The effect of Saturn's rings on the upper-boundary insolation of its atmosphere

In this paper, the daily solar radiation incident at the top of Saturn's atmosphere and taking into account both the oblateness of the planet and the shadow of the ring system is calculated. It is found that the decrease of the daily insolation in winter is important near the solstices up to mid-latitudes and in the neighborhood of the equinoxes for equatorial and low latitudes. The combined effect of Saturn's rings and its flattening on the mean winter and annual daily insolations is also studied. The numerical results show that the mean wintertime insolation falls gradually in the (0–20 °) latitude region to a peak value of about 50%. Beyond 20° the loss of insolation decreases and from approximately 45 up to polar region latitudes the decrease reaches a practically constant level of 35%. The mean annual daily insolation is maximally reduced by about 20° at localities of 20°.     

The oblateness effect on the mean seasonal daily insolations at the martian surface during global dust storms

In this short paper, the combined effect of global dust storms and the oblateness on the mean seasonal daily insolations at the Martian surface is investigated. Due to the flattening, the mean summertime insolation is increased at equatorial and low latitudes, decreased at mid- and high latitudes. When comparing a spherical with an oblate planet Mars, it is found that the percentage differences of the mean summer daily insolations are dependent upon the optical depths () considered. For an atmosphere without aerosols, the maximum percentage differences are respectively equal to + 0.05 and – 0.2%; at = 3.0 the corresponding values amount to about 0.1 and 2%. In winter, the mean daily insolations are decreased over the entire latitudinal interval, where the maximum values are found at polar region latitudes; at e.g. a latitude of 85 the loss of solar energy enhances from 2 ( = 0.0) to more than 30% ( = 3.0). The mean annual daily insolation is maximally reduced by about 0.5 and 2% for optical thicknesses of 0.0 and 3.0, respectively.     

On the variations in the insolation at Mercury resulting from oscillations of the orbital eccentricity

This paper describes variations in the insolation on Mercury resulting from fluctuations of the orbital eccentricity (0.11≤e≤0.24) of the planet. Equations for the instantaneous and the daily insolation are briefly discussed and several numerical examples are given illustrating the sensitivity of the solar radiation to changes ine. Special attention is paid to the behavior of the solar radiation distribution curves near sunrise and sunset which at the warm pole of Mercury (longitudes ±90°) occur as the planet goes through perihelion. It has been found that for eccentricities larger than about 0.194 there exists two permanent thermal bulges on opposite sides of the Mercurian surface that alternately point to the Sun at every perihelion passage. The critical value ofe past which the Sun shortly sets after perihelion is near 0.213.     

The solar radiation incident at the top of the atmospheres of Uranus and Neptune

The latitudinal and seasonal variation of the direct solar radiation incident at the top of the atmosphere of Uranus and Neptune has been recalculated by use of updated values for the period of axial rotation and the oblateness. Values for the solar radiation are given in Watt per square meter instead of the unit used in earlier papers (calories per square centimeter per planetary day). The solar radiation averaged over a season and a year as a function of planetocentric latitude has also been reviewed. In addition, attention is made to the ratio of the solar radiation incident on an oblate planet to that incident on a spherical planet.     

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.     

The insolation at Pluto

Calculations of the daily solar radiation incident at the top of Pluto's atmosphere and its variability with latitude and season and of the latitudinal variation of the mean annual daily insolation are presented. The large eccentricity of Pluto produces significant north-south seasonal asymmetries in the daily insolation. As for Uranus, having a similarly large obliquity, the equator receives less annual average energy than the poles.     

A seasonal model of the Saturnian upper troposphere: Comparison with Voyager infrared measurements

An extension of the seasonal climate model of R. D. Cess and J. Caldwell (1979, Icarus, 38, 349–357) to Saturn's upper troposphere is presented. The ring-modulated latitudinal dependence of the insolation, the ring thermal emission, the oblateness of the planet, the orbit eccentricity, and the latitudinal variation of the internal heat flux are taken into account. Calculations agree closely with the temperature—latitude profiles retrieved from Voyager IRIS measurements at atmospheric levels located above the 0.2-bar pressure level; they reproduce the observed large-scale hemispheric asymmetry which is then shown to result from the seasonally variable insolation. Aerosol absorption is found to be the dominant source of atmospheric solar heating in the troposphere and the model suggests an aerosol mean unit optical depth around the 0.25-bar level in the equatorial region and around the 0.35-bar level at other latitudes. The model fails to predict the retrieved temperature—latitude profiles below the 0.3-bar level. This discrepancy is attributed to the existence of clouds at these levels which are responsible for an additional far-infrared opacity not taken into account in the temperature retrieval. The cloud-top altitude would be about 0.3 bar except in the 20 to 40°N region where these clouds would be confined below the 0.6-bar level. The poor correlation between infrared measurements and visible images is discussed and a possible model of Saturn's cloud structure is proposed.     

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.     

The influence of global dust storms on the mean seasonal daily insolations at the Martian surface

In this paper, we compare changes in the mean seasonal daily insolations at the Martian surface caused by global dust storms characterized by various atmospheric optical thickness (). The calculations, made for optical depths equal to 0, 0.1, 0.5, 1.0, 2.0, and 3.0, are based on the assumption of planet encircling storms lasting one season or one year. The variations in the latitudinal and seasonal surface insolation distributions are important, mainly at the poles where e.g. the mean annual and summer daily insolations decrease by nearly a factor of 3000 as goes from 0 to 3.0. At equatorial latitudes the corresponding loss is much smaller, reaching a value of approximately 40. Concerning the mean wintertime solar radiations it is found that the decrease is even more spectacular, especially at high latitudes.     

The response of the African summer monsoon to remote and local forcing due to precession and obliquity

In this paper, we examine the orbital signal in Earth's climate with a coupled model of intermediate complexity (ECBilt). The orbital influence on climate is studied by isolating the obliquity and precession signal in several time-slice experiments. Focus is on monsoonal systems with emphasis on the African summer monsoon. The model shows that both the precession and the obliquity signal in the African summer monsoon consists of an intensified precipitation maximum and further northward extension during minimum precession and maximum obliquity than during maximum precession and minimum obliquity. In contrast to obliquity, precession also influences the seasonal timing of the occurrence of the maximum precipitation. The response of the African monsoon to orbital-induced insolation forcing can be divided into a response to insolation forcing at high northern latitudes and a response to insolation forcing at low latitudes, whereby the former dominates. The results also indicate that the amplitude of the precipitation response to obliquity depends on precession, while the precipitation response to precession is independent of obliquity. Our model experiments provide an explanation for the precession and obliquity signals in sedimentary records of the Mediterranean (e.g., Lourens et al. [Paleoceanography 11 (1996) 391, Nature 409 (2001) 1029]), through monsoon-induced variations in Nile river outflow and northern Africa aridity.     

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.     

Response of the intermediate complexity Mars Climate Simulator to different obliquity angles

A climate model of intermediate complexity, named the Mars Climate Simulator, has been developed based on the Portable University Model of the Atmosphere (PUMA). The main goal of this new development is to simulate the climate variations on Mars resulting from the changes in orbital parameters and their impact on the layered polar terrains (also known as permanent polar ice caps). As a first step towards transient simulations over several obliquity cycles, the model is applied to simulate the dynamical and thermodynamical response of the Martian climate system to different but fixed obliquity angles. The model is forced by the annual and daily cycle of solar insolation. Experiments have been performed for obliquities of φ=15^° (minimum), φ=25.2^° (present), and φ=35^° (maximum). The resulting changes in solar insolation mainly in the polar regions impact strongly on the cross-equatorial circulation which is driven by the meridional temperature gradient and steered by the Martian topography. At high obliquity, the cross-equatorial near surface flow from the winter to the summer hemisphere is strongly enhanced compared to low obliquity periods. The summer ground temperature ranges from 200 K (φ=15^°) to 250 K (φ=35^°) at 80^°N in northern summer, and from 220 K (φ=15^°) to 270 K (φ=35^°) at 80^°S in southern summer. In the atmosphere at 1 km above ground, the respective range is 195-225 K in northern summer, and 210-250 K in southern summer.     

Large seasonal variations in Triton's atmosphere

Triton's seasons differ materially from those of Pluto owing to four important differences in the governing physics: First, the obliquity of Triton is significantly less than Pluto's obliquity. Second, Triton's inclined orbit precesses rapidly about Neptune so that a complicated seasonal variation in the latitude of the Sun occurs for Triton. Third, Neptune's orbit is much more circular than Pluto's orbit so that the sunlight intercepted by Triton's disk does not vary seasonally. Finally, Triton's atmosphere cannot be saturated at the lower latitudes so that the mass of the atmosphere is controlled by the temperature of the high-latitude ices or liquids (polar caps), as for CO₂ on Mars. The consequences of Triton's entire surface being covered with volatile substances have been examined. It is found that the circularity of Neptune's orbit then implies that Triton would have hardly any seasonal variation at all in surface temperature or atmospheric bulk, in spite of the complicated precessional effects of Triton's orbit. The only seasonal effect would be the migration of surface ices and liquids. This scenario is ruled out because it implies a column CH₄ abundance much higher than that observed and because it quickly depletes the lower latitudes of volatiles. It is concluded that Triton's most volatile surface substances are probably relegated to latitudes higher than 35° and probably form polar caps. The temperature of the polar caps should be nearly equal, even during midwinter/midsummer when the insolation of the summer pole is greatest. If the summer pole completely sublimates during one of the “major” summers, Triton's atmosphere may begin to freeze out over the winter caps. It is therefore expected that Triton's atmosphere undergoes large and complex seasonal variations. Triton is currently approaching a “maximum southern summer”, and over the remainder of this century, a dramatic increase in CH₄ abundance above the current upper limit of 1 m-Am may be witnessed.     

The atmospheric circulation and dust activity in different orbital epochs on Mars

A general circulation model is used to evaluate changes to the circulation and dust transport in the martian atmosphere for a range of past orbital conditions. A dust transport scheme, including parameterized dust lifting, is incorporated within the model to enable passive or radiatively active dust transport. The focus is on changes which relate to surface features, as these may potentially be verified by observations. Obliquity variations have the largest impact, as they affect the latitudinal distribution of solar heating. At low obliquities permanent CO₂ ice caps form at both poles, lowering mean surface pressures. At higher obliquities, solar insolation peaks at higher summer latitudes near solstice, producing a stronger, broader meridional circulation and a larger seasonal CO₂ ice cap in winter. Near-surface winds associated with the main meridional circulation intensify and extend polewards, with changes in cap edge position also affecting the flow. Hence the model predicts significant changes in surface wind directions as well as magnitudes. Dust lifting by wind stress increases with obliquity as the meridional circulation and associated near-surface winds strengthen. If active dust transport is used, then lifting rates increase further in response to the larger atmospheric dust opacities (hence circulation) produced. Dust lifting by dust devils increases more gradually with obliquity, having a weaker link to the meridional circulation. The primary effect of varying eccentricity is to change the impact of varying the areocentric longitude of perihelion, l, which determines when the solar forcing is strongest. The atmospheric circulation is stronger when l aligns with solstice rather than equinox, and there is also a bias from the martian topography, resulting in the strongest circulations when perihelion is at northern winter solstice. Net dust accumulation depends on both lifting and deposition. Dust which has been well mixed within the atmosphere is deposited preferentially over high topography. For wind stress lifting, the combination produces peak net removal within western boundary currents and southern midlatitude bands, and net accumulation concentrated in Arabia and Tharsis. In active dust transport experiments, dust is also scoured from northern midlatitudes during winter, further confining peak accumulation to equatorial regions. As obliquity increases, polar accumulation rates increase for wind stress lifting and are largest for high eccentricities when perihelion occurs during northern winter. For dust devil lifting, polar accumulation rates increase (though less rapidly) with obliquity above o=25°, but increase with decreasing obliquity below this, thus polar dust accumulation at low obliquities may be increasingly due to dust lifted by dust devils. For all cases discussed, the pole receiving most dust shifts from north to south as obliquity is increased.     

The effects of reduced land fraction and solar forcing on the general circulation: results from the NCAR CCM

Land fraction and the solar energy at the top of the atmosphere (solar constant) may have been significantly lower early in Earth's history. It is likely that both of these factors played some important role in the climate of the early earth. The climate changes associated with a global ocean(i.e. no continents) and reduced solar constant are examined with a general circulation model and compared with the present-day climate simulation. The general circulation model used in the study is the NCAR CCM with a swamp ocean surface. First, all land points are removed in the model and then the solar constant is reduced by 10% for this global ocean case.Results indicate that a 4 K increase in air temperature occurs with global ocean simulation compared to the control. When solar constant is reduced by 10% under global ocean conditions a 23 K decrease in air temperature is noted. The global ocean warms much of the troposphere and stratosphere, while a reduction in the solar constant cools the troposphere and stratosphere. The largest cooling occurs near the surface with the lower solar constant.Global mean values of evaporation, water vapor amounts, absorbed solar radiation and the downward longwave radiation are increased under global ocean conditions, while all are reduced when the solar constant is lowered. The global ocean simulation produces sea ice only in the highest latitudes. A frozen planet does not occur when the solar constant is reduced—rather, the ice line settles near 30° of latitude. It is near this latitude that transient eddies transport large amounts of sensible heat across the ice line acting as a negative feedback under lower solar constant conditions keeping sea ice from migrating to even lower latitudes.Clouds, under lower solar forcing, also act as a negative feedback because they are reduced in higher latitudes with colder atmospheric temperatures allowing additional solar radiation to reach the surface. The overall effect of clouds in the global ocean is to act as a positive feedback because they are slightly reduced thereby allowing additional solar radiation to reach the surface and increase the warming caused by the removal of land. The relevance of the results to the “Faint-Young Sun Paradox” indicates that reduced land fraction and solar forcing affect dynamics, heat transport, and clouds. Therefore the associated feedbacks should be taken into account in order to understand their roles in resolving the “Faint-Young Sun Paradox”.     

A Hill Problem with Oblate Primaries and Effect of Oblateness on Hill Stability of Orbits

We introduce a new version of Hill's problem to include the effect of oblateness of the primaries, and briefly discuss its equilibrium points and zero velocity curves. As a first application we use this to study Hill stability of direct orbits around the small primary. This can be employed to study the stability of a planet's moon perturbed by an oblate Sun, or of a star's planet perturbed by a distant disk-shaped galaxy. Oblateness of the `Sun' is found to decrese the maximum distance of Hill stable direct `moon' orbits. This revised version was published online in July 2006 with corrections to the Cover Date.     

Rapid changes in the sodium exosphere of Mercury

We imaged Mercury in sodium D₁ and D₂ emission for 6 days during the period 13–20 November 1997 using a 10×10-arc s aperture image slicer coupled to a high-resolution spectrograph. We corrected the sodium images for smearing by the terrestrial atmosphere by computing the actual seeing function from surface reflection images, and used this function to correct the sodium images. During the period of observation, large daily changes took place in both the total amount of sodium and its distribution over the planet. Total sodium increased by a factor of about 3 during this period. The sodium emission was brightest at longitudes near the subsolar longitude in the range 130–150°, with excess sodium at northern latitudes on some days, and excess sodium at southern latitudes on other days. There are no obviously outstanding geologic features at this longitude. The rapid changes observed during this period suggest a connection with solar activity, since the planet itself is apparently geologically inactive. The F10.7 cm solar flux during this period varied only slightly, with an increase of about 15%, probably insufficient to account for the observed changes. However, there were a number of coronal mass ejection (CME) events, some of which were directed towards the general area of Mercury. We suggest that the changes in the visible neutral sodium atmosphere might be a result of the effect of CMEs on Mercury.     

Collinear equilibrium points of Hill’s problem with radiation and oblateness and their fractal basins of attraction

We discuss the existence, location, and stability of the collinear equilibrium points of a generalized Hill problem with radiation of the primary (the Sun) and oblateness of the secondary (the planet), and present some remarkable fractals created as basins of attraction of Newton’s method applied for their computation in several cases of the parameters.     

The lunar orbit revisited,III

In this paper we present an investigation on the tidal evolution of a system of three bodies: the Earth, the Moon and the Sun. Equations are derived including dissipation in the planet caused by the tidal interaction between the planet and the satellite and between the planet and the sun. Dissipation within the Moon is included as well. The set of differential equations obtained is valid as long as the solar disturbances dominate the perturbations on the satellite's motion due to the oblateness of the planet, namelya/R _e greater than 15, and closer than that point equations derived in a preceding paper are used.The result shows the Moon was closer to the Earth in the past than now with an inclination to the ecliptic greater than today, whereas the obliquity was smaller. Toward the past, the inclination to the Earth's equator begins decreasing to 12° fora/R _e=12 and suddenly grows. During the first stage the results are weakly dependant on the magnitude of the dissipation within the satellite, whereas the distance of the closest approach and the prior history are strongly dependent on that dissipation. In particular, the crossing of the Roche limit can be avoided.     

Sun-synchronous orbits near critical inclination

The long period dynamics of Sun-synchronous orbits near the critical inclination 116.6° are investigated. It is known that, at the critical inclination, the average perigee location is unchanged by Earth oblateness. For certain values of semimajor axis and eccentricity, orbit plane precession caused by Earth oblateness is synchronous with the mean orbital motion of the apparent Sun (a Sun-synchronism). Sun-synchronous orbits have been used extensively in meteorological and remote sensing satellite missions. Gravitational perturbations arising from an aspherical Earth, the Moon, and the Sun cause long period fluctuations in the mean argument of perigee, eccentricity, inclination, and ascending node. Double resonance occurs because slow oscillations in the perigee and Sun-referenced ascending node are coupled through the solar gravity gradient. It is shown that the total number and infinitesimal stability of equilibrium solutions can change abruptly over the Sun-synchronous range of semimajor axis values (1.54 to 1.70 Earth radii). The effect of direct solar radiation pressure upon certain stable equilibria is investigated.