Allowance for the phase of Jupiter when determining the contact times in some phenomena of its Galilean satellites

We suggest a new method for predicting the phenomena observed in Jovian system of Galilean satellites that takes into account the planet’s phase effect. The method allows one to determine the geocentric times of the contacts of the satellite and its shadow with the illuminated part of the planet’s visible disk that occur near its inferior geocentric and inferior heliocentric conjunctions, respectively. The calculation is performed in the orthographic approximation for the geometric center of the satellite and its shadow by taking into account the curvature of the satellite’s orbit and the visible flattening of Jovian disk. The correction for the phase to the satellite’s contact time is determined from the phase shift of the center of the planet’s disk.     

Refinement of the phase of a spherical planet located at a small distance from the Sun

Formulas for refining the phase of a spherical planet located a small distance from the Sun are derived. Finite heliocentric distance of the planet results in the formation on its visible disk of the geometric terminator, which is not coincident with the orthographic terminator. The visible disk is assumed to be observed from Earth in orthographic projection. We suggest introducing linear and surface phases for the geometric terminator in accordance with two existing definitions of the phase of a planet. Linear and surface phases of a planet are shown to be given by different sets of formulas. An example of the computation of the phase of Mercury is given.     

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.     

Models of Jupiter's growth incorporating thermal and hydrodynamic constraints

We model the growth of Jupiter via core nucleated accretion, applying constraints from hydrodynamical processes that result from the disk-planet interaction. We compute the planet's internal structure using a well tested planetary formation code that is based upon a Henyey-type stellar evolution code. The planet's interactions with the protoplanetary disk are calculated using 3-D hydrodynamic simulations. Previous models of Jupiter's growth have taken the radius of the planet to be approximately one Hill sphere radius, RH. However, 3-D hydrodynamic simulations show that only gas within ∼0.25RH remains bound to the planet, with the more distant gas eventually participating in the shear flow of the protoplanetary disk. Therefore in our new simulations, the planet's outer boundary is placed at the location where gas has the thermal energy to reach the portion of the flow not bound to the planet. We find that the smaller radius increases the time required for planetary growth by ∼5%. Thermal pressure limits the rate at which a planet less than a few dozen times as massive as Earth can accumulate gas from the protoplanetary disk, whereas hydrodynamics regulates the growth rate for more massive planets. Within a moderately viscous disk, the accretion rate peaks when the planet's mass is about equal to the mass of Saturn. In a less viscous disk hydrodynamical limits to accretion are smaller, and the accretion rate peaks at lower mass. Observations suggest that the typical lifetime of massive disks around young stellar objects is ∼3 Myr. To account for the dissipation of such disks, we perform some of our simulations of Jupiter's growth within a disk whose surface gas density decreases on this timescale. In all of the cases that we simulate, the planet's effective radiating temperature rises to well above 1000 K soon after hydrodynamic limits begin to control the rate of gas accretion and the planet's distended envelope begins to contract. According to our simulations, proto-Jupiter's distended and thermally-supported envelope was too small to capture the planet's current retinue of irregular satellites as advocated by Pollack et al. [Pollack, J.B., Burns, J.A., Tauber, M.E., 1979. Icarus 37, 587-611].     

Latitudinal and longitudinal variation of a planetary atmosphere and the occultation experiment

The distribution of neutral and ionized particles about a planet depends, at any time, on angular coordinates (latitude and longitude) as well as altitude. Measurements of the Venusian and Martian atmospheres and ionospheres have been made by means of the ‘occultation’ experiment on-board the Mariner spacecrafts, and the same or similar experiment is planned for future missions to the planets. The conventional method of reducing the residual doppler data assumes spherical symmetry, in which the refractivity of the medium depends only on radius from the center of the planet, or altitude. It is shown that the neglect of angular dependence may introduce serious errors, even for media in which this dependence is slight compared to that in the radial direction, when the plane of motion of the spacecraft about the planet is inclined with respect to the direction of the Earth. The magnitude of the errors may be greatest for a planet such as Mercury and least for Jupiter, if planetary size and atmospheric temperature are the principal factors considered. Mars and Venus being intermediate. These results are most significant for an orbiter in which the orbital plane is inclined to obtain planetary coverage in a matter of months of measurements. Results of calculations for a particular model show that scale height measurements, and, thereby, atmospheric temperature, may be in error by a factor greater than 2 for inclined orbital configurations.     

Optical reflectance polarimetry of Saturn's globe and rings: IV. Aerosols in the upper atmosphere of Saturn

From 1958 to 1976 the degree and direction of polarization of the light at Saturn's disk center were measured in orange light over 74 nights and at five wavelenghts over 19 nights. Measurements were also recorded at limb, terminator, and pole. In addition, extensive regional polarization measurements were collected over Saturn's disk and several polarization maps were produced. These data were analyzed on the basis Mie scattering theory and of transfer theory in planetary atmospheres. A model of the Saturn upper atmosphere aerosol structure is derived in which the top part of the the main cloud layer is composed of spherical transparent particles of radius 1.4 μm and refractive index 1.44. Above this layer, a fine haze of submicron-sized grains was detected by its production of a component of polarization which is always directed poleward; this upper haze is interpreted as having nonspherical particles which are systematically oriented. This upper haze layer covers approximately the whole planet uniformly but varies in thickness from year to year. The clear gas above the cloud layer has an optical thickness of around 0.1.     

The distribution of the 9 cm radio emission over the solar disk during the sunspot minimum

The brightness distribution of the quiet sun on 9.1 cm wavelength is determined from the Stanford pencil-beam radioheliograms for three periods in the recent solar activity minimum, centred at July 15 and September 15, 1964 and at April 5, 1965. The brightness maxima near the limbs are not symmetric with respect to the central meridian, but are situated at 76 °E and 66 °W longitude, respectively. On the disk, the brightness temperature is likewise distributed asymmetrically, but the direction of this asymmetry changes as the new cycle starts. The asymmetries are tentatively explained by assuming the presence of inhomogeneous streamers in the solar atmosphere, which are tilted by the solar rotation. The eastward shift of the limb maxima with respect to the optical disk is confirmed by the 21 cm-heliograms obtained at Fleurs near Sydney, Australia.     

Holomorphy of coordinates with respect to eccentricities in the planetary three-body problem

The boundaries of the domains of holomorphy of the coordinates of unperturbed elliptic motion with respect to the eccentricities of planetary orbits are determined for the cases when any of the five anomalies of one of the planets-eccentric, true, tangential, or one of two mutual anomalies suggested by M.F. Subbotin—is used as an independent variable. The resulting equations are a generalization of the known equations for the boundaries of the domains of the holomorphy of coordinates for the cases when the time is the independent variable and determine the bisymmetric ovals, whose size and shape depend on the eccentricities and on the ratio of the planetary mean motions. The largest domains of holomorphy are obtained when the tangential anomaly or one of the Subbotin mutual anomalies is used. A function was found that conformally maps the domain of holomorphy to the unit disk. It was demonstrated that the application of any anomaly of the outer planet as the independent variable can result in a significant shrinking of the domain of the holomorphy of the coordinates of the inner planet, so that the analytic continuation of the initial power series with the center at the origin of the coordinates of a complex plane becomes impossible.     

The formation of an eccentric gap in a gas disc by a planet in an eccentric orbit

We investigate the effect of a planet on an eccentric orbit on a two-dimensional low-mass gaseous disc. At a planet eccentricity above the planet's Hill radius divided by its semimajor axis, we find that the disc morphology differs from that exhibited by a disc containing a planet in a circular orbit. An eccentric gap is created with eccentricity that can exceed the planet's eccentricity and precesses with respect to the planet's orbit. We find that a more massive planet is required to open a gap when the planet is on an eccentric orbit. We attribute this behaviour to spiral density waves excited at corotation resonances by the eccentric planet. These act to increase the disc's eccentricity and exert a torque opposite in sign to that exerted by the Lindblad resonances. The reduced torque makes it more difficult for waves driven by the planet to overcome viscous inflow in the disc.     

Automated cloud tracking system for the Akatsuki Venus Climate Orbiter data

Japanese Venus Climate Orbiter, Akatsuki, is cruising to approach to Venus again although its first Venus orbital insertion (VOI) has been failed. At present, we focus on the next opportunity of VOI and the following scientific observations.We have constructed an automated cloud tracking system for processing data obtained by Akatsuki in the present study. In this system, correction of the pointing of the satellite is essentially important for improving accuracy of the cloud motion vectors derived using the cloud tracking. Attitude errors of the satellite are reduced by fitting an ellipse to limb of an imaged Venus disk. Next, longitude–latitude distributions of brightness (cloud patterns) are calculated to make it easy to derive the cloud motion vectors. The grid points are distributed at regular intervals in the longitude–latitude coordinate. After applying the solar zenith correction and a highpass filter to the derived longitude–latitude distributions of brightness, the cloud features are tracked using pairs of images. As a result, we obtain cloud motion vectors on longitude–latitude grid points equally spaced. These entire processes are pipelined and automated, and are applied to all data obtained by combinations of cameras and filters onboard Akatsuki. It is shown by several tests that the cloud motion vectors are determined with a sufficient accuracy. We expect that longitude–latitude data sets created by the automated cloud tracking system will contribute to the Venus meteorology.     

Détermination quantitative de l'effect de phase dans la mesure des longitudes sur Jupiter

We have quantitatively determined the phase exaggeration effect (Phillips effect) as a function of the planet's phase angle for the correction of the longitude of spots on the Jupiter disk. This was done on the basis of over 1000 visual observations of the longitude of permanent details of Jupiter's surface compared with photographic observations. We also propose the existence of a systematic error (+0°.6 zenographic) in our visual observations. As this error is probably caused by unidirectional motion of the detail over the planetary disk, we named it the “shift effect”.     

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.     

Faculae and east-west asymmetry of sunspot area

Asymmetry of sunspot area with respect to the central meridian is found to depend strongly on the location of the spot group in its chromospheric facula or plage. The usual area excess for spots in the eastern half of the disk is reversed for the relatively rare spot groups situated in the following part of the plage. Qualitatively, the observed asymmetries can be explained by supposing that the apparent area of the spot is decreased by overlying bright facula, especially west of central meridian where the spot (in the usual preceding position) is viewed through the relatively bright and extensive follower part of the plage. However, the variation with central meridian distance of the mean area of spots and of faculae demands a more complex model, in which the spatial distribution of facula and plage also depends on the location of the spot group. Since both facula and spot effects are seen along the same line of sight, optical depth must change slowly with geometric depth, that is, in the active region the atmosphere is relatively transparent.     

Chaotic zone boundary for low free eccentricity particles near an eccentric planet

We consider particles with low free or proper eccentricity that are orbiting near planets on eccentric orbits. Through collisionless particle integration, we numerically find the location of the boundary of the chaotic zone in the planet's corotation region. We find that the distance in semimajor axis between the planet and boundary depends on the planet mass to the 2/7 power and is independent of the planet eccentricity, at least for planet eccentricities below 0.3. Our integrations reveal a similarity between the dynamics of particles at zero eccentricity near a planet in a circular orbit and with zero free eccentricity particles near an eccentric planet. The 2/7th law has been previously explained by estimating the semimajor at which the first-order mean motion resonances are large enough to overlap. Orbital dynamics near an eccentric planet could differ due to first-order corotation resonances that have strength proportional to the planet's eccentricity. However, we find that the corotation resonance width at low free eccentricity is small; also the first-order resonance width at zero free eccentricity is the same as that for a zero-eccentricity particle near a planet in a circular orbit. This accounts for insensitivity of the chaotic zone width to planet eccentricity. Particles at zero free eccentricity near an eccentric planet have similar dynamics to those at zero eccentricity near a planet in a circular orbit.     

Gravitational microlensing of planets: the influence of planetary phase and caustic orientation

Recent studies have demonstrated that detailed monitoring of gravitational microlensing events can reveal the presence of planets orbiting the microlensed source stars. With the potential of probing planets in the Galactic bulge and Magellanic Clouds, such detections greatly increase the volume over which planets can be found. This paper expands on the original studies by considering the effect of planetary phase on the form of the resultant microlensing light curve. It is found that crescent-like sources can undergo substantially more magnification than a uniformly illuminated disc, the model typically employed in studying such planets. In fact, such a circularly symmetric model is found to suffer a minimal degree of magnification when compared with the crescent models. The degree of magnification is also a strong function of the planet's orientation with respect to the microlensing caustic. The form of the magnification variability is strongly dependent on the planetary phase and from which direction the planet is swept by the caustic, providing further clues to the geometry of the planetary system. As the amount of light reflected from a planet also depends on its phase, the detection of extreme crescent-like planets requires the advent of 30-m class telescopes, while light curves of planets at more moderate phases can be determined with today's 10-m telescopes.     

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.     

Galilean satellite mutual occultation data processing

Results of processing seven mutual occultation lightcurves are presented. The lightcurves were obtained using the 60-inch telescope (152 cm) at Mt. Wilson to observe six J1 occulting J2 events and one J3 occulting J2 event. Using a uniformly illuminated disk model, local satellite Jovicentric longitude corrections of 675 ± 150 km, 275 ± 240 km, and 1175 ± 350 km for J1, J2, and J3, respectively, were determined. These corrections enabled the event midpoint times to be computed to ±5sec of the observed midpoint times for all seven events. These longitude corrections have been verified by Pioneer 10 and recent (1973 and 1974) conventional Jovian eclipse observations. A relative J1:J2 out-of-plane error of less than a few hundred kilometers has been indicated; however, it appears that the relative J3:J2 out-of-plane error is larger than 600 km. Deficiencies in both the uniformly illuminated disk model and Sampson's theory of the Galilean satellite motions for the reduction of mutual event data are described.     

Potential of a gaussian ring. A new approach

A fundamentally new approach to an elliptic Gaussian ring has been developed. It has been ascertained that it can be produced from a uniform plane elliptic disk by mass balayage into an elementary homothetic layer with the center of homothety at an ellipse focus. An advantage of new interpretation is in the fact that the spatial potential of a Gaussian ring is expressed in terms of the potential of a uniform elliptic disk, well-known in the finite form, and its derivatives. A general formula for the potential of a two-dimensional homothetic layer has been derived with this purpose. As a result, the potential of a Gaussian ring is represent-able in a simple analytical form in terms of standard complete elliptic integrals in both elliptic and Cartesian coordinates. The mass asymmetry along the ring is considered explicitly. The potential formulas are verified numerically and have no singular points at ellipse foci. Particular cases are considered; the 3D potential surface and system of equipotentials are constructed. Knowledge of the potential extends the range of application of a Gaussian ring in the problem of calculation of secular perturbations in celestial mechanics.     

Bending instability of stellar disks: The stabilizing effect of a compact bulge

The saturation conditions for bending modes in inhomogeneous thin stellar disks that follow from an analysis of the dispersion relation are compared with those derived from N-body simulations. In the central regions of inhomogeneous disks, the reserve of disk strength against the growth of bending instability is smaller than that for a homogeneous layer. The spheroidal component (a dark halo, a bulge) is shown to have a stabilizing effect. The latter turns out to depend not only on the total mass of the spherical component, but also on the degree of mass concentration toward the center. We conclude that the presence of a compact (not necessarily massive) bulge in spiral galaxies may prove to be enough to suppress the bending perturbations that increase the disk thickness. This conclusion is corroborated by our N-body simulations in which we simulated the evolution of near-equilibrium, but unstable finite-thickness disks in the presence of spheroidal components. The final disk thickness at the same total mass of the spherical component (dark halo + bulge) was found to be much smaller than that in the simulations where a concentrated bulge is present.