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1.
The results of a simultaneous solution for the orbital elements of Moon and planets are given and their derivation is discussed. A modern Cowell integrator is used for orbit computations, and least-squares fits are made to some 40000 optical observations taken since 1913. The model includes relativistic terms, the leading zonal harmonics of Earth and Moon, the precession of the lunar equator, and the tidal couple between Earth and Moon. The tidal term in the Moon's mean longitude is found to be –19±4 per century squared. The solution also yields an extrapolation of the atomic time scale back to 1912.5. At that time, the difference between atomic and ephemeris time is about 6±2 s. Lunar declinations observed by the Washington transit circles, after receiving limb corrections and thus with respect to the center of Watts' reference sphere, are smaller than computed values by 0.33±0.01. It is found that solar oblateness cannot quite be determined with optical data covering about 50 yr, butJ
2 is unlikely to be much larger than 10–5. The advance of Mercury's perihelion is verified to within our resolution of 2 per century to match that predicted by Einstein.The solution presented here is believed to be the only simultaneous improvement of the orbits of Moon and planets. This simultaneity is found to be an essential feature in separating the Moon's mean motion, the lunar tidal deceleration, and the corrections to the Earth rotation rate. It is now possible to refer all astronomical events of the past 60 yr to a time with uniform rate, namely the atomic clock system. Considering the long baseline, this model should facilitate the prediction of fast variables, such as the lunar longitude, with considerably increased confidence. The planetary orbital elements compete with efforts of similar scope and accuracy at the Massachusetts Institute of Technology and the Jet Propulsion Laboratory. 相似文献
2.
On the basis of the model proposed by Matsui and Abe, we will show that two major factors — distance from the Sun and the efficiency of retention of accretional energy — control the early evolution of the terrestrial planets. A diagram of accretional energy versus the optical depth of a proto-atmosphere provides a means to follow the evolutionary track of surface temperature of the terrestrial planets and an explanation for why the third planet in our solar system is an aqua-planet. 相似文献
3.
V. P. Tomanov 《Kinematics and Physics of Celestial Bodies》2007,23(5):196-206
We analyze our earlier data on the numerical integration of the equations of motion for 274 short-period comets (with the period P<200 yr) on a time interval of 6000 yr. As many as 54 comets had no close approaches to planets, 13 comets passed through the Saturnian sphere of action, and one comet passed through the Uranian sphere of action. The orbital elements of these 68 comets changed by no more than ±3 percent in a space of 6000 yr. As many as 206 comets passed close to Jupiter. We confirm Everhart’s conclusion that Jupiter can capture long-period comets with q = 4–6 AU and i < 9° into short-period orbits. We show that nearly parabolic comets cross the solar system mainly in the zone of terrestrial planets. No relationship of nearly parabolic comets and terrestrial planets was found for the epoch of the latest apparition of comets. Guliev’s conjecture about two trans-Plutonian planets is based on the illusory excess of cometary nodes at large heliocentric distances. The existence of cometary nodes at the solar system periphery turns out to be a solely geometrical effect. 相似文献
4.
We consider a model of the in situ Oort cloud which is isotropic with a random distrihution of perihelia directions and angular momenta. The energy distribution adopted has a continuous range of values appropriate for long-period (>200 yr) comets. Only the tidal torque of the Galaxy is included as a perturbation of comet orbits and it is approximated to be that due to a quasi-steady state distribution of matter with disk-like symmetry. The time evolution of all orbital elements can be analytically obtained for this case. In particular, the change in the perihelion distance per orbit and its dependence on other orbital elements is readily found. We further make the assumption that a comet whose perihelion distance was beyond 15 AU during its last passage through the Solar System would have orbit parameters that are essentially unchanged by planetary perturbations. Conversely, if the prior passage was inside 15 AU we assume that planetary perturbations would have removed the comet from the in situ energy distribution accessible by the galactic tide. Comets which had their perihelia changed from beyond 15 AU to within 5 AU in a single orbit are taken to be observable. We are able to track the evolution of 106 comets as they are made observable by the galactic tidal touque. Detailed results are obtained for the predicted distribution of new (0 < 1/ < 10–4 AU–1) comets. Further, correlations between orbital elements can be studied. We present predictions of observed distributions and compare them with the random in situ results as well as with the actual observed distributions of class I comets. The predictions are in reasonable agreement with actual observations and, in many cases, are significantly different from random when perihelia directions are separated into galactic northern and southern hemispheres. However the well-known asymmetry in the north-south populations of perihelia remains to be explained. Such an asymmetry is consistent with the dominance of tidal torques today if a major stochastic event produced it in the past since tidal torques are unable to cause the migration of perihelia across the latitude barriers ±26°.6 in the disk model. 相似文献
5.
Zdeněk Kopal 《Astrophysics and Space Science》1972,17(1):161-185
The aim of the present paper will be to give a mathematical outline of the theory of tidal evolution in close binary systems of secularly constant total momentum — an evolution activated by viscous friction of dynamical tides raised by the two components on each other. The first section contains a general outline of the problem; and in Section 2 we shall establish the basic expressions for the energy and momenta of close binaries consisting of components of arbitrary internal structure. In Section 3 we shall investigate the maximum and minimum values of the energy (kinetic and potential) which such systems can attain for given amount of total momentum; while in Section 4 we shall compare these results with the actual facts encountered in binaries with components whose internal structure (and, therefore, rotational momenta) are known to us from evidence furnished by the observed rates of apsidal advance.The results show that all such systems — be these of detached or semi-detached type — disclose that more than 99% of their total momenta are stored in the orbital momentum. The sum of the rotational momenta of the constituent components amounts to less than a percent of the total — a situation characteristic of a state close to the minimum energy for given total momentum. This appears, moreover, to be true not only of the systems with both components on the Main Sequence, but also of those possessing evolved components in contact with their Roche limits.Under such conditions, a synchronism between rotation and revolution (characteristic of both extreme states of maximum and minimum energy) is not only possible, but appears to have been actually approached — if not attained — in the majority of cases. In other words, it would appear that — in at least a large majority of known cases — the existing close binaries have already attained orbits of maximum distension consistent with their momenta; and tidal evolution alone can no longer increase the present separations of the components to any appreciable extent.The virtual absence, in the sky, of binary systems intermediate between the stages of maximum and minimum energy for given momentum leads us to conjecture that the process of dynamical evolution activated by viscous tides may enroll on a time-scale which is relatively short in comparison with their total age — even for systems like Y Cygni or AG Persei, whose total age can scarcely exceed 107 yr. A secular increase of the semi-major axes of relative orbits is dynamically coupled with a corresponding variation in the velocity of axial rotation of both components through the tidal lag arising from the viscosity of stellar material. The differential equations of so coupled a system are given in Section 5; but their solution still constitutes a task for the future.The Lunar Science Institute Contribution No. 90. The Lunar Science Institute is operated by the Universities Space Research Association under Contract No. NSR 09-051-001 with the National Aeronautics and Space Administration. 相似文献
6.
Since 20 years, a large population of close-in planets orbiting various classes of low-mass stars (from M-type to A-type stars) has been discovered. In such systems, the dissipation of the kinetic energy of tidal flows in the host star may modify its rotational evolution and shape the orbital architecture of the surrounding planetary system. In this context, recent observational and theoretical works demonstrated that the amplitude of this dissipation can vary over several orders of magnitude as a function of stellar mass, age and rotation. In addition, stellar spin-up occurring during the Pre-Main-Sequence (PMS) phase because of the contraction of stars and their spin-down because of the torque applied by magnetized stellar winds strongly impact angular momentum exchanges within star–planet systems. Therefore, it is now necessary to take into account the structural and rotational evolution of stars when studying the orbital evolution of close-in planets. At the same time, the presence of planets may modify the rotational dynamics of the host stars and as a consequence their evolution, magnetic activity and mixing. In this work, we present the first study of the dynamics of close-in planets of various masses orbiting low-mass stars (from \(0.6~M_\odot \) to \(1.2~M_\odot \)) where we compute the simultaneous evolution of the star’s structure, rotation and tidal dissipation in its external convective envelope. We demonstrate that tidal friction due to the stellar dynamical tide, i.e. tidal inertial waves excited in the convection zone, can be larger by several orders of magnitude than the one of the equilibrium tide currently used in Celestial Mechanics, especially during the PMS phase. Moreover, because of this stronger tidal friction in the star, the orbital migration of the planet is now more pronounced and depends more on the stellar mass, rotation and age. This would very weakly affect the planets in the habitable zone because they are located at orbital distances such that stellar tide-induced migration happens on very long timescales. We also demonstrate that the rotational evolution of host stars is only weakly affected by the presence of planets except for massive companions. 相似文献
7.
Iapetus (S8) is unique in our solar system in that the albedo of its leading hemisphere is only 0.05 while that of the trailing side is 0.5. Several existing hypotheses are examined and found inadequate. Photometric studies of the dark side are compared to comet nuclei and class D asteroids. It is hypothesized that in the last 106–108 yrs the leading side suffered a high-velocity collision with a cometary body of mass 1013–1015 kg and traveling at a speed of 20 km s–1. About 5–16% of the excavated material was ejected into space, where the vaporized ices dissipated while the dark carbonaceous/silicate material was reaccreted on the leading side. The collision, although not sufficient to break Iapetus' tidal lock, resulted in a period of oscillation of about 5 yr. Until tidal friction reasserted a lock, the oscillation gave rise to the longitude effect, viz., the observed fact that the dark material covers more than 220 of longitude but only 110 of latitude. 相似文献
8.
Shashanka R. Gurumath K. M. Hiremath V. Ramasubramanian 《Journal of Astrophysics and Astronomy》2017,38(2):19
By considering the physical and orbital characteristics of G type stars and their exoplanets, we examine the association between stellar mass and its metallicity that follows a power law. Similar relationship is also obtained in case of single and multiplanetary stellar systems suggesting that, \(\hbox {Sun}^{\prime }\)s present mass is about 1% higher than the estimated value for its metallicity. Further, for all the stellar systems with exoplanets, association between the planetary mass and the stellar metallicity is investigated, that suggests planetary mass is independent of stellar metallicity. Interestingly, in case of multiplanetary systems, planetary mass is linearly dependent on the stellar absolute metallicity, that suggests, metal rich stars produce massive (\(\ge \)1 Jupiter mass) planets compared to metal poor stars. This study also suggests that there is a solar system planetary missing mass of \({\sim }\)0.8 Jupiter mass. It is argued that probably 80% of missing mass is accreted onto the Sun and about 20% of missing mass might have been blown off to the outer solar system (beyond the present Kuiper belt) during early history of solar system formation. We find that, in case of single planetary systems, planetary mass is independent of stellar metallicity with an implication of their non-origin in the host star’s protoplanetary disk and probably are captured from the space. Final investigation of dependency of the orbital distances of planets on the host stars metallicity reveals that inward migration of planets is dominant in case of single planetary systems supporting the result that most of the planets in single planetary systems are captured from the space. 相似文献
9.
A method due to Schuster is used to test the hypothesis that solar activity is influenced by tides raised in the Sun's atmosphere by planets. We calculate the distribution in longtitude of over 1000 flares occurring in a 61/2 yr segment of solar cycle 19, referring the longitude system in turn to the orbital positions of Jupiter and Venus. The resulting distributions show no evidence for a tidal effect. 相似文献
10.
We have investigated the final accretion stage of terrestrial planets from Mars-mass protoplanets that formed through oligarchic growth in a disk comparable to the minimum mass solar nebula (MMSN), through N-body simulation including random torques exerted by disk turbulence due to Magneto-Rotational Instability. For the torques, we used the semi-analytical formula developed by Laughlin et al. [Laughlin, G., Steinacker, A., Adams, F.C., 2004. Astrophys. J. 608, 489-496]. The damping of orbital eccentricities (in all runs) and type-I migration (in some runs) due to the tidal interactions with disk gas is also included. Without any effect of disk gas, Earth-mass planets are formed in terrestrial planet regions in a disk comparable to MMSN but with too large orbital eccentricities to be consistent with the present eccentricities of Earth and Venus in our Solar System. With the eccentricity damping caused by the tidal interaction with a remnant gas disk, Earth-mass planets with eccentricities consistent with those of Earth and Venus are formed in a limited range of disk gas surface density (∼10−4 times MMSN). However, in this case, on average, too many (?6) planets remain in terrestrial planet regions, because the damping leads to isolation between the planets. We have carried out a series of N-body simulations including the random torques with different disk surface density and strength of turbulence. We found that the orbital eccentricities pumped up by the turbulent torques and associated random walks in semimajor axes tend to delay isolation of planets, resulting in more coagulation of planets. The eccentricities are still damped after planets become isolated. As a result, the number of final planets decreases with increase in strength of the turbulence, while Earth-mass planets with small eccentricities are still formed. In the case of relatively strong turbulence, the number of final planets are 4-5 at 0.5-2 AU, which is more consistent with Solar System, for relatively wide range of disk gas surface density (∼10−4-10−2 times MMSN). 相似文献
11.
Rory Barnes 《Celestial Mechanics and Dynamical Astronomy》2017,129(4):509-536
Potentially habitable planets can orbit close enough to their host star that the differential gravity across their diameters can produce an elongated shape. Frictional forces inside the planet prevent the bulges from aligning perfectly with the host star and result in torques that alter the planet’s rotational angular momentum. Eventually the tidal torques fix the rotation rate at a specific frequency, a process called tidal locking. Tidally locked planets on circular orbits will rotate synchronously, but those on eccentric orbits will either librate or rotate super-synchronously. Although these features of tidal theory are well known, a systematic survey of the rotational evolution of potentially habitable exoplanets using classic equilibrium tide theories has not been undertaken. I calculate how habitable planets evolve under two commonly used models and find, for example, that one model predicts that the Earth’s rotation rate would have synchronized after 4.5 Gyr if its initial rotation period was 3 days, it had no satellites, and it always maintained the modern Earth’s tidal properties. Lower mass stellar hosts will induce stronger tidal effects on potentially habitable planets, and tidal locking is possible for most planets in the habitable zones of GKM dwarf stars. For fast-rotating planets, both models predict eccentricity growth and that circularization can only occur once the rotational frequency is similar to the orbital frequency. The orbits of potentially habitable planets of very late M dwarfs ( Open image in new window ) are very likely to be circularized within 1 Gyr, and hence, those planets will be synchronous rotators. Proxima b is almost assuredly tidally locked, but its orbit may not have circularized yet, so the planet could be rotating super-synchronously today. The evolution of the isolated and potentially habitable Kepler planet candidates is computed and about half could be tidally locked. Finally, projected TESS planets are simulated over a wide range of assumptions, and the vast majority of potentially habitable cases are found to tidally lock within 1 Gyr. These results suggest that the process of tidal locking is a major factor in the evolution of most of the potentially habitable exoplanets to be discovered in the near future. 相似文献
12.
A heuristic model is proposed of the mean distances between the solar-system planets, their satellites and the primaries. The model is based on: (i) the concept of the solar system structure wave nature; (ii) the micro-mega analogy (MM analogy) of the micro- and megasystem structures, and (iii) the oscillator amplitude quantization phenomenon, occuring under wave action, discovered on the basis of the classical oscillations theory (Damgov et al., 1990, 1991).From the equation, describing the charge rotation under the action of an electromagnetic wave, an expression is obtained for the discrete set of probable stationary motion amplitudes. The discrete amplitude values — the quantization phenomenon — are defined by the argument values at the extreme points of the N-order Bessel functions. Using this expression, the mean related distances are computed from the solar system planets and the Saturn, Uranian and Jovian satellites to the primaries. 相似文献
13.
This work investigates the solar quasi-periodic cycles with multi-timescales and the possible relationships with planetary motions. The solar cycles are derived from long-term observations of the relative sunspot number and microwave emission at frequency of 2.80 GHz. A series of solar quasi-periodic cycles with multi-timescales are registered. These cycles can be classified into three classes: (1) the strong PLC (PLC is defined as the solar cycle with a period very close to the ones of some planetary motions, named as planetary-like cycle) which is related strongly with planetary motions, including nine periodic modes with relatively short period (P<12 yr), and related to the motions of the inner planets and of Jupiter; (2) the weak PLC, which is related weakly to planetary motions, including two periodic modes with relatively long period (P>12 yr), and possibly related to the motions of outer planets; (3) the non-PLC, for which so far there has been found no clear evidence to show the relationship with any planetary motions. Among the planets, Jupiter plays a key role in most periodic modes due to its sidereal motion or spring tidal motions associated with other planets. Among planetary motions, the spring tidal motion of the inner planets and of Jupiter dominates the formation of most PLCs. The relationships between multi-timescale solar periodic modes and the planetary motions will help us to understand the essential nature and prediction of solar activities. 相似文献
14.
Joseph A. Burns 《Icarus》1976,28(4):453-458
Mercury, currently rotating very slowly, probably rotated faster in the past. If Mercury's rotation period had been near 8 hours initially, similar to that of most solar system bodies today, it would have been flattened by a few percent. As Mercury was slowed by solar tides, craters which were circular when they were emplaced would have been distorted by the same few percent. Substantial surface stresses, well above the fracture stress, would have been produced unless stress relief occurred; these stresses should have produced tensional fractures near the poles and two intersecting sets of shear planes in equatorial regions. Satellite orbits about the slowly spinning Mercury have been shown to collapse onto its surface: the impact craters resulting from these hypothetical lost satellites should be elongated along the orbit paths, which probably lie near the equator. However, none of these features has been found on the Mariner 10 images. They may be obscured by the effects of tidal heating that should cause an overall internal temperature increase of about 100°K although the increase would be substantially more in certain regions. Radial tides, sometimes called push-pull tides, are important at the present time because Mercury's large orbital eccentricity causes the planet to undergo significant tidal flexing each orbital period; the contemporary tidal heating due to this mechanism is estimated at more than 1016 erg/sec. 相似文献
15.
- Introduction and Survey. The method for studying the structure and evolution of the solar system is discussed. It is pointed out that theories that account for the origin of planets alone are basically insufficient. Instead one ought to aim for a general theory for the formation of secondary bodies around a central body, applicable both to planet and satellite formation. A satisfactory theory should not start from assumed properties of the primitive Sun, which is a very speculative subject, but should be based on an analysis of present conditions and a successive reconstruction of the past states.
- Orbits of Planets and Satellites. As a foundation for the subsequent analysis, the relevant properties of planets and satellites are presented.
- The Small Bodies. The motion of small bodies is influenced by non-gravitational forces. Collisions (viscosity) are of special importance for the evolution of the orbits. It is pointed out that the focusing property of a gravitational field (which has usually been neglected) leads to the formation of jet streams. The importance of this concept for the understanding of the comet-meteoroid relations and the structure of the asteroidal belt is shown.
- Resonance Structure. A survey is given of the resonances in the solar system and their possible explanation. It is concluded that in many cases the resonances must already be produced at the times when the bodies formed. It is shown that resonance effects put narrow limits on the post-accretional changes of orbits.
- Spin and Tides. Tidal effects on planetary spins and satellite orbits are discussed. It is very doubtful if any satellite except the Moon and possibly Triton has had its orbit changed appreciably by tidal effects. The isochronism of planetary and asteroidal spins is discussed, as well as its bearing on the accretional process.
- Post-accretional Changes in the Solar System. The stability of the solar system and upper limits for changes in orbital and spin data are examined. It is concluded that much of the present dynamic structure has direct relevance to the primordial processes.
16.
Martyn J. Fogg 《Earth, Moon, and Planets》1988,43(2):123-130
Current protostellar theory has determined a lower limit to the mass of a pre-stellar gas cloud fragment of ~0.01 M. This suggests that isolated interstellar bodies in the mass range ~10 M-710-2 M must have originated within a planetary system. Two possible mechanisms whereby planets are lost from their parental systems to interstellar space are discussed and the abundance and distribution of such unbound planets within the Galaxy is examined. It is found that, except within the central regions of the Galaxy, unbound planets are expected to be scarce. In the solar neighbourhood for instance, the number density ratio of unbound planets to stars is estimated to range between extremes of ~4 × 10–4–3 × 10–2 with a most probable value of ~6 x 10–3. The faint possibility that the hypothetical Planet X might be of extra-solar origin is also discussed. 相似文献
17.
Sho Sasaki 《Astrophysics and Space Science》1994,212(1-2):33-41
When planetary accretion proceeds in the gas disk-solar nebula, a protoplanet attracts surrounding gas to form a distended H2-He atmosphere. The blanketing effect of the atmosphere, hampering the escape of accretional energy, enhances the surface temperature of planets. Furthermore, evaporation of ice or reduction of surface silicate and metallic oxide can supply a huge amount of water vapor into the atmosphere, which would raise the temperature and promote evaporation. Evaporated materials can be efficiently conveyed outward by vigorous convection, and condensed dust particles should keep the atmosphere opaque during accretion. The size of this opaque atmosphere dust blob is defined by the gravitational radius, which exceeds 3 × 108 m when the planetary mass is the Earth's mass (5.97 × 1024 kg). This is larger than the radii of present Jovian planets and so-called brown dwarfs. The expected lifetime of dust blobs is 106–107 yr, which is longer than that of the later gas accreting and cooling stages of Jovian planets. The number of dust blobs could exceed that of Jovian planets. If the gas disk is rather transparent, the possibility of observing such objects with a distended atmosphere may be higher than that of detecting Jovian planets. Contamination of the gas disk by the dust from primary atmospheres is negligible.Paper presented at the Conference on Planetary Systems: Formation, Evolution, and Detection held 7–10 December, 1992 at CalTech, Pasadena, California, U.S.A. 相似文献
18.
Zdenêk Kopal 《Astrophysics and Space Science》1969,4(4):427-458
In preceding papers of this series (Kopal, 1968; 1969) the Eulerian equations have been set up which govern the precession and nutation of self-gravitating fluid globes of arbitrary structures in inertial coordinates (space-axes) as well as with respect to the rotating body axes; with due account being taken of the effects arising from equilibrium as well as dynamical tides.In Section 1 of the present paper, the explicit form of these equations is recapitulated for subsequent solations. Section 2 contains then a detailed discussion of the coplanar case (in which the equation of the rotating configuration and the plane of its orbit coincide with the invariable plane of the system); and small fluctuations in the angular velocity of axial rotation arising from the tidal breathing in eccentric binary systems are investigated.In Section 3, we consider the angular velocity of rotation about theZ-axis to be constant, but allow for finite inclination of the equator to the orbital plane. The differential equations governing such a problem are set up exactly in terms of the time-dependent Eulerian angles and , and their coefficients averaged over a cycle. In Section 4, these equations are linearized by the assumption that the inclinations of the equator and the orbit to the invariable plane of the system are small enough for their squares to be negligible; and the equations of motion reduced to their canonical form.The solution of these equations — giving the periods of precession and nutation of rotating components of close binary systems, as well as the rate of nodal regression which is synchronised with precession — are expressed in terms of the physical properties of the respective system and of its constituent components; while the concluding Section 6 contains a discussion of the results, in which the differences between the precession and nutation of rigid and fluid bodies are pointed out. 相似文献
19.
W. J. Baggaley 《Earth, Moon, and Planets》1995,68(1-3):127-139
Summary Radar facilities providing routine measurements of the heliocentric orbits of meteoroids are valuable in providing a data-base of the orbital characteristics of the solar system small body population in the mass range about 10–2 down to 10–6 g. Such an orbital information background is essential for an understanding of the evolutionary processes of this component.An outline is presented of orbit-finding systems; their inherent limitations and associated selection effects with some emphasis given to the on-going southern hemisphere routine survey provided by the AMOR facility which provides orbits down to a limiting magnitude +13. 相似文献
20.
Paolo Farinella Andrea Milani Anna M. Nobili Giovanni B. Valsecchi 《Earth, Moon, and Planets》1979,20(4):415-421
We analyze the system formed by Pluto and its satellite Charon from the point of view of the theory of tidal evolution. The singular feature of the system, i.e. the configuration of complete synchronism which has been suggested by the available data, is found to represent the stable end-product of the evolution. The time needed for the synchronization is shown to be less than the age of the solar system, provided that Pluto's tidal dissipation function is smaller than 104–105. Moreover, the initial orbital radius of the system could not be largerthan two or three times the present radius, so that Charon has been always a close satellite.Finally, we discuss Lyttleton's hypothesis that Pluto is an escaped satellite of Neptune, suggesting that a possible mechanism of Pluto's ejection could be connected with a retrograde capture of Triton by Neptune or with the subsequent tidal evolution of Triton's orbit. 相似文献