caused by the loss of the mass M _⊙ of the Sun due to its radiation and solar wind; these effects are partly compensated by the material falling onto the Sun. Allowing for the maximum bounds on the possible change in the Sun’s mass M _⊙, it has been found from the change obtained in GM _⊙ that the annual change Ġ/G of the gravitational constant G falls within the interval −4.2 × 10⁻¹⁴ < ȧ/G < +7.5 × 10⁻¹⁴ with a 95% probability. The astronomical unit (AU) is connected by its definition only with the heliocentric gravitational constant. The decrease of GM _⊙ obtained in this paper should correspond to a secular decrease in the AU. It is shown, however, that the modern level of accuracy does not allow us to determine a change in the AU. The attained posibility of determining changes in GM _⊙ using high-accuracy observations encourages us to have a relation between GM _⊙ and the AU fixed for a certain moment in time, since it is inconvenient to have a time-dependent length for the AU.     

Resonance in a geo-centric synchronous satellite under the gravitational forces of the Sun,the Moon and the Earth including it’s equatorial ellipticity

Resonances in a geo-centric synchronous satellite under the gravitational forces of the Sun, the Moon and the Earth including it’s equatorial ellipticity have been investigated. The resonance at two points resulting from the commensurability between the mean motion of the satellite and Γ (angle measured from the minor axis of the Earth’s equatorial ellipse to the projection of the satellite on the plane of the equator) is analyzed. The amplitude and the time period of the oscillation have been determined by using the procedure of Brown and Shook. We have observed that the amplitude and the time period of the oscillation decrease as Γ increases in the first quadrant. The radial deviation (Δr) and the tangential deviation (r _c Δθ) have been determined. Here r _c represents the synchronous altitude. The effects of the arithmetic sum of amplitudes λ _i involved in the perturbation equations on orbital inclination 0^°≤α ₀≤90^° are shown. It is observed that $\sum_{i = 1}^{46} \lambda_{i}$ increases as α ₀ increases. We have also determined the displacement ΔD (called drift) due to the oscillatory terms under the summation sign involved in the equations of motion of the satellite. We have observed that the value of ΔD is less than 0.5^°.     

Is dark matter an illusion created by the gravitational polarization of the quantum vacuum?

Assuming that a particle and its antiparticle have the gravitational charge of the opposite sign, the physical vacuum may be considered as a fluid of virtual gravitational dipoles. Following this hypothesis, we present the first indications that dark matter may not exist and that the phenomena for which it was invoked might be explained by the gravitational polarization of the quantum vacuum by the known baryonic matter.     

Iron deficiency in pyrrhotite of suevites from the Chesapeake Bay impact crater,USA—A consequence of shock metamorphism?

Abstract– Pyrrhotite from suevite of the 35 Ma Chesapeake Bay impact structure (CBIS) shows a shock metamorphism and we report on several mineralogical and magnetic features. Pyrrhotite shows strong brittle deformation with a high density of stacking faults, twinning parallel to the hexagonal (001) planes and average fault distances in the order of 10 nm. Although the determination of a superstructure was not possible due to the lattice defects, the reflections of the NiAs subcell, which is typical of all pyrrhotite modifications, were clearly detected. This phase is ferrimagnetic with a Curie temperature (T_C) between 350 and 365 °C, and suevite with this phase does not show the 34 K transition. The most peculiar feature is the low metal/sulfur ratio of 0.81, which indicates a distinctly higher vacancy concentration than for 4C pyrrhotite and a composition close to smythite (Fe₉S₁₁). This phase carries a stable natural remanent magnetization and is relatively hard magnetic. Steep inclinations of the natural remanent magnetization vector, however, suggest that this phase has been remagnetized by the drilling process. A possible explanation is the magnetic domain size of faultless areas of about 10 nm in diameter, which is at the lower limit of the single domain size near the threshold, below which superparamagnetic behavior occurs. The low thermal stability of this phase excludes postshock heating above 300 °C for the suevite of the CBIS. Our results imply that the iron‐deficient pyrrhotite is produced by shock metamorphism, although an iron loss due to shock has never been reported before for pyrrhotite.     

Complete hydrothermal re‐equilibration of zircon in the Maniitsoq structure,West Greenland: A 3001 Ma minimum age of impact?

Zircon in five samples of variably comminuted, melted, and hydrothermally altered orthogneiss from the Maniitsoq structure of southern West Greenland yield a weighted mean ²⁰⁷Pb/²⁰⁶Pb age of 3000.9 ± 1.9 Ma (ion probe data, n = 37). The age data constitute a rare example of pervasive and nearly complete isotopic resetting of zircon during a regional hydrothermal event. Many zircon grains are homogeneous or display weak flame‐like patterns in backscattered electron images. Other grains show complex internal textures, where homogeneous, high‐U fronts commonly cut across relict igneous‐type oscillatory zonation. Inclusions of quartz, plagioclase, mica, and other Al ± Na ± Ca ± Fe‐bearing silicates are very common. In two samples, selective replacement of zircon with baddeleyite occurs along concentric zones with relict igneous zonation, and as specks a few microns large within recrystallized, high‐U areas. We interpret the 3000.9 ± 1.9 Ma date as the minimum age of the recently proposed impact structure at Maniitsoq. The great geographical extent and intensity of the hydrothermal event suggest massive invasion of water into the currently exposed crust, implying that the age of the hydrothermal alteration would closely approximate the age of the proposed impact at Maniitsoq. At the western margin of the Taserssuaq tonalite complex, which postdates the Maniitsoq event, a ²⁰⁷Pb/²⁰⁶Pb mean age of 2994.6 ± 3.4 Ma obtained from zircon has mostly retained igneous‐type oscillatory zonation. A subsequent thermal event at approximately 2975 Ma is recorded in several samples by zircon with baddeleyite replacement textures.     

Glass‐bearing inclusions in Shergotty and Chassigny: Consistent samples of a primary trapped melt?

Glass‐bearing inclusions hosted by different mineral phases in SNC meteorites provide important information on the conditions that prevailed during formation of early phases and/or on the composition of the primary trapped liquids/melts of these rocks. Although extensive previous work has been reported on such inclusions, several questions are still unresolved. We performed a chemical and petrographic study of the constituents (glasses and mineral assemblage) of glassy and multiphase inclusions in Shergotty and Chassigny. We focused on obtaining accurate trace element contents of glasses and co‐existing minerals and discussing their highly variable REE contents. Our results reveal an unusual geochemistry of trace element contents that appear to be independent of their major element compositions. Chemical equilibrium between phases inside inclusions as well as between glasses and host minerals could not be established. The LREE contents of glasses in glass inclusions can vary by up to two orders of magnitude. The depletion in trace element abundances shown by glasses seem to be inconsistent with these phases being residual melts. The light lithophile element contents of glasses are highly variable with enrichment in incompatible elements (e.g., Be, Sr, Ba, and LREE) indicating some processes involving percolation of fluids. All of these features are incompatible with glass‐bearing inclusions in the host minerals acting as closed systems preserving unmodified primary liquids/melts. Glass‐bearing inclusions in Shergotty and Chassigny appear to have been altered (as was the rock itself) by different postformational processes (e.g., shock, metamorphism, metasomatic [?] fluids) that affected these meteorites with different degree of intensity. Our results indicate that these inclusions could not preserve a reliable sample of the primary trapped melt.     

Hydrothermally enhanced magnetization at the center of the Haughton impact structure?

Haughton is a ~24 Myr old midsize (apparent diameter 23 km) complex impact structure located on Devon Island in Nunavut, Canada. The center of the structure shows a negative gravity anomaly of ?12 mGal coupled to a localized positive magnetic field anomaly of ~900 nT. A field expedition in 2013 led to the acquisition of new ground magnetic field mapping and electrical resistivity data sets, as well as the first subsurface drill cores down to 13 m depth at the top of the magnetic field anomaly. Petrography, rock magnetic, and petrophysical measurements were performed on the cores and revealed two different types of clast‐rich polymict impactites: (1) a white hydrothermally altered impact melt rock, not previously observed at Haughton, and (2) a gray impact melt rock with no macroscopic sign of alteration. In the altered core, gypsum is present in macroscopic veins and in the form of intergranular selenite associated with colored and zoned carbonate clasts. This altered core has a natural remanent magnetization (NRM) four to five times higher than materials from the other core but the same magnetic susceptibility. Their magnetization is still higher than the surrounding crater‐fill impact melt rocks. X‐ray fluorescence data indicate a similar proportion of iron‐rich phases in both cores and an enrichment in silicates within the altered core. In addition, alternating‐field demagnetization results show that one main process remagnetized the rocks. These results support the hypothesis that intense and possibly localized post‐impact hydrothermal alteration enhanced the magnetization of the clast‐rich impact melt rocks by crystallization of magnetite within the center of the Haughton impact structure. Subsequent erosion was followed by in situ concentration in the subsurface leading to large magnetic gradient on surface.     

How does inflation depend upon the nature of fluids filling up the universe in brane world scenario?

By constructing different parameters which are able to give us the information about our universe during inflation, (specially at the start and the end of the inflationary universe) a brief idea of brane world inflation is given in this work. What will be the size of the universe at the end of inflation, i.e., how many times will it grow than the original size is been speculated and analysed thereafter. Different kinds of fluids are taken to be the matter inside the brane. It is observed that in the case of highly positive pressure giving gas like polytropic, the size of the universe at the end of inflation is comparatively smaller. Whereas for negative pressure creators (like Chaplygin gas) this size is much bigger. Except these two cases, inflation has been studied for barotropic fluid and linear red shift parametrization ω(z)=ω ₀+ω ₁ z too. For them the size of the universe after inflation is much more high. We also have seen that this size does not depend upon the potential energy at the end of the inflation. On the contrary, there is a high impact of the initial potential energy upon the size of inflation.     

The impact of Earth’s shadow on the long-term evolution of space debris

Direct solar radiation pressure and Earth’s shadow crossings are known to be responsible for short-term variations of space debris orbital elements, the higher the area-to-mass ratio the larger the perturbation. Nevertheless, existing studies have always been performed on periods of time shorter than 150 years. Considering longer time scales of the order of a 1000 years, this paper focuses on the long-term periodic evolution of space debris trajectories caused by successive Earth’s shadow crossings. Other perturbations as the geopotential and third-body gravitational attractions obviously play a role and compete with the one which is described in this paper. Symplectic numerical propagations and new (semi-)analytical models are developed to identify a frequency associated to shadow entry and exit eccentric anomalies. It is shown that Earth’s shadow is responsible for large deviations from the initial orbital elements, even on shorter period of times, and that this effect increases along with the area-to-mass ratio.     

Origin of 30 ∼ 100 kev protons observed in the upstream region of the Earth's bow shock

a Fermi-type acceleration model is constructed to explain the origin of energetic protons (30 ～ 100 keV) which have been observed upstream of the bow shock. It is shown that the suprathermal protons (with energy of several keV) can be accelerated up to several tens of keV through the Fermi-type process in which the reflection at the shock front and the scattering in the upstream region are coupled. The efficiency of the scattering process is estimated by using the result of Barnes' quasilinear treatment of the wave excitation. The resultant energy spectrum and flux intensity ($\text{10}{}^3\text{～ 10}{}^4\text{protons}\text{(}\text{cm}{}^2\text{s ster keV}$) in 32 ～ 45.3keV) are consistent with the observation, and the softening of the energy spectrum observed in the dawn region can be explained by the decrease in the efficiency of the acceleration process in the dawn region due to the curvature of the bow shock and the reduction of shock strength. The spatial distribution of the flux predicted by the model is also consistent with the observation. In view of these consistencies the Fermi-type acceleration process is suggested as a possible candidate mechanism to explain the upstream protons although we do not intend to exclude other possibilities.     

The Dakhleh Glass: Product of an impact airburst or cratering event in the Western Desert of Egypt?

Abstract— Impact cratering is a ubiquitous geological process on the terrestrial planets. Meteorite impact craters are the most visible product of impact events, but there is a growing recognition that large aerial bursts or airbursts should occur relatively frequently throughout geological time. In this contribution, we report on an unusual impact glass‐the Dakhleh Glass (DG)–which is distributed over an area of ?400 km ²of the Dakhleh Oasis, Egypt. This region preserves a rich history of habitation stretching back to over 400,000 years before the emergence of Homo sapiens. We report on observations made during recent fieldwork and subsequent analytical analyses that strengthen previous suggestions that the DG formed during an impact event. The wide distribution and large size of DG specimens (up to ?50 cm across), the chemistry (e.g., CaO and Al₂O₃ contents up to ?25 and ?18 wt, respectively), the presence of lechatelierite and burnt sediments, and the inclusion of clasts and spherules in the DG is inconsistent with known terrestrial processes of glass formation. The age and other textural characteristics rule out a human origin. Instead, we draw upon recent numerical modeling of airbursts to suggest that the properties of DG, coupled with the absence of a confirmed crater, can best be explained by melting of surficial sediments as a result of a large airburst event. We suggest that glass produced by such events should, therefore, be more common in the rock record than impact craters, assuming that the glass formed in a suitable preserving environment.     

Where are the broad lines in Seyfert 2s?

The unified model for Seyfert 2s postulates that these galaxies are in fact normal Seyfert ls whose innermost regions are hidden from a direct view by an opaque torus. Galaxies seen from a line-of-sight within the opening angle of this torus have the central continuum source and the Broad Line Region unobstructed, and are classified as Seyfert 1/QSO. In Seyfert 2s, on the other hand, periscopic views of the hidden nucleus may be obtained through scattering of the nuclear light in the extranuclear regions. If this model is correct, the Blue and Featureless Continuum observed in many Seyfert 2s is simply a mirror image of the obscured nucleus. In this case, the light from the Broad Line Region must also be reflected towards the observer. Seyfert 2s should therefore exhibit broad lines in their spectrum, which, by definition, they do not! In this contribution we examine this issue and the complications it brings to the basic unification picture of Seyfert galaxies. We fail to find a consistent explanation for this question in the framework of the unified model. An alternative modified-unified model for Seyfert 2s is proposed.     

Aerosol in the upper layer of earth’s atmosphere

The upper atmospheric layer of Venus, Mars, Jupiter, Saturn, and earth contains an aerosol layer. The meteorites, rings, and removal of small planetary particles may be responsible for its appearance. The observations from 1979–1992 have shown that the optical aerosol thickness over the earth’s polar regions varies from τ ≈ 0.0002 to 0.1 to λ = 1 μm. The highest τ value was in 1984 and 1992 and was preceded by intense activity of the El Chichon (1982) and Pinatubo (1991) volcanoes. We have shown that increase in τ of the stratospheric aerosol may lead to decrease in ozone layer registered in the 1970s. The nature of the stratospheric aerosol (a real part of the refraction index), effective size particles r, and latitudinal variation τ remain unknown. The analysis of phase dependence of the degree of polarization is effective among the distal methods of determination of n _r and r. The observation value of intensity and degree of polarization in the visible light are caused by the optical surface properties and optical atmospheric thickness, whose values varied with latitude, longitude, and in time. Thus, it is impossible to correctly distinguish the contribution of the stratospheric aerosol. In UV-rays (λ < 300 nm), the ozone layer stops the influence of the surface and earth’s atmosphere up to height of 20–25 km. In this spectrum area, the negative factors are emission of various depolarizating gases, horizontal heterogeneity of the effective optical height of the ozone layer, and oriented particles indicated by variation of the polarization plane.     

Regions of a satellite��s motion in a Maxwell��s ring system of?N?bodies

The study of a dynamical system comprises a variety of processes, each one of which requires careful analysis. A fundamental preliminary step is to detect and limit the regions where solutions may exist. In the case of the ring problem of (N+1)-bodies or, otherwise, the regular polygon problem of (N+1) bodies, the existence of a Jacobian-type integral of motion constitutes the key for the investigation of the areas where the motions of the small particle are realized. Based on the aforementioned integral, we present an extended study of the parametric evolution of the regions where 3-D particle motions may exist.     

Large silica‐rich igneous‐textured inclusions in the Buzzard Coulee chondrite: Condensates,differentiates, or impact melts?

Abstract– We studied three large (2–4 mm diameter) igneous‐textured inclusions in the Buzzard Coulee (H4) chondrite using microanalytical techniques (OLM, SEM, EMPA, SIMS) to better elucidate the origins of igneous inclusions in ordinary chondrites. The inclusions are clasts that come in two varieties (1) white inclusions Bz‐1 and Bz‐2 represent a nearly holocrystalline assemblage of low‐Ca and high‐Ca pyroxene (63–66 area%) and cristobalite (33–36%) and (2) tan inclusion Bz‐3 is glass‐rich (approximately 60%) with low‐Ca and high‐Ca pyroxene phenocrysts. The bulk compositions of the inclusions determined by modal reconstruction are all SiO₂‐rich (approximately 67 wt% for Bz‐1 and Bz‐2, approximately 62% for Bz‐3), but Bz‐3 is enriched in incompatible elements (e.g., REE approximately 4–5 × CI abundances), whereas Bz‐2 and Bz‐1 are depleted in those elements that are most incompatible in pyroxene (e.g., La‐Ho approximately 0.15–0.4 × CI abundances). These bulk compositions do not resemble what one would expect for partial or complete shock melting of a chondritic precursor, and show no evidence for overall volatility control. We infer that the inclusions originated through igneous differentiation and FeO reduction, with Bz‐3 forming as an “andesitic” partial melt (approximately 30–40% partial melting of an H chondrite precursor), and Bz‐1 and Bz‐2 forming as pyroxene‐cristobalite cumulates from an Si‐rich melt. We suggest that both types of melts experienced a period of transit through a cold, low‐pressure space environment in which cooling, FeO reduction, and interaction with a vapor occurred. Melts may have been lofted into space by excavation or splashing during collisions, or by pyroclastic volcanism. Our results indicate intriguing similarities between the inclusions in Buzzard Coulee and the silicates in some iron (IIE‐type) and stony iron (IVA‐type) meteorites, suggesting a genetic relationship.     

The effect of the Earth’s oblateness on the Moon’s physical libration in latitude

The Moon’s physical libration in latitude generated by gravitational forces caused by the Earth’s oblateness has been examined by a vector analytical method. Libration oscillations are described by a close set of five linear inhomogeneous differential equations, the dispersion equation has five roots, one of which is zero. A complete solution is obtained. It is revealed that the Earth’s oblateness: a) has little effect on the instantaneous axis of Moon’s rotation, but causes an oscillatory rotation of the body of the Moon with an amplitude of 0.072″ and pulsation period of 16.88 Julian years; b) causes small nutations of poles of the orbit and of the ecliptic along tight spirals, which occupy a disk with a cut in a center and with radius of 0.072″. Perturbations caused by the spherical Earth generate: a) physical librations in latitude with an amplitude of 34.275″; b) nutational motion for centers of small spiral nutations of orbit (ecliptic) pole over ellipses with semi-major axes of 113.850″ (85.158″) and the first pole rotates round the second one along a circle with radius of 28.691″; c) nutation of the Moon’s celestial pole over an ellipse with a semi-major axis of 45.04″ and with an axes ratio of about 0.004 with a period of T = 27.212 days. The principal ellipse’s axis is directed tangentially with respect to the precession circumference, along which the celestial pole moves nonuniformly nearly in one dimension. In contrast to the accepted concept, the latitude does not change while the Moon’s poles of rotation move. The dynamical reason for the inclination of the Moon’s mean equator with respect to the ecliptic is oblateness of the body of the Moon.     

Dynamics of the Jupiter Trojans with Saturn’s perturbation in the present configuration of the two planets

The dynamics of the two Jupiter triangular libration points perturbed by Saturn is studied in this paper. Unlike some previous works that studied the same problem via the pure numerical approach, this study is done in a semianalytic way. Using a literal solution, we are able to explain the asymmetry of two orbits around the two libration points with symmetric initial conditions. The literal solution consists of many frequencies. The amplitudes of each frequency are the same for both libration points, but the initial phase angles are different. This difference causes a temporary spatial asymmetry in the motions around the two points, but this asymmetry gradually disappears when the time goes to infinity. The results show that the two Jupiter triangular libration points should have symmetric spatial stable regions in the present status of Jupiter and Saturn. As a test of the literal solution, we study the resonances that have been extensively studied in Robutel and Gabern (Mon Not R Astron Soc 372:1463–1482, 2006). The resonance structures predicted by our analytic theory agree well with those found in Robutel and Gabern (Mon Not R Astron Soc 372:1463–1482, 2006) via a numerical approach. Two kinds of chaotic orbits are discussed. They have different behaviors in the frequency map. The first kind of chaotic orbits (inner chaotic orbits) is of small to moderate amplitudes, while the second kind of chaotic orbits (outer chaotic orbits) is of relatively larger amplitudes. Using analytical theory, we qualitatively explain the transition process from the inner chaotic orbits to the outer chaotic orbits with increasing amplitudes. A critical value of the diffusion rate is given to separate them in the frequency map. In a forthcoming paper, we will study the same problem but keep the planets in migration. The time asymmetry, which is unimportant in this paper, may cause an observable difference in the two Jupiter Trojan groups during a very fast planet migration process.