The oblateness effect on the solar radiation incident at the top of the atmospheres of the outer planets

Calculations of the daily solar radiation incident at the top of the atmospheres of Jupiter, Saturn, Uranus, and Neptune, with and without the effect of the oblateness, are presented in a series of figures illustrating the seasonal and latitudinal variation of the ratio of both insolations. It is shown that for parts of the summer, the daily insolation of an oblate planet is increased, the zone of enhanced solar radiation being strongly dependent upon the obliquity, whereas the rate of increase is fixed by both the flattening and the obliquity. In winter, the oblateness effect results in a more extensive polar region, the daily solar radiation of an oblate planet always being reduced when compared to a spherical planet. In addition, we also numerically studied the mean daily solar radiation. As previously stated by A.W. Brinkman and J. McGregor (1979, Icarus, 38, 479–482), it is found that in summer the horizon plane is tilted toward the Sun for latitudes less than the subsolar point, but is titled away from the Sun beyond this latitude. It follows that the mean summer daily insolation is increased between the equator and the subsolar point, but decreased poleward of the above-mentioned limit. In winter, however, the horizon plane is always tilted away from the Sun, causing the mean winter daily insolation to be reduced. The partial gain of the mean summertime insolation being much smaller than the loss during winter season evidently yields a mean annual daily insolation which is decreased at all latitudes.     

The effect of orbital element variations on the mean seasonal daily insolation on Mars

In this paper we briefly study changes in the mean seasonal insolations on the planet Mars caused by significant large-scale variations in the following orbital elements: the eccentricity (e), the obliquity (ε) and the longitude of perihelion (λ _p ). Three orbital configurations have been investigated. In the first, the eccentricity equals successively 0, 0.075, and 0.15, whereas for the obliquity and the longitude of perihelion we took the present values which amount, respectively to 25° and 250°. In the second situation, ε=15, 25, and 35° for a circular orbit (e=0) and with λ _p =250°. In the last model we have sete=0.075 and ε=25° for λ _p =?90,0, and 90°. Although long-term periodic oscillations ofe (first case) and λ _p (third case) produce, respectively, very small or no variations in the average yearly insolation, fluctuations of the above mentioned planetary data strongly effect the mean summer and winter daily insolations. Indeed, the calculations reveal that between the two extreme values of the orbital elements used, the seasonal insolations exhibit a change in amplitude of about 15 to 20% difference over the entire latitude interval. Considering more particularly the second case it is found that the summertime insolation experiences a nearly similar variation as the mean annual daily insolation — i.e., a decrease of about 7% at the equator and a more than twofold increase at the poles. The corresponding mean winter daily insolation varies maximally by approximately 60% in the 60–80° latitude range.     

A comment on the insolation at Mercury

E. Van Hemelrijck and J. Vercheval [Icarus48, 167–179 (1981)] presented calculations of the insolation at Mercury and Venus which neglect the finite angular size of the Sun. To determine the temperature structure in the subsurface a more accurate calculation is needed, especially at longitudes ±90° on Mercury, where the Sun takes 18 days to rise or set. These calculations are presented here.     

Observations of the sodium tail of Mercury

Cross-sections of the sodium emission tail of Mercury were measured at various distances down the tail when Mercury was moving away from the Sun (true anomaly angles <180°), and again when Mercury was moving towards the Sun (true anomaly angles >180°). As predicted in early modeling studies, significant differences were expected between these two cases, as the result of Doppler shifts to higher solar intensity in the former case, and to lower solar intensity for the latter case. For observations with Mercury moving away from the Sun, the sodium tail was observed out to about 40,000 kilometers (16 Mercury radii, RM) downstream, expanding, on average, at a rate of 1.9±0.3 km/s. The source rates for sodium generation from Mercury into the tail were found to be in the range 2-5×¹⁰²³ atoms/s, corresponding to between 1 and 10% of the estimated total sodium production rate on the planet. The limiting value of radiation acceleration required to produce an observable sodium tail was estimated to be 112±24 cm/s². For observations where Mercury was moving towards the Sun, the emission intensity in the sodium tail decreased very rapidly with distance downstream, disappearing entirely beyond 12,000 (6 RM) kilometers for radiation accelerations of 128.7 and 135.4 cm/s². For smaller radiation accelerations, the sodium tail was not detectable at all, yielding a limiting value for tail generation of about 122±2 cm/s². Interpretation of the limiting radiation acceleration values suggests that the process that generates the sodium tail yields atoms with energies greater than 3 eV. Particle sputtering is the most reasonable source process.     

Insolation changes on pluto caused by orbital element variations

In this paper, we compare changes in the insolation at Pluto, corresponding to three epochs during the dynamical history of the planet: t = – 1, 0 and 0.5, where t is the time in millions of years A.D. The two extreme values of t coincide respectively with a maximum (126 ) and a minimum (102 ) value of the obliquity (). The other orbital elements i.e. the eccentricity (e) and the longitude of the perihelion ( _p ) which affect solar radiation and which are apt to significant periodic changes are also calculated for the times under consideration. In a series of figures, the combined influence of the evolving dynamic parameters on the daily insolation and on the mean (summer, winter, annual) daily insolation is illustrated.     

Spin states and climates of eccentric exoplanets

The known extrasolar planets exhibit a wide range of orbital eccentricities e. This has a profound influence on their rotations and climates. Because of tides in their interiors, mostly solid exoplanets are expected eventually to despin to a state of spin-orbit resonance, where the orbital period is some integer or half-integer times the rotation period. The most important of these resonances is the synchronous state, where the planet's spin period exactly equals its orbital period (like Earth's Moon, and indeed most of the regular satellites in the Solar System). Such planets seem doomed to roast on one side and freeze on the other. However, synchronous planets rock back and forth by an angle of ∼2Arcsine with respect to the sub-stellar point. For e=0.055 (as for the Moon), this optical libration amounts to only ∼6°; but for a synchronous planet with e=0.50, for example, it would rise to ∼59°. This greatly expands the temperate “twilight zone” near the terminator and considerably improves the planet's prospects for habitability. For e?0.72389, the optical libration exceeds 90°; for such planets, the sector of permanent night vanishes, while the sunniest region splits in two. Furthermore, the synchronous state is not the only possible spin resonance. For example, Mercury (with e≈0.206) has an orbital period exactly 1.5 times its rotation period. A terrestrial exoplanet with e=0.40, say, is liable to have an orbital period of 2.0, 2.5, or 3.0 times its spin period. The corresponding insolation patterns are generally complicated, and all different from the synchronous state. Yet these non-synchronous resonances also protect certain longitudes from the worst extremes of temperature and solar radiation, and improve the planet's habitability, compared to non-resonant rotation. These results also have implications for the direct detectability of extrasolar planets, and the interpretation of their thermal emissions.     

Some aspects of the solar radiation incident at the top of the atmospheres of Mercury and Venus

A formalism has been developed for the calculation of the insolation on the planets Mercury and Venus neglecting any atmospheric absorption. For Mercury, the instantaneous insolation curves are repeated in a 2-tropical year cycle, the distribution of the solar radiation being perfectly symmetric between both hemispheres. In addition to latitudinal variations, one observes a longitudinal effect expressed by different instantaneous insolation distributions during the course of the time; on the equator, the relative diurnal insolation variability may attain a factor of 3. The small obliquity of Venus results in a nearly symmetric solar radiation distributions with respect to the equator except at the poles, where an important seasonal effect has been found. It has to be noted that no longitudinal dependence exists. Finally, the insolation curves are repeated in a nearly half-year cycle.     

Effect of Planetary Eccentricity on Ballistic Capture in the Solar System

Ballistic capture of spacecraft and celestial bodies by planets of the solar system is studied considering the elliptic restricted three body model. A preferential region, due to the eccentricity of the planet and the Sun-gravity-gradient effect is found for the capture phenomenon. An analytical formula is derived which determines the limiting value of the satellite capture eccentricity e_c as a function of the pericenter distance x_p and planet’s true anomaly. The analytic values e_c are tested by a numerical propagator, which makes use of planetary ephemeris, and only a small difference with respect to numerical integration is found. It turns out that lower values of e_c occur when the planet anomaly is close to zero; that is, capture is easier when the planet is at its perihelion. This fact is confirmed by the capture of celestial bodies. It is shown that Jupiter comets are generally captured when Jupiter is in its perihelion region. Ballistic capture is also important in interplanetary missions. The propellant saved using the minimum ballistic capture eccentricity is evaluated for different missions and compared with respect to the case in which the insertion orbit is a parabola: a significant saving can be accomplished.     

The space environment of Mercury at the times of the second and third MESSENGER flybys

The second and third flybys of Mercury by the MESSENGER spacecraft occurred, respectively, on 6 October 2008 and on 29 September 2009. In order to provide contextual information about the solar wind properties and the interplanetary magnetic field (IMF) near the planet at those times, we have used an empirical modeling technique combined with a numerical physics-based solar wind model. The Wang–Sheeley–Arge (WSA) method uses solar photospheric magnetic field observations (from Earth-based instruments) in order to estimate the inner heliospheric radial flow speed and radial magnetic field out to 21.5 solar radii from the Sun. This information is then used as input to the global numerical magnetohydrodynamic model, ENLIL, which calculates solar wind velocity, density, temperature, and magnetic field strength and polarity throughout the inner heliosphere. WSA-ENLIL calculations are presented for the several-week period encompassing the second and third flybys. This information, in conjunction with available MESSENGER data, aid in understanding the Mercury flyby observations and provide a basis for global magnetospheric modeling. We find that during both flybys, the solar wind conditions were very quiescent and would have provided only modest dynamic driving forces for Mercury's magnetospheric system.     

A dynamical investigation of the conjecture that Mercury is an escaped satellite of Venus

The possibility that Mercury might once have been satellite of a Venus, suggested by a number of anomalies, is investigated by a series of numerical computer experiments. Tidal interaction between Mercury and Venus would result in the escape of Mercury into a solar orbit. Only two escape orbits are possible, one exterior and one interior to the Venus orbit. For the interior orbit, subsequent encounters are sufficiently distant to avoid recapture or large perturbations. The perihelion distance of Mercury tends to decrease, while the orientation of perihelion librates for the first few thousand revolutions. If dynamical evolution or nonconservative forces were large enough in the early solar system, the present semimajor axes could have resulted. The theoretical minimum quadrupole moment of the inclined rotating Sun would rotate the orbital planes out of coplanarity. Secular perturbations by the other planets would evolve the eccentricity and inclination of Mercury's orbit through a range of possible configurations, including the present orbit. Thus the conjecture that Mercury is an escaped satellite of Venus remains viable, and is rendered more attractive by our failure to disprove it dynamically.     

The Non-Gravitational Perturbations impact on the BepiColombo Radio Science Experiment and the key rôle of the ISA accelerometer: direct solar radiation and albedo effects

The paper is focused on the estimate of the impact of the non-gravitational perturbations on the orbit of the Mercury Planetary Orbiter (MPO), one of the two spacecrafts that will be placed in orbit around the innermost planet of the solar system by the BepiColombo space mission. The key rôle of the Italian Spring Accelerometer (ISA), that has been selected by the European Space Agency (ESA) to fly on-board the MPO, is outlined. In the first part of the paper, through a numerical simulation and analysis we have estimated, over a time span of several years, the long-period behaviours of the disturbing accelerations produced by the incoming direct solar radiation pressure, and the indirect effects produced by Mercury’s albedo. The variations in the orbital parameters of the spacecraft, together with their spectral contents, have been estimated over the analysed period. The direct solar radiation pressure represents the strongest non-gravitational perturbation on the MPO in the very complex radiation environment of Mercury. The order-of-magnitude of this acceleration is quite high, about 10^?6 m/s², because of the proximity to the Sun and the large area-to-mass ratio of the spacecraft. In the second part of the paper, we concentrated upon the short-period effects of direct solar radiation pressure and Mercury’s albedo. In particular, the disturbing accelerations have been compared with the ISA measurement error and the advantages of an on-board accelerometer are highlighted with respect to the best modelling of the non-gravitational perturbations in the strong radiation environment of Mercury. The readings from ISA, with an intrinsic noise level of about $10^{-9}\,m/s^{2}/\sqrt{Hz}The paper is focused on the estimate of the impact of the non-gravitational perturbations on the orbit of the Mercury Planetary Orbiter (MPO), one of the two spacecrafts that will be placed in orbit around the innermost planet of the solar system by the BepiColombo space mission. The key r?le of the Italian Spring Accelerometer (ISA), that has been selected by the European Space Agency (ESA) to fly on-board the MPO, is outlined. In the first part of the paper, through a numerical simulation and analysis we have estimated, over a time span of several years, the long-period behaviours of the disturbing accelerations produced by the incoming direct solar radiation pressure, and the indirect effects produced by Mercury’s albedo. The variations in the orbital parameters of the spacecraft, together with their spectral contents, have been estimated over the analysed period. The direct solar radiation pressure represents the strongest non-gravitational perturbation on the MPO in the very complex radiation environment of Mercury. The order-of-magnitude of this acceleration is quite high, about 10⁻⁶ m/s², because of the proximity to the Sun and the large area-to-mass ratio of the spacecraft. In the second part of the paper, we concentrated upon the short-period effects of direct solar radiation pressure and Mercury’s albedo. In particular, the disturbing accelerations have been compared with the ISA measurement error and the advantages of an on-board accelerometer are highlighted with respect to the best modelling of the non-gravitational perturbations in the strong radiation environment of Mercury. The readings from ISA, with an intrinsic noise level of about in the frequency band of 3·10⁻⁵–10⁻¹ Hz, guarantees a very significant reduction of the non-gravitational accelerations impact on the space mission accuracy, especially of the dominant direct solar radiation pressure.     

Constraining the Angular Momentum of the Sun with Planetary Orbital Motions and General Relativity

The angular momentum of a star is an important astrophysical quantity related to its internal structure, formation, and evolution. Helioseismology yields $S_{\odot}= 1.92\times10^{41}\ \mathrm{kg\ m^{2}\ s^{-1}}$ for the angular momentum of the Sun. We show how it should be possible to constrain it in a near future by using the gravitomagnetic Lense?CThirring effect predicted by General Relativity for the orbit of a test particle moving around a central rotating body. We also discuss the present-day situation in view of the latest determinations of the supplementary perihelion precession of Mercury. A fit by Fienga et al. (Celestial Mech. Dynamical Astron. 111, 363, 2011) of the dynamical models of several standard forces acting on the planets of the solar system to a long data record yielded milliarcseconds per century. The modeled forces did not include the Lense?CThirring effect itself, which is expected to be as large as from helioseismology-based values of S _??. By assuming the validity of General Relativity, from its theoretical prediction for the gravitomagnetic perihelion precession of Mercury, one can straightforwardly infer $S_{\odot}\leq0.95\times10^{41}\ \mathrm{kg\, m^{2}\, s^{-1}}$ . It disagrees with the currently available values from helioseismology. Possible sources for the present discrepancy are examined. Given the current level of accuracy in the Mercury ephemerides, the gravitomagnetic force of the Sun should be included in their force models. MESSENGER, in orbit around Mercury since March 2011, will collect science data until 2013, while BepiColombo, to be launched in 2015, should reach Mercury in 2022 for a year-long science phase: the analysis of their data will be important in effectively constraining S _?? in about a decade or, perhaps, even less.     

Mercury: Internal structure and thermal evolution

Astronomical observations and cosmochemical calculations suggest that the planet Mercury may be composed of materials which condensed at relatively high temperatures in the primitive solar nebula and may have a basaltic crust similar to parts of the moon. These findings, plus the long standing inference that Mercury is much richer in metallic iron than the other terrestrial planets, provide important constraints which we apply to models of the thermal evolution and density structure of the planet. The thermal history calculations include explicitly the differing thermal properties of iron and silicates and account for core segregation, melting and differentiation of heat sources, and simulated convection during melting. If the U and Th abundances of Mercury are taken from the cosmochemical model of Lewis, then the planet would have fully differentiated a metal core from the silicate mantle for all likely initial temperature distributions and heat transfer properties. Density distributions for the planet are calculated from the mean density and estimates of the present-day temperature. For the fully differentiated model, the moment of inertia C/MR² is 0.325 (J₂=0.302×10^?6). For models with lower heat source abundances, the planet may not yet have differentiated. The density profiles for such models give C/MR²=0.394 (J₂=0.487×10^?6). These results should be useful for preliminary interpretation of the Mariner 10 measurements of Mercury's gravitational field.     

Secular perihelion advances of the inner planets and asteroid Icarus

A small effect expected from a recently proposed gravitational impact model (Wilhelm et al., 2013) is used to explain the remaining secular perihelion advance rates of the planets Mercury, Venus, Earth, Mars, and the asteroid (1566) Icarus—after taking into account the disturbances related to Newton’s Theory of Gravity. Such a rate was discovered by Le Verrier (1859) for Mercury and calculated by Einstein (1915, 1916) in the framework of his General Theory of Relativity (GTR). Accurate observations are now available for the inner Solar System objects with different orbital parameters. This is important, because it allowed us to demonstrate that the quantitative amount of the deviation from an 1/r potential is—under certain conditions—only dependent on the specific mass distribution of the Sun and not on the characteristics of the orbiting objects and their orbits. A displacement of the effective gravitational from the geometric centre of the Sun by about 4400 m towards each object is consistent with the observations and explains the secular perihelion advance rates.     

Cometary impacts with the Sun: Physical and dynamical considerations

D. J. Michels, N. R. Sheeley, Jr., R. A. Howard, and M. J. Koomen (Science215, 1097–1102, 1982) observed a comet which appears to have impacted the Sun. Z. Sekanina (Astron. J..87, 1059–1072, 1982) showed that the comet, 1979XI, was probably a member of the Kreutz group of sungrazing comets. The sungrazers typically have perihelia of 1.2–1.9 solar radii but Sekanina found q = 0.35 R_⊙ for 1979XI. It is interesting to speculate how the perihelion may have been reduced to this small value. The change in perihelion can not be explained by planetary, stellar, or nongravitational perturbations. Tidal splitting of the nucleus on a previous perihelion passage is also ruled out, through a random splitting event near aphelion of the comet's orbit is a remote possibility. The most plausible explanation is collision with another body, most likely a comet, at large heliocentric distance. However, the expected probability of such an event is exceedingly small. Another aspect of the problem is whether the nucleus of 1979XI sublimated completely before impacting the Sun. Assuming a water ice nucleus, it is shown that a surface layer of only 5–15 m thickness would be sublimated prior to impact. Although it is likely that the nucleus tidally disrupted after crossing the solar Roche limit, the ultimate destruction of the nucleus probably resulted from the shock of hitting the denser regions of the solar atmosphere, just above the photosphere.     

The adapted solar wind system as cause for a momentum transfer to the sun and its consequences for the orbital motions of keplerian objects

In the following paper we argue that each wind-driving star in relative motion with respect to the ambient interstellar medium experiences a force exerted on its central wind-generating body. The exact magnitude of this force depends on the actual geometry of the counterflow configuration of stellar and interstellar winds for a particular kinematic situation which is especially sensitive to whether the interstellar flow is subsonic or supersonic. It will, however, be demonstrated here that this force is of an accelerating nature, i.e., it operates like a rocket-motor, as long as the peculiar motion of the wind-driving star with respect to the ambient interstellar medium remains subsonic.Here we use a specific analytical model to describe theoretically the specific counterflow configuration for the case of the solar system in a subsonic peculiar motion with respect to the local interstellar medium assuming irrotational and incompressible flows. We can work out a quantitative number for the accelerating force governing the Sun's motion at present. The net reaction force exerted on the solar body is then mediated by the asymmetric boundary conditions to which the distant solar wind field has to adapt.Next we study the indirect action of such a force on orbiting Keplerian objects like planets, planetesimals and comets. Since this force only influences the central solar body, but not the planets themselves, the problem is different from the treatment of a constant perturbation force perturbing the Keplerian orbits. We present a perturbation analysis treating the action of a corresponding position-dependent perturbation force resulting in secular changes of the orbital elements of Keplerian objects. It is found that changes are accumulating more rapidly in time the closer to the sun the orbiting bodies are. Main axis and perihelion distances are systematically increasing. Especially pronounced are changes in the perihelion position angle of the objects. For solar wind mass losses larger than the Sun's present value by a factor of 1000 (T-Tauri phase of the Sun,) the migration periods calculated for the planet Mercury are of the same order of magnitude as that for corresponding general relativistic migration.     

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.     

Observation of Mercury's sodium exosphere during the transit on November 9, 2006

A rare, but normal, astronomical event occurred on November 9th 2006 (JST) as Mercury passed in front of the Sun from the perspective of the Earth. The abundance of the sodium vapor above the planet limb was observed by detecting an excess absorption in the solar sodium line D₁ during this event. The observation was performed with a 10-m spectrograph of Czerny-Turnar system at Domeless Solar Tower Telescope at the Hida Observatory in Japan. The excess absorption was red-shifted by 10 pm relative to the solar line, and was measured at the dawnside (eastside) and duskside (westside) of Mercury. Between the dawn and dusksides, an asymmetry of total sodium abundance was clearly identified. At the dawnside, the total sodium column density was 6.1×10¹⁰ Na atoms/cm², while it was 4.1×10¹⁰ Na atoms/cm² at the duskside. The investigation of dawn-dusk asymmetry of the sodium exosphere of Mercury is a clue to understand the release mechanism of sodium from the surface rock. Our result suggests that a thermal desorption is a main source process for sodium vapor in the vicinity of Mercury.     

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.     

Fan-shaped coma,orientation of rotation axis,and surface structure of a cometary nucleus I. Test of a model on four comets

Conspicuous anisotropy in the outgassing from comets, especially from short-period ones, appears to be the factor responsible for a frequent occurrence of a fan-shaped coma, extending in the general direction of the Sun. It is proposed that the pattern of deviations from the sunward direction contains information on the orientation of the spin axis and on the time lag in the sublimation process, which in turn provides insight into the nature of the nuclear surface. A simple model of a spherical rotating nucleus is formulated and a trial-and-error technique devised to determine the axis-orientation constants and a lage angle, a meaasure of the time lag in units of the rotation period. The results of application of this method to periodic comets Encke, Tempel 2, Borrelly, and Schwassmann-Wachmann 3 are presented. It is shown that the sense of rotation determined in this fashion is consistent with the results established for three of the four comets from the transverse component of the nongravitational force affecting their orbital motions. It is found that in general the time lag is strongly time dependent and that lag angles approaching 90° are rather common near perihelion, suggesting a complex surface structure that involves an insulting crust of dust of variable thickness and strength. These results are compared with the observed lightcurves of the four comets and with the calculated distributions of integrated insolation at the nuclear surface as functions of the cometocentric latitude and time. Noticed is a tendency of the comets to turn their spin axes to the Sun near perihelion and to replace, on the outbound leg of orbit, the established fan-orientation pattern by a “late”-tail pattern indicative of old, slowly accelerated particles. It is suggested that the motion of P/Schwassmann-Wachmann 3, which is due for a favorable return in 1979, was affected by a secular deceleration in 1930.