The seasonal variation of the thermal structure of the atmosphere of Uranus

A series of time-dependent radiative/convective models are presented for the atmosphere of Uranus. The effects of atmospheric dynamics have been omitted from the models. The inclination of the pole of rotation to the pole of the orbit, approximately 90°, produces large seasonal changes in the insolation. Because of the relatively small flow of heat from the interior, these seasonal changes cause the effective temperature, which is about 60°K, to vary through the 84-year orbital period by ～5°K at the poles, ～4°K at ±60° latitude, ～2°K at ±30° latitude, and ～0.5°K at the equator. For a particular latitude, the minimum effective temperature and the maximum convective flow of heat from the interior occur near the end of the period when the sun remains below the horizon during the Uranian day. If the methane mixing ratio is not limited by its saturated vapor pressure (SVP) in the convective region, the maximum convective flow would be a few times the orbital average convective flow and persist for an interval of several years. On the other hand, if the methane mixing ratio is limited by its SVP in the convective regions, the maximum convective flow could be orders of magnitude greater than the orbital average and could persist for less than an hour. If the orbital mean internal heat flow is negligible, the difference in effective temperatures between 30 and 60° latitude would be in the range 2 to 4°K. If the internal heat is taken to be about the maximum allowable and is assumed to be redistributed in the interior in a manner to compensate for the minimum in insolation at low latitudes, the corresponding temperature difference would be in the range $\text{1}\text{2}$ to 2°K. In either case, the existing theory of atmospheric dynamics for the outer planets indicates that such large temperature differences will drive large-scale motions which would in turn reduce these temperature differences.     

Pole orientation of 16 psyche by two independent methods

Nineteen new lightcurves of 16 Psyche are presented along with a pole orientation derived using two independent methods, namely, photometric astrometry (PA) and magnitude-amplitude-shape-aspect (MASA). The pole orientations found using these two methods agree to within 4°. The results from applying photometric astrometry were prograde rotation, a sidereal period of $\text{0}\text{d}\text{dot}\text{1748143 ± 0}\text{d}\text{dot}\text{0000003}$, and a pole at longitude 223° and latitude +37°, with an uncertainty of 10°; and, from applying magnitude-amplitude-shape-aspect a pole at 220 ± 1°, +40 ± 4°, and a modeled triaxial ellipsoid shape (a > b > c) with a/b = 1.33 ± 0.02 and b/c = 1.33 ± 0.07. The discrepancy between the high pole latitude found here and the low latitudes reported by others is discussed.     

Features of the upper atmosphere revealed by analysis of the orbit of cosmos 1009 rocket, 1978-50B

COSMOS 1009 rocket was launched on 19 May 1978 into an orbit with initial perigee height 150 km and apogee 1100 km: its lifetime was only 17 days. The orbit has been determined daily during the final 14 days of its life, using the RAE orbit refinement program PROP6,with about 1100 observations supplied by NORAD. An average accuracy of about 60 m, radial and cross-track, was achieved.The orbits were analysed to reveal three features of the upper atmosphere at heights between 125 and 175 km. From the decrease in perigee height, five values of density scale height, accurate to ±4%, were obtained. The first three were within 10% of those from CIRA 1972; the fourth, after a magnetic storm, was higher than expected; the fifth gave evidence of the decrease in drag coefficient at heights below 130 km.Atmospheric oblateness produced a change of 4° in perigee position during the last four days of the life. Analysis showed that the ellipticity of the upper atmosphere was approximately equal to that of the Earth, f, for the first two of the four days, and about $\text{1}\text{2}\text{f}$ in the last two.The orbital inclination decreased during the 14 days by about 50 times its standard deviation, and the observed variation was analysed to determine zonal winds at heights of 150–160 km at latitudes near 47° north. The zonal wind was very weak (0±30 m/s) for 23–28 May at local times near 03h; and 90±30 m/s east-to-west for 29 May to 4 June at local times near 01 h.     

Global color variations on the Martian surface

Surface materials exposed throughout the equatorial region of Mars have been classified and mapped on the basis of spectral reflectance properties determined by the Viking II Orbiter vidicon cameras. Frames acquired at each of three wavelengths (0.45 ± 0.03 μm, 0.53 ± 0.05 μm, and 0.59 ± 0.05 μm) during the approach of Viking Orbiter II in Martian summer (L_s = 105°) were mosaicked by computer. The mosaics cover latitudes 30°N to 63°S for 360° of longitude and have resolutions between 10 and 20 km per line pair. Image processing included Mercator transformation and removal of an average Martian photometric function to produce albedo maps at three wavelengths. The classical dark region between the equator and ～30°S in the Martian highlands is composed of two units: (i) and ancient unit consisting of topographic highs (ridges, crater rims, and rugged plateaus riddled with small dendritic channels) which is among the reddest on the planet $\text{(0.59/0.45 μ}\text{m}\text{? 3)}$; and (ii) intermediate age, smooth, intercrater volcanic plains displaying numerous mare ridges which are among the least red on Mars $\text{(0.59/0.45 μ}\text{m}\text{? 2)}$. The relatively young shield volcanoes are, like the oldest unit, dark and very red. Two probable eolian deposits are recognized in the intermediate and high albedo regions. The stratigraphically lower unit is intermediate in both color $\text{(0.59/ 0.45 μ}\text{m}\text{? 2.5)}$ and albedo. The upper unit has the highest albedo, is very red $\text{(0.59/0.45 μ}\text{m}\text{? 3)}$, and is apparently the major constituent of the annual dust storms as its areal extent changes from year to year. The south polar ice cap and condensate clouds dominate the southernmost part of the mosaics.     

The orbit of the Dhajala meteorite

Observations of the trail caused by the meteorite which fell around Dhajala, Gujarat (India), on 28 January 1976 have been used to compute the probable orbit of the meteoroid in space. The cosmic ray effects in the meteorite fragments indicate high mass ablation (?90%), suggesting a high velocity (?20 km/sec) of entry into the Earth's atmosphere. The atmospheric trajectory is reasonably well documented and its deviation from the projected ground fallout can be understood in terms of the ambient wind pattern. The apparent radiant of the trail was at a point in the sky with right ascension 165°, declination +60°. Considering the errors in estimating the radiant, we get a range of orbits with a = 2.3 ± 0.8 AU, e = 0.6 ± 0.1, and i = 28 ± 4° with the constraints of a ? 1.5 AU and V_∞ < 25 km/sec (which causes nearly complete evaporation of the meteoroid). Taking V_∞ = 21.5 lm/sec as indicated by the measured mass ablation of the meteorite, the orbital elements are deduced to be $\text{a = 1.8}\text{AU}\text{, e = 0.59, i = 27°.6, ω = 109°.1, Ω = 307°.8,}\text{and}\text{q = 0.74}$.     

Numerical experiment applicable to the latest stage of planet growth

A three-dimensional numerical model was developed with the goal of studying limited dynamical problems relevant to the latest stage of planet growth in the accretion theory. A small number of large protoplanets (～ Moon size) of different masses, moving around the Sun, are considered. The dynamical evolution and growth of the population is studied under mutual gravitational perturbations, accretion, and collisional fragmentation processes. Gravitational encounters are treated exactly by numerical integration of the N-body problem. Outcomes of collisional fragmentation are modeled according to the results of R. Greenberg et al. (1978, Icarus, 35, 1–26). In the present work, we consider 25 protoplanets with uniform mass distribution in the range 2 × 10²⁵?4 × 10²⁶ g on heliocentric orbits in the Earth zone. These bodies are initially confined to a small volume of space to permit gravitational perturbations by close approaches and collisions within a finite length of integration time. The dynamical evolution of the swarm is followed for four different sets of initial ranges in semimajor axis, eccentricity, and inclination: Δa=0.01, 0.02, 0.04, 0.08 AU; Δe= 0.005, 0.01, 0.02, 0.04; Δi=0°3, 0°6, 1°2, 2°4. Among other results, it is found that average eccentricities and inclinations evolve toward a steady state such that $\text{i}\text{?}\text{1}\text{2}\text{,}\text{e}$; it is also found that, whatever the initial conditions, the population evolves toward a quasi-equilibrium relative velocity distribution corresponding to a Safronov parameter value $\text{θ?10}$. Moreover, the growth process of the growing planet presents very similar behavior in the four cases considered, except for the time scale of evolution, which increases with the initial range of orbital elements. Earlier works of this kind have been presented by L.P. Cox and J.S. Lewis (1980, Icarus, 44, 706–721) and by G.N. Wetherill (1980b, In Geol. Soc. Canad. Spec. Publ., p. 20), although a number of differences exist between the three approaches.     

Saturn's rings. I. Optical thickness of rings A,B, D and structure of ring B

A photometric study of high-resolution (～0″.3) plates of Saturn taken at the Lowell Observatory in 1943 and 1945 is presented. N-S scans were taken over both the planet and rings. The excess brightness due to the planet seen through the rings is found by taking the difference between the central meridian (CM) scans and scans displaced by 5″.7. Adopting a value for the albedo of the planet, it is possible to obtain the optical thickness, τ_CM(r). In particular, for the regions of maximum brightness in rings A and B, we find τ_CM(I_{A max}) = 0.38 ± 0.11 and τ_CM(I_{B max}) = 0.61 ± 0.11. Observations by Barnard made in 1890 show evidence of ring D, recently discovered by Guerin (1969). The value for the optical thickness of this ring is τ_D(I_{D max}) = 0.03 ± 0.01. Ring B exhibits a pronounced (7–10%) decrease in brightness from the extremity of the major axis to the CM. After considering several possible explanations, we conclude that the ring particles are nonspherical and are in synchronous rotation around the planet with their long axis toward it. The mean value for the ratio of major to minor axis for the particles at 15″ is $\text{(a/b)}\text{? 1.08}$. Because of the shape and orientation of the particles, the optical thickness at the extremity of the major axis and at the CM are different for any saturnicentric latitude B ≠ 90°. Under these circumstances, only a minimum value for τ at the extremity can be derived.     

Planetary impact probabilities for long-period comets

Planetary impact probabilities for long-period (near-parabolic) comets are determined by averaging Öpik's equations over inclination and perihelion distance for each planet. These averaged values compare well with the results of more elaborate Monte Carlo calculations. The impact probabilities are proportional to the square of the normalized capture radius of each planet, which in turn is a function of the planet's radius and mass, so that the major planets have the highest impact probabilities. Encounter velocities have an average value of $\text{3}\text{1}\text{2}$ times the planetary orbital velocity but the most probable encounter velocities are slightly higher than this for the terrestrial planets and slightly lower for the major planets. Comparison of the impact probabilities with the cratering record, corrected for gravity and velocity effects, indicates that long-period comets may account for 3 to 9% of the observed large crattes (diameter > 10 km) on the terrestrial planets. The inclination and perihelion properties of the impact probabilities obtained from numerical averaging provide a simple method for determining the impact probabilities for nonuniform distributions. The perihelion distribution of long period comets from J. A. Fernandez ((1981) Astron. Astrophys.96, 26–35) results in a crater production rate quite similar throughout the solar system, unlike that of a uniform perihelion distribution.     

10 μm polarimetry of ceres

Linear polarimetry of Ceres at 10 μm is presented. These data represent the first published polarization measurements of an asteroid in the thermal infrared. It is found that Ceres is polarized at the 0.2-0.6% level. This data set is compared with theoretical models of the linear polarization of emitted radiation from a spherical plane. These models are used to derive the pole position and thermal inertia of Ceres. Ceres is best fit with a thermal inertia of $\text{0.0010±0.0003}\text{cal}\text{cm}{}^{\mathrm{?2}}\text{°}\text{K}{}^{\mathrm{?1}}\text{sec}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ and a pole orientation of β_p = 36° ± 5°, λ_p = 270° ± 3°. It is concluded that 10μm polarimetry is a potentially powerful technique for remotely sensing the pole orientation and thermal inertia of asteroids.     

Asteroids in cometary orbits

Orbital integrations are presented for a total of 14 asteroids with perihelia inside 1.7 AU and with aphelion distances in excess of 4 AU, 10 of which were discovered in 1979–1984. The integrations were normally extended over approximately ±1000 years in a three-body model (Sun-Jupiter-asteroid). The effects of uncertainties of starting orbits are not treated in this work, and as far as the real asteroids are concerned, the results should be regarded mostly as preliminary indications. A wide variety of orbital evolutions is found, and some of them evidently belong to the cometary, chaotic type. Three such cases are identified with certainty (1983 SA, 1983 XF, and 1984 BC) and two or three more with various degrees of likelihood. An asteroidal motion is found for the well-observed object 1979 VA. A stable libration around the $\text{2}\text{1}$ resonance is found for 1981 FD, which obviously adds to the Griqua group. A long-lasting libration around the $\text{5}\text{3}$ resonance performed by 1982 YA is probably unstable. Temporary librations are also found for 1983 SA ($\text{4}\text{3}$ resonance) and 1983 XF ($\text{2}\text{1}$ resonance), but these objects appear to transit into irregular motions with close approaches to Jupiter (less than 0.01 AU for 1983 XF). A very rapid large-amplitude ω libration around 90° is found in the future motion of 1983 VA. If this will indeed occur for the real asteroid, the object will oscillate with a period of only 750 years between a main-belt orbit of very high inclination and a low-inclination Apollo-type orbit.     

Lumped geopotential harmonics of order 29, from analysis of the orbit of Cosmos 837 rocket

The orbit of Cosmos 837 rocket (1976-62E) has been determined at 36 epochs between January and September 1978, using the RAE orbit refinement program PROP 6 with about 3000 observations. The inclination was 62.7° and the eccentricity 0.039. The orbital accuracy achieved was between 30m and 150m, both radial and crosstrack. The orbit was near 29:2 resonance in 1978 (exact resonance occurred on 14 May) and the values of orbital inclination obtained have been analysed to derive lumped 29th-order geopotential harmonic coefficients, namely:

$\text{10}{}^9\text{C}{}^{\mathrm{0,2}}{}_{29}\text{= ? 10 ± 15}$

and

$\text{10}{}^9\text{S}{}^{\mathrm{0,2}}{}_{29}\text{= ?76 ± 12}$

. These will be used in future, when enough results at different inclinations have accumulated, to determine individual coefficients of order 29. The values of lumped harmonics obtained from analysis of the values of eccentricity were not well defined, because of the high correlations between them and the errors in removing the very large perturbation (31 km) due to odd zonal harmonics.     

Analysis of the orbital inclination of Tansei 3 rocket 1977-12B

The orbit of Tansei 3rocket(1977-12B) has been determined at 47 epochs between 1 October 1977 and 19 March 1979 using over 1700 observations and the RAE orbit refinement program PROP6. The rate of change of the inclination was examined to evaluate values of the atmospheric rotation rate, Λ rev day^?1. Analysis yielded the value Λ = 1.1 ± 0.05 at height 315 ± 30 km, average conditions; or alternatively Λ = 1.1 ± 0.1 at height 347 ± 12 km, slight winter bias and Λ = 1.07 ± 0.1 at height 270 ± 18 km, average conditions, supplying further evidence of a decrease in rotation rates from the 1960s to the 1970s.Analysis of the inclination at 15th-order resonance yielded the lumped harmonic values

$\text{10}{}^9\text{C}{}^{\mathrm{0,1}}{}_{15}\text{= 13.4 ± 6.2, 10}{}^9\text{S}{}^{\mathrm{0,1}}{}_{15}\text{= 0.7 ± 13.3}$

for inclination 65.485°.     

CoRoT-2a Magnetic Activity: Hints for Possible Star–Planet Interaction

CoRoT-2a is a young (≈0.5 Gyr) G7V star accompanied by a transiting hot-Jupiter, discovered by the CoRoT satellite (Alonso et al. Astron Astrophys 482:L21, 2008; Bouchy et al. Astron Astrophys 482:L25, 2008). An analysis of its photospheric activity, based on spot modelling techniques previously developed by our group for the analysis of the Sun as a star, shows that the active regions on CoRoT-2a arised within two active longitudes separated by about 180° and rotating with periods of 4.5221 and 4.5543 days, respectively, at epoch of CoRoT observations (112 continous days centered at ≈2007.6). We show that the total spotted area oscillates with a period of about 28.9 days, a value close to 10 times the synodic period of the planet with respect to the active longitude pattern rotating in 4.5221 days. Moreover, the variance of the stellar flux is modulated in phase with the planet orbital period. This suggests a possible star–planet magnetic interaction, a phenomenon already seen in other extrasolar planetary systems hosting hot-Jupiters.     

Airborne spectroscopy and spacecraft radiometry of Venus in the far infrared

In March 1979, the spectrum of Venus was recorded in the far infrared from the G.P. Kuiper Airborne Observatory when the planet subtended a phase angle of 62°. The brightness temperature was observed to be 275°K near 110 cm^?1, dropping to 230°K near 270 cm^?1. Radiance calculations, using temperature and cloud structure formation from the Pioneer Venus mission and including gaseous absorption by the collision-induced dipole of CO₂, yield results consistently brighter than the observations. Supplementing the spectral data, Pioneer Venus OIR data at similar phase angles provide the constraint that any additional infrared opacity must be contained in the upper cloud, H₂SO₄ to the Pioneer-measured upper cloud structure serves to reconcile the model spectrum and the observations, but cloud microphysics strongly indicates that such a high particle density haze $\text{(N ? 1.6 × 10}{}^7\text{cm}{}^{\mathrm{?3}}\text{)}$ is implausible. The atmospheric environment is reviewed with regard to the far infrared opacity and possible particle distribution modifications are discussed. We conclude that the most likely possibility for supplementing the far-infrared opacity is a population of large particles $\text{(}\text{r}\text{? 1 μm)}$ in the upper cloud with number densities less than 1 particle cm^?3 which has remained undetected by in situ measurements.     

Secular resonance,solar spin down,and the orbit of Mercury

A mechanism capable of accounting for the large mean eccentricity (0.175) and inclination (7°.2) of Mercury is discussed. Provided the gravitational field of the rapidly rotating primordial Sun had a sufficiently large second degree harmonic (i.e., J₂ ? order 10^?3), subsequent solar spin down would drive the orbit of Mercury through two secular resonances with Venus, one involving the precession of the line of apsides, the other one involving the regression of the nodal line. Resonance passage generates contributions to the eccentricity and inclination that are proportional to the square root of the characteristic solar spin down time. We find that an initial solar rotation l period of $\text{P ? 5}\text{1}\text{2}\text{hr}$ guarantees passage through resonance and that a spin down time of $\text{τ = Ω|dΩ/dt|}{}^{\mathrm{?1}}$ of order 10⁶ years could have produced the observed eccentricity and inclination. Such a primordial rotation rate is comparable to the measured rotations of very young stars and the spin down time appears consistent with the time scale derived for magnetic braking of the Sun's rotation by an intense solar wind during a T-Tauri stage of solar evolution.     

Seasonal changes on Jupiter: 1. Factor of activity of the hemispheres

To identify temporal variations of the characteristics of Jupiter’s cloud layer, we take into account the geometric modulation caused by the rotation of the planet and planetary orbital motion. Inclination of the rotation axis to the orbital plane of Jupiter is 3.13°, and the angle between the magnetic axis and the rotation axis is β ≈ 10°. Therefore, over a Jovian year, the jovicentric magnetic declination of the Earth φ _m varies from–13.13° to +13.13°, and the subsolar point on Jupiter’s magnetosphere is shifted by 26.26° per orbital period. In this connection, variations of the Earth’s jovimagnetic latitude on Jupiter will have a prevailing influence in the solar-driven changes of reflective properties of the cloud cover and overcloud haze on Jupiter. Because of the orbit eccentricity (e = 0.048450), the northern hemisphere receives 21% greater solar energy inflow to the atmosphere, because Jupiter is at perihelion near the time of the summer solstice. The results of our studies have shown that the brightness ratio A _j of northern to southern tropical and temperate regions is an evident factor of photometric activity of Jupiter’s atmospheric processes. The analysis of observational data for the period from 1962 to 2015 reveals the existence of cyclic variations of the activity factor A _j of the planetary hemispheres with a period of 11.86 years, which allows us to talk about the seasonal rearrangement of Jupiter’s atmosphere.     

Precession of the orbital nodes of Jupiter and Saturn triggered by the mutual perturbation: A model of two rings

The problem of the precession of the orbital planes of Jupiter and Saturn under the influence of mutual gravitational perturbations was formulated and solved using a simple dynamical model. Using the Gauss method, the planetary orbits are modeled by material circular rings, intersecting along the diameter at a small angle α. The planet masses, semimajor axes and inclination angles of orbits correspond to the rings. What is new is that each ring has an angular momentum equal to the orbital angular momentum of the planet. Contrary to popular belief, it was proved that the orbital resonance 5: 2 does not preclude the use of the ring model. Moreover, the period of averaging of the disturbing force (T ≈ 1332 yr) proves to be appreciably greater than a conventionally used period (≈900 yr). The mutual potential energy of rings and the torque of gravitational forces between the rings were calculated. We compiled and solved the system of differential equations for the spatial motion of rings. It was established that a perturbing torque causes the precession and simultaneous rotation of the orbital planes of Jupiter and Saturn. Moreover, the opposite orbit nodes on the Laplace plane coincide and perform a secular movement in retrograde direction with the same velocity of 25.6″/yr and the period T _J = T _S ≈ 50687 yr. These results are close to those obtained in the general theory (25.93″/yr), which confirms the adequacy of the developed model. It was found that the vectors of the angular velocity of orbital rings move counterclockwise over circular cones and describe circles on the celestial sphere with radii β₁ ≈ 0.8403504° (Saturn) and β₂ ≈ 0.3409296° (Jupiter) around the point which is located at an angular distance of 1.647607° from the ecliptic pole.     

Orbital dynamics of the planetary system HD 196885

The orbital dynamics of the single known planet in the binary star system HD 196885 has been considered. The Lyapunov characteristic exponents and Lyapunov time of the planetary system have been calculated for possible values of the planetary orbit parameters. It has been shown that the dynamics of the planetary system HD 196885 is regular with the Lyapunov time of more than 5 × 10⁴ years (the orbital period of the planet is approximately 3.7 years), if the motion occurs at a distance from the separatrix of the Lidov–Kozai resonance. The values of the planet’s orbital inclination to the plane of the sky and longitude of the ascending node lie either within ranges 30° < i _p < 90° and 30° < Ω_p < 90°, or 90° < i _p < 180° and 180° < Ω_p < 300°.     

Analysis of the orbit of ariel 1, 1962-15A,near 15th-order resonance

Ariel 1, the first international satellite, was launched on 26 April 1962, into an orbit inclined at 53.85° to the equator, with an initial perigee height near 390 km. On 8 May 1973 the orbit passed through 15th-order resonance and has been determined, with the RAE orbit refinement program PROP, at eight epochs between February and August 1973 using 500 observations.The orbital inclinations during the time of 15th-order resonance, as given by these eight orbits and 31 U.S. Navy orbits, were fitted with a theoretical curve using the THROE computer program, the best fit giving $\text{10}{}^9\text{C}\text{?}{}_{15}\text{= ?370 ± 14}$ and 10⁹S₁₅ = ?114 ± 31.The values of eccentricity were also successfully fitted using THROE, and the results are discussed.