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

E. Van Hemelrijck 《Earth, Moon, and Planets》1983,29(1):83-93

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.  相似文献   

Insolation changes on pluto caused by orbital element variations     

E. van Hemelrijck 《Earth, Moon, and Planets》1985,33(2):163-177

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.  相似文献   

The astronomical theory of climatic change on Mars     

Owen B. Toon  James B. Pollack  William Ward  Joseph A. Burns  Kenneth Bilski 《Icarus》1980,44(3):552-607

We examine the response of Martian climate to changes in solar energy deposition caused by variations of the Martian orbit and obliquity. We systematically investigate the seasonal cycles of carbon dioxide, water, and dust to provide a complete picture of the climate for various orbital configurations. We find that at low obliquity (15°) the atmospheric pressure will fall below 1 mbar; dust storms will cease; thick permanent CO₂ caps will form; the regolith will release CO₂; and H₂O polar ice sheets will develop as the permafrost boundaries move poleward. At high obliquity (35°) the annual average polar temperature will increase by about 10°K, slightly desorbing the polar regolith and causing the atmospheric pressure to increase by not more than 10 to 20 mbar. Summer polar ground temperatures as high as 273°K will occur. Water ice caps will be unstable and may disappear as the equilibrium permafrost boundary moves equatorward. However, at high eccentricity, polar ice sheets will be favored at one pole over the other. At high obliquity dust storms may occur during summers in both hemispheres, independent of the eccentricity cycle. Eccentricity and longitude of perihelion are most significant at modest obliquity (25°). At high eccentricity and when the longitude of perihelion is close to the location of solstice hemispherical asymmetry in dust-storm generation and in polar ice extent and albedo will occur.The systematic examination of the relation of climate and planetary orbit provides a new theory for the formation of the polar laminae. The terraced structure of the polar laminae originates when eccentricity and/or obliquity variations begin to drive water ice off the dusty permanent H₂O polar caps. Then a thin (meters) layer of consolidated dust forms on top of a dirty, slightly thicker (tens of meters) ice sheet and the composite is preserved as a layer of laminae composed predominately of water ice. Because of insolation variation on slopes, a series of poleward- and equatorward-facing scarps are formed where the edges of the laminae are exposed. Independently of orbital variations, these scarps propagate poleward both by erosion of the equatorward slopes and by deposition on the poleward slopes. Scarp propagation resurfaces and recycles the laminae forming the distinctive spiral bands of terraces observed and provides a supply of water to form new permanent ice caps. The polar laminae boundary marks the furthest eqautorward extension of the permanent H₂O caps as the orbit varies. The polar debris boundary marks the furthest equatorward extension of the annual CO₂ caps as the orbit varies.The Martian regolith is now a significant geochemical sink for carbon dioxide. CO₂ has been irreversibly removed from the atmosphere by carbonate formation. CO₂ has also benn removed by regolith adsorption. Polar temperature increases caused by orbital variations are not great enough  相似文献   

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

Claire E. Newman  Stephen R. Lewis 《Icarus》2005,174(1):135-160

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.  相似文献   

Insolation patterns on synchronous exoplanets with obliquity     

Anthony R. Dobrovolskis 《Icarus》2009,204(1):1-1318

A previous paper [Dobrovolskis, A.R., 2007. Icarus 192, 1-23] showed that eccentricity can have profound effects on the climate, habitability, and detectability of extrasolar planets. This complementary study shows that obliquity can have comparable effects.The known exoplanets exhibit a wide range of orbital eccentricities, but those within several million kilometers of their suns are generally in near-circular orbits. This fact is widely attributed to the dissipation of tides in the planets. Tides in a planet affect its spin even more than its orbit, and such tidally evolved planets often are assumed to be in synchronous rotation, so that their rotation periods are identical to their orbital periods. The canonical example of synchronous spin is the way that our Moon always keeps nearly the same hemisphere facing the Earth.Tides also tend to reduce the planet’s obliquity (the angle between its spin and orbital angular velocities). However, orbit precession can cause the rotation to become locked in a “Cassini state”, where it retains a nearly constant non-zero obliquity. For example, our Moon maintains an obliquity of about 6.7° with respect to its orbit about the Earth. In comparison, stable Cassini states can exist for practically any obliquity up to ∼90° or more for planets of binary stars, or in multi-planet systems with high mutual inclinations, such as are produced by scattering or by the Kozai mechanism.This work considers planets in synchronous rotation with circular orbits, but arbitrary obliquity β; this affects the distribution of insolation over the planet’s surface, particularly near its poles. For β=0, one hemisphere bakes in perpetual sunshine, while the opposite hemisphere experiences eternal darkness. As β increases, the region of permanent daylight and the antipodal realm of endless night both shrink, while a more temperate area of alternating day and night spreads in longitude, and especially in latitude. The regions of permanent day or night disappear at β=90°. The insolation regime passes through several more transitions as β continues to increase toward 180°, but the surface distribution of insolation remains non-uniform in both latitude and longitude.Thus obliquity, like eccentricity, can protect certain areas of the planet from the worst extremes of temperature and solar radiation, and can improve the planet’s habitability. These results also have implications for the direct detectability of extrasolar planets, and for the interpretation of their thermal emissions.  相似文献   

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

E. Van Hemelrijck 《Icarus》1982,51(1):39-50

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.  相似文献   

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

J. Segschneider  B. Grieger  F. Lunkeit  K. Fraedrich  R. Greve 《Planetary and Space Science》2005,53(6):659-670

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.  相似文献   

MAIC-2, a latitudinal model for the Martian surface temperature, atmospheric water transport and surface glaciation     

R. Greve  B. Grieger 《Planetary and Space Science》2010,58(6):931-940

The Mars Atmosphere-Ice Coupler MAIC-2 is a simple, latitudinal model, which consists of a set of parameterisations for the surface temperature, the atmospheric water transport and the surface mass balance (condensation minus evaporation) of water ice. It is driven directly by the orbital parameters obliquity, eccentricity and solar longitude (L_s) of perihelion. Surface temperature is described by the Local Insolation Temperature (LIT) scheme, which uses a daily and latitude-dependent radiation balance. The evaporation rate of water is calculated by an expression for free convection, driven by density differences between water vapor and ambient air, the condensation rate follows from the assumption that any water vapour which exceeds the local saturation pressure condenses instantly, and atmospheric transport of water vapour is approximated by instantaneous mixing. Glacial flow of ice deposits is neglected. Simulations with constant orbital parameters show that low obliquities favour deposition of ice in high latitudes and vice versa. A transient scenario driven by a computed history of orbital parameters over the last 10 million years produces essentially monotonically growing polar ice deposits during the most recent 4 million years, and a very good agreement with the observed present-day polar layered deposits. The thick polar deposits sometimes continue in thin ice deposits which extend far into the mid latitudes, which confirms the idea of “ice ages” at high obliquity.  相似文献   

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

A. P. Vidmachenko 《Kinematics and Physics of Celestial Bodies》2016,32(4):189-195

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.  相似文献   

The three-dimensional motion of Trojan asteroids     

Bálint Érdi 《Celestial Mechanics and Dynamical Astronomy》1978,18(2):141-161

The problem is considered within the framework of the elliptic restricted three-body problem. The asymptotic solution is derived by a three-variable expansion procedure. The variables of the expansion represent three time-scales of the asteroids: the revolution around the Sun, the libration around the triangular Lagrangian pointsL ₄,L ₅, and the motion of the perihelion. The solution is obtained completely in the first order and partly in the second order. The results are given in explicit form for the coordinates as functions of the true anomaly of Jupiter. As an example for the perturbations of the orbital elements the main perturbations of the eccentricity, the perihelion longitude and the longitude of the ascending node are given. Conditions for the libration of the perihelion are also discussed.  相似文献   

Investigation of the parameters of the massive binary X-ray system IGR J17544-2619     

E. A. Nikolaeva  I. F. Bikmaev  S. S. Melnikov  A. I. Galeev  R. Ya. Zhuchkov  E. N. Irtuganov 《Bulletin of the Crimean Astrophysical Observatory》2013,109(1):27-31

The paper presents the results of spectroscopic research of the high-mass X-ray binary IGRJ17544-2619 optical component that were carried out with the RTT-150. The analysis of a long series of spectroscopic observations of the optical star of IGRJ17544-2619 system in 2007–2011 was carried out. Orbital parameters of the system were obtained: γ-velocity of 47 km/s, semiamplitude of radial velocity curve K = 30.5 km/s, eccentricity e = 0.44, longitude of the periastron ω = 142°, and an orbital period of the system of 12.17 days. The lower limit of the compact object mass was found to be equal to M = 2.82M _⊙.  相似文献   

Orbital change experiments with a Mars general circulation model     

Robert M Haberle  James R Murphy 《Icarus》2003,161(1):66-89

We use a Mars general circulation model to examine the effect of orbital changes on the planet’s general circulation and climate system. Experiments are performed for obliquities ranging from 0° to 60° for two different longitudes of perihelion. Each experiment simulates a full Mars year assuming a fixed atmospheric dust distribution and fixed amount of CO₂ in the atmosphere/cap system. We find that global mean surface temperatures and pressures decline with increasing obliquity due to the increasing extent of the winter polar caps. The seasonal CO₂ cycle and intensity of the solstice circulation amplify considerably with increasing obliquity such that global dust storms are likely at both solstices. The most significant feature of the high obliquity solstice circulations is the development of an intense low-level jet associated with the return branch of the Hadley circulation.Model surface stresses are used to map regions of preferred dust lifting, which are defined in terms of an annual deflation potential. For the present obliquity, the model-predicted regions of high deflation potential are in good agreement with Cantor et al.’s (2001, J. Geophys. Res.106, 23653-23688) observations, which gives us some confidence in the model’s ability to predict where lifting might occur when Mars’ orbit parameters are different than they are today. In general we find that the dust lifting potential increases sharply with obliquity and is greatest at times of high obliquity when perihelion coincides with northern summer solstice. Over an obliquity cycle, the model global annual deflation potential ranges from several tenths of a millimeter at 0° obliquity to almost 15 mm at 60° obliquity. Much higher values are possible when the atmosphere is very dusty.We find a strong correlation between the deflation potential and surface thermal inertia: regions of high deflation potential correspond to regions of high thermal inertia (high rock abundance), and regions of low deflation potential correspond to regions of low thermal inertia (high dust/sand abundance). Furthermore, while the regions of preferred lifting (high deflation potential) expand somewhat with increasing obliquity and dust loading, the central parts of Tharsis, Arabia, and Elysium show no tendency for significant lifting at any obliquity or longitude of perihelion. These regions may therefore be very old and represent net long-term sinks for atmospheric dust. It is the topography of the planet, through its influence on surface pressure and wind systems, which ultimately determines where dust accumulates.Finally, as was found by Fenton and Richardson (2001, J. Geophys. Res.106, 32885-32909), we find no tendency for the development of east-southeasterly winds at the Pathfinder site for any of our orbital change experiments. This suggests that the ancient wind regime discussed by Greeley et al. (2000, J. Geophys. Res.105, 1829-1840) was produced by other factors, such as polar wander.  相似文献   

Orbital dynamics of the planetary system HD 196885     

A. V. Melnikov 《Solar System Research》2017,51(4):327-334

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°.  相似文献   

Effect of Planetary Eccentricity on Ballistic Capture in the Solar System     

Christian Circi  Paolo Teofilatto 《Celestial Mechanics and Dynamical Astronomy》2005,93(1-4):69-86

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.  相似文献   

Analysis of the orbit of cosmos 395 rocket (1971-13B) near 15th-order resonance     

D.G. King-Hele  A.N. Winterbottom 《Planetary and Space Science》1974,22(7):1045-1057

Cosmos 395 rocket (1971-13B) is moving in a near-circular orbit inclined at 74° to the equator. Its average height, near 540 km after launch in February 1971, slowly decreased under the action of air drag and on 24 March 1972 it experienced exact 15th-order resonance, with the successive equator crossings 24° apart in longitude. Its orbit has been determined at 21 epochs between September 1971 and September 1972 using 1100 observations, including 55 from the Malvern Hewitt camera: the mean S.D. in inclination is 0.001° and in eccentricity 0.00001.The variations in inclination i, eccentricity e, right ascension of the node $\text{Ω}$, and argument of perigee ω, near 15th-order resonance are analysed to determine values of lumped 15th-order harmonic coefficients in the geopotential. The inclination yields equations accurate to 4 per cent for coefficients of order 15 and degree 15,17,19..., which are in excellent agreement with those from Cosmos 387 (1970-111A) in an orbit of similar inclination but different resonant longitude. Analysis of the variations in e gives two pairs of equations for the coefficients of order 15 and degree 16, 18..., which are used to obtain tentative values of the (16,15) coefficients. For the first time the resonant variation of other elements ($\text{Ω}\text{and}\text{ω}$) has also been analysed with partial success.  相似文献   

The insolation at Pluto     

E. Van Hemelrijck 《Icarus》1982,52(3):560-564

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.  相似文献   

Critical inclination of Trojan asteroids     

Bálint Érdi 《Celestial Mechanics and Dynamical Astronomy》1984,34(1-4):435-441

The author's earlier solution for Trojan asteroids is developed further. It is shown that depending on the amplitude of libration around the Lagrangian point L₄, there is a critical inclination which determines the sign of the variation of the ascending node. If the orbital inclination of a Trojan is smaller than the critical one, then the ascending node decreases and otherwise it increases. The variation of the eccentricity and of the longitude of the perihelion has also a dependence on the critical inclination.  相似文献   

Long term evolution of quasi-circular Trojan orbits     

C. Marchal 《Celestial Mechanics and Dynamical Astronomy》2009,104(1-2):53-67

Trojan asteroids undergo very large perturbations because of their resonance with Jupiter. Fortunately the secular evolution of quasi circular orbits remains simple—if we neglect the small short period perturbations. That study is done in the approximation of the three dimensional circular restricted three-body problem, with a small mass ratio μ—that is about 0.001 in the Sun Jupiter case. The Trojan asteroids can be defined as celestial bodies that have a “mean longitude”, M + ω + Ω, always different from that of Jupiter. In the vicinity of any circular Trojan orbit exists a set of “quasi-circular orbits” with the following properties: (A) Orbits of that set remain in that set with an eccentricity that remains of the order of the mass ratio μ. (B) The relative variations of the semi-major axis and the inclination remain of the order of ${\sqrt{\mu}}$ . (C) There exist corresponding “quasi integrals” the main terms of which have long-term relative variations of the order of μ only. For instance the product c(1 – cos i) where c is the modulus of the angular momentum and i the inclination. (D) The large perturbations affect essentially the difference “mean longitude of the Trojan asteroid minus mean longitude of Jupiter”. That difference can have very large perturbations that are characteristics of the “horseshoes orbit”. For small inclinations it is well known that this difference has two stable points near ±60° (Lagange equilibrium points L₄ and L₅) and an unstable point at 180° (L₃). The stable longitude differences are function of the inclination and reach 180° for an inclination of 145°41′. Beyond that inclination only one equilibrium remains: a stable difference at 180°.  相似文献   

Trapping in three-planet resonances during gas-driven migration     

Anne-Sophie Libert  Kleomenis Tsiganis 《Celestial Mechanics and Dynamical Astronomy》2011,111(1-2):201-218

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Editorial     

Joseph A. Burns 《Icarus》1981,45(1):1-3

The Galilean satellites Io, Europa, and Ganymede interact through several stable orbital resonances where $\text{λ}{}_1\text{? 2λ}{}_2\text{+}\text{ω}{}_1\text{= 0, λ}{}_1\text{? 2λ}{}_2\text{+}\text{ω}{}_2\text{= 180°, λ}{}_2\text{? 2λ}{}_3\text{+}\text{ω}{}_2\text{= 0}$ and λ₁ ? 3λ₂ + 2λ₃ = 180°, with λ_i being the mean longitude of the ith satellite and $\text{ω}{}_{\mathrm{i}}$ the longitude of the pericenter. The last relation involving all three bodies is known as the Laplace relation. A theory of origin and subsequent evolution of these resonances outlined earlier (C. F. Yoder, 1979b, Nature279, 747–770) is described in detail. From an initially quasi-random distribution of the orbits the resonances are assembled through differential tidal expansion of the orbits. Io is driven out most rapidly and the first two resonance variables above are captured into libration about 0 and 180° respectively with unit probability. The orbits of Io and Europa expand together maintaining the 2:1 orbital commensurability and Europa's mean angular velocity approaches a value which is twice that of Ganymede. The third resonance variable and simultaneously the Laplace angle are captured into libration with probability ～0.9. The tidal dissipation in Io is vital for the rapid damping of the libration amplitudes and for the establishment of a quasi-stationary orbital configuration. Here the eccentricity of Io's orbit is determined by a balance between the effects of tidal dissipation in Io and that in Jupiter, and its measured value leads to the relation $\text{k}{}_1\text{?}{}_1\text{/Q}{}_1\text{≈ 900k}{}_{\mathrm{<mtext>J</mtext>}}\text{/Q}{}_{\mathrm{<mtext>J</mtext>}}$ with the k's being Love numbers, the Q's dissipation factors, and f a factor to account for a molten core in Io. This relation and an upper bound on Q₁ deduced from Io's observed thermal activity establishes the bounds 6 × 10⁴ < Q_J < 2 × 10⁶, where the lower bound follows from the limited expansion of the satellite orbits. The damping time for the Laplace libration and therefore a minimum lifetime of the resonance is 1600 Q_J years. Passage of the system through nearby three-body resonances excites free eccentricities. The remnant free eccentricity of Europa leads to the relation $\text{Q}{}_2\text{/?}{}_2\text{? 2 × 10}{}^{\mathrm{?4}}\text{Q}{}_{\mathrm{<mtext>J</mtext>}}$ for rigidity μ₂ = 5 × 10¹¹ dynes/cm². Probable capture into any of several stable 3:1 two-body resonances implies that the ratio of the orbital mean motions of any adjacent pair of satellites was never this large.A generalized Hamiltonian theory of the resonances in which third-order terms in eccentricity are retained is developed to evaluate the hypothesis that the resonances were of primordial origin. The Laplace relation is unstable for values of Io's eccentricity e₁ > 0.012 showing that the theory which retains only the linear terms in e₁ is not valid for values of e₁ larger than about twice the current value. Processes by which the resonances can be established at the time of satellite formation are undefined, but even if primordial formation is conjectured, the bounds established above for Q_J cannot be relaxed. Electromagnetic torques on Io are also not sufficient to relax the bounds on Q_J. Some ideas on processes for the dissipation of ideal energy in Jupiter yield values of Q_J within the dynamical bounds, but no theory has produced a Q_J small enough to be compatible with the measurements of heat flow from Io given the above relation between Q₁ and Q_J. Tentative observational bounds on the secular acceleration of Io's mean motion are also shown not to be consistent with such low values of Q_J. Io's heat flow may therefore be episodic. Q_J may actually be determined from improved analysis of 300 years of eclipse data.  相似文献