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1.
The classical Poisson equations of rotational motion are used to study the attitude motions of an Earth orbiting, rapidly spinning gyroscope perturbed by the effects of general relativity (Einstein theory). The center of mass of the gyroscope is assumed to move about a rotating oblate Earth in an evolving elliptic orbit which includes all first-order oblateness effects produced by the Earth.A method of averaging is used to obtain a transformation of variables, for the nonresonance case, which significantly simplifies the Poisson differential equations of motion of the gyroscope. Longterm solutions are obtained by an exact analytical integration of the simplified transformed equations. These solutions may be used to predict both the orientation of the gyroscope and the motion of its rotational angular momentum vector as viewed from its center of mass. The results are valid for all eccentricities and all inclinations not near the critical inclination.This paper represents a part of the author's Ph. D. dissertation for the Mathematics Department, Auburn University.  相似文献   

2.
We considered the impacts of very large cosmic bodies (with radii in the range 100–200 to 1000–2000 km) on the early Earth, whose mass, radius and density distribution are close to the current values. The impacts of such bodies were possible during the first hundreds of million years after the formation of the Earth and the Moon. We present and analyze the results of a numerical simulation of the impact of a planetesimal, the size of which is equal to that of the contemporary Moon (1700 km). In three-dimensional computations, the velocity (15 and 30 km/s) and the angle (45°, 60°, and 90°) of the impact are varied. We determined the mass losses and traced the evolution of the shape of the Earth's surface, taking into account the self-consistent gravitational forces that arise in the ejected and remaining materials in accordance with the real, time-dependent mass distribution. Shock waves reflected from the core are shown to propagate from the impact site deep into the Earth. The core undergoes strong, gradually damped oscillations. Although motions in the Earth's mantle gradually decline, they have enough time to put the Earth in a rotational motion. As a result, a wave travels over the Earth's surface, whose amplitude, in the case of an oblique impact, depends on the direction of the wave propagation. The maximum height of this wave is tremendous—it attains several hundred kilometers. Some portion of the ejected material (up to 40% of the impactor mass) falls back onto Earth under the action of gravity. This portion is equivalent to the layer of a condensed material with a thickness on the order of ten kilometers. The appearance of this hot layer should result in a global melting of near-surface layers, which can limit the age of terrestrial rocks by the time of the impact under consideration. For lesser-sized impactors, say, for impactors with radii of about 160 km, the qualitative picture resembles that described above but the amplitude of disturbances is considerably smaller. This amplitude, however, is sufficient to cause a crustal disruption (if such a crust has already formed) and intense volcanic activity.  相似文献   

3.
Application of boundary value techniques in the case of an electron performing relativistic motions within a magnetic dipole such as that of the Earth supplemented by a scanning process by means of which the entire phase space of the problem can be investigated, six new types of periodic motion have been discovered and computed. The stability of these motions is investigated and their direct bearing on formation and shape of the Van Allen zones of the Earth is discussed.  相似文献   

4.
This paper deals with fluctuating motions which are caused by a given stochastical temperature field acting in a gas with gravitation and T¯ = const. It results that the often used BOUSSINESQ approximation much underestimates the horizontal motions in case wide-spread temperature fluctuations occur. For sufficiently large scales the horizontal motion exceeds the vertical ones even in the case of the temperature field fluctuating completely isotropically. Scales of 1000 km and 1 day in the Earth atmosphere lead to the observed value u′horiz/|u′vertic ≈︁ 10. Finally besides the relation between density correlation and pressure correlation we determine the expression for the turbulent mass transport vanishing with the molecular viscosity.  相似文献   

5.
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6.
If static gravity or spacetime curvature information is carried by classical propagating particles or waves, a modern Laplace experiment places a lower limit on their speed of 1010 c. The so-called Lorentzian modification of special relativity permits such speeds without need of tachyons. But there are other consequences. If ordinary gravity is carried by particles with finite collision cross-section, such collisions would progressively diminish its inverse square character, converting to inverse linear behavior on the largest scales. At scales greater than several kiloparsecs gravity can apparently be modeled, without need for dark matter, by an inverse linear law. The orbital motions of Mercury and Earth may also show traces of this effect. If gravity were carried by particles, a mass between two bodies could partially shield each of them from the gravity of the other. Anomalies are seen in the motions of certain artificial Earth satellites during eclipse seasons that behave like shielding of the Sun's gravity. Certain types of radiation pressure might cause a similar behavior but require many free parameters. Particle-gravity models would change our understanding of gravitation and our views of the nature of time in relativity theory.  相似文献   

7.
地球自转速率对海平面纬向变化影响的初步研究   总被引：10，自引：0，他引：10  
郑大伟  萧耐园 《天文学报》1996,37(1):97-104
本文用了太平洋地区内近３００个验潮站的海平面观测资料，计算了不同纬度带平均海症状贩 年际变化与地球自转速率年际变化之间的相关性，利用简化的地球海洋模型，从理论上定性地讨论了地球自转速率变化影响海洋纬向运动的可能物理机制。  相似文献   

8.
The Commission 19 (Earth Rotation) of the International Astronomical Union—IAU established the Working Group on Earth Rotation in the Hipparcos Reference Frame—WG ERHRF at 1995 to collect the optical observations of latitude and universal time variations, made during 1899.7-1992.0 in line with Earth orientation programmes (to derive Earth Orientation Parameters—EOP), with Dr. Jan Vondrák (Astronomical Institute of Academy of Sciences of the Czech Republic, Prague) as the head of WG ERHRF. Dr. Vondrák collected about 4.4 million optical observations of latitude/universal time variations made at 33 observatories. These data were used for EOP investigations, Hipparcos Catalogue—radio sources connection, etc. Nowadays, it is used to correct the positions and proper motions of stars of Hipparcos Catalogue (as an optical reference frame) using ground-based observations of some Hipparcos stars. After Hipparcos Catalogue, some new astrometric catalogues appeared (as ARIHIP, EOC-2, etc.) with better accuracy of proper motions. We use the latitude observations made by visual zenith-telescope (ZT), as classical astrometric instrument, at seven observatories (all over the world) of International Latitude Service—ILS. The observations were used in the programmes of monitoring the Earth orientation during the 20th century. We received the data from Dr. Vondrák via private communication. The observatories are Carloforte—CA, Cincinnati—CI, Gaithersburg—GT, Kitab—KZ, Mizusawa—MZZ, Tschardjui—TS and Ukiah—UK. The task is to improve proper motions in declination of the observed Hipparcos stars. The original method was developed. We removed from the instantaneous observed latitudes, all known effects (polar motion and some local instrumental errors), and the corrected latitudes were then the input data to calculate the corrections of Hipparcos proper motions in declination using the least squares method—LSM with the linear model. We did an improvement of Hipparcos proper motions in declination via mentioned latitude variations with time by using a long-term (a few decades) visual zenith-telescope data of ILS. The calculated results were compared with the ARIHIP and EOC-2 data, and the consistency were good. The main steps of the calculations and some of the results are presented here.  相似文献   

9.
刚体地球章动序列和非刚体地球章动的转换函数都和地球动力学扁率有关。ＩＡＵ１９８０章动理论中采用了一个不一致的地球动力学扁率值,从而影响了章动振幅的计算。本文介绍了章动序列计算中地球动力学扁率的取值。由地球模型１０６６Ａ或ＰＲＥＭ得到的地球动力学扁率值比由岁差观测得到的约小１％,并且不可靠。当考虑体静力学平衡被破坏时新的地球物理模型,可得到与岁差常数相一致的地球动力学扁率值。地球动力学扁率值Ｈ＝０．  相似文献   

10.
The chaotic behaviour of the motion of the planets in our Solar System is well established. In this work to model a hypothetical extrasolar planetary system our Solar System was modified in such a way that we replaced the Earth by a more massive planet and let the other planets and all the orbital elements unchanged. The major result of former numerical experiments with a modified Solar System was the appearance of a chaotic window at κ E ∈ (4, 6), where the dynamical state of the system was highly chaotic and even the body with the smallest mass escaped in some cases. On the contrary for very large values of the mass of the Earth, even greater than that of Jupiter regular dynamical behaviour was observed. In this paper the investigations are extended to the complete Solar System and showed, that this chaotic window does still exist. Tests in different ‘Solar Systems’ clarified that including only Jupiter and Saturn with their actual masses together with a more ‘massive’ Earth (4 < κ E < 6) perturbs the orbit of Mars so that it can even be ejected from the system. Using the results of the Laplace‐Lagrange secular theory we found secular resonances acting between the motions of the nodes of Mars, Jupiter and Saturn. These secular resonances give rise to strong chaos, which is the cause of the appearance of the instability window. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

11.
The giant impact hypothesis for the origin of the Moon has been widely accepted. One of the most important features of this hypothesis is that the impactor's metallic core was incorporated in the Earth after impact. If the mass of the impactor is 0.82 × 1027 g, the mass of the impactor core was estimated to be 0.19 × 1027 g, which is about 1/10 of present Earth's core. Liu (1982) derived the bulk composition of the Earth from CI chondrites, and concluded that the Fe content of his model appears to be low in comparison with the present Earth, which, however, can be rationalized by the addition of impactor core into the proto-Earth developed by Liu (1982). If the impactor's mantle contains 14 wt% FeO as suggested, the mass ratio of impactor/proto-Earth should not exceed 0.22. The same ratio is not likely to exceed 0.30, if a giant blowoff did not occur during impact.  相似文献   

12.
The present work deals with constructing a conditionally periodic solution for the motion of an Earth satellite taking into consideration the oblateness of the Earth and the Luni-Solar attractions. The oblatenessof the Earth is truncated beyond the second zonal harmonic J 2. The resonance resulting from the commensurability between the mean motions of the satellite, the Moon, and the Sun is analyzed.  相似文献   

13.
Abstract– A calibrated lightcurve is presented of the near‐Earth asteroid 2008 TC3, obtained before it impacted Earth on October 7, 2008. The asteroid was observed in unfiltered images from the end of astronomical twilight until the object entered Earth’s shadow about 2 h later. The observations covered a wide range of phase angles from 14.79° to 2.93°, during which the asteroid ranged from 82,000 km to 29,000 km distance from the observer. A method is presented for obtaining photometrically filtered brightness values for the asteroid using unfiltered imaging techniques. Over 1,700 images of the asteroid produce a lightcurve with a peak‐to‐peak variation in V of 0.76 magnitude. Analysis of the lightcurve yields values for H = 30.86 ± 0.01 and G = 0.33 ± 0.03. Combined with other constraints on the kinetic energy and diameter of the asteroid, which suggest a low 1.8 g cm?3 density and albedo 0.05 ± 0.01, the value of H implies an asteroid of about 4.1 m in diameter, 28 m3 in volume, and 51,000 kg in mass. The determined value of G is out of range for normal, larger asteroids of albedo 0.05–0.15.  相似文献   

14.
After publication of the Hipparcos catalogue (in 1997), a few new astrometric catalogues have appeared (TYCHO‐2, ARIHIP, etc.), as a good combination of the Hipparcos satellite and ground‐based data, to get more accurate coordinates and proper motions of stars than the Hipparcos catalogue ones. There are also investigations on improving the Hipparcos coordinates and proper motions by using the astrometric observations of latitude and universal time variations (via observed stars referred to Hipparcos catalogue), together with Hipparcos data, carried out during the last few years. These kind of ground‐based data were collected at the end of the last century by J. Vondrák. There are about 4.4 million optical observations made worldwide at 33 observatories and with 47 instruments during 1899.7–1992.0; our Belgrade visual zenith telescope data (for the period 1949.0‐1986.0) were included. First of all, these data were used to determine the Earth Orientation Parameters – EOP, but they are also useful for the opposite task – to check the accuracy of coordinates and proper motions of Hipparcos stars which were observed from the ground over many decades. Here, we use the latitude part of ten Photographic Zenith Tubes – PZT data (more than 0.9 million observations made at 6 observatories during the time interval 1915.8–1992.0), and combine them with the Hipparcos catalogue ones, with suitable weights, in order to check the proper motions in declination for 807 common PZT/Hipparcos stars (and to construct the PZT catalogue of μδ for 807 stars). Our standard errors in proper motions in declination of these stars are less than or equal to the Hipparcos ones for 423 stars. The mean value of standard errors of 313 stars observed over more than 20 years by PZT is 0.40 mas/yr. This is 53% of 0.75 mas/yr (the suitable value from the Hipparcos catalogue). We used the Least Squares Method – LSM with the linear model. Our results are in good agreement with the Earth Orientation Catalogue – EOC‐2 and the new Hipparcos ones. The main steps of the method and the investigations of systematic errors in determined proper motions (the proper motion differences with respect to the Hipparcos values, the EOC‐2 ones and the new Hipparcos ones, as a function of α, δ, and magnitude) are presented here. A comparison of the four catalogues by pairs shows that there is no significant relationship between the differences of their μδ values and magnitudes and color indices of the common 807 stars. All catalogues have relatively small random and systematic errors which are close to each other. However, the comparison shows that our formal errors are too small. They are underestimated by a factor of nearly 1.7 (for EOC‐2, it is 2.0) if we take the new Hipparcos (or Hipparcos) data as reference (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

15.
Tidal forces acting on the Earth cause deformations and mass redistribution inside the planet involving surface motions and variation in the gravity field, which may be observed in geodetic experiments. Because for space geodesy it is now necessary to achieve the mm level in tidal displacements, we take into account the hydrostatic flattening of the Earth in the computation of the elasto-gravitational deformations. Analytical solutions are derived for the semi-diurnal tides on a slightly elliptical homogeneous incompressible elastic model. That simple analytical Earth’s model is not a realistic representation of any real planet, but it is useful to understand the physics of the problem and also to check numerical procedures. We rediscover and discuss the Love’s solutions and obtain new analytical solutions for the tangential displacement. We extend these analytical results to some geodetic responses of the Earth to tidal forces such as the perturbation of the surface gravity field, the tilt and the deviation of the vertical with reference to the Earth’s axis.  相似文献   

16.
The origin of water on Mars   总被引：1，自引：0，他引：1  
This paper considers the origin of water on Mars, in the context of a dynamical model that accounts for most of the Earth's water as a product of collisions between the growing Earth and planet-sized “embryos” from the asteroid belt. Mars' history is found to be different; to explain the present mass of Mars requires that it suffer essentially no giant collisions and the bulk of its growth is through addition of smaller bodies. Asteroids and comets from beyond 2.5 AU provide the source of Mars' water, which totals 6-27% of the Earth's present ocean (1 Earth ocean≡1.5×1021 kg), equivalent to 600-2700-m depth on the martian surface. The D/H ratio of this material is 1.2-1.6 times Standard Mean Ocean Water, the smaller value obtaining for the larger amount of water accreted. The upper half of the range of total water accreted, while many times less than that acquired by the Earth, is consistent with geological data on Mars, and the D/H value is that derived for martian magmatic water from SNC meteorites. Both together are consistent with published interpretations of the high D/H in present-day martian atmospheric water in terms of water loss through atmospheric escape.  相似文献   

17.
From modeling the evolution of disks of planetesimals under the influence of planets, it has been shown that the mass of water delivered to the Earth from beyond Jupiter’s orbit could be comparable to the mass of terrestrial oceans. A considerable portion of the water could have been delivered to the Earth’s embryo, when its mass was smaller than the current mass of the Earth. While the Earth’s embryo mass was growing to half the current mass of the Earth, the mass of water delivered to the embryo could be near 30% of the total amount of water delivered to the Earth from the feeding zone of Jupiter and Saturn. Water of the terrestrial oceans could be a result of mixing the water from several sources with higher and lower D/H ratios. The mass of water delivered to Venus from beyond Jupiter’s orbit was almost the same as that for the Earth, if normalized to unit mass of the planet. The analogous per-unit mass of water delivered to Mars was two?three times as much as that for the Earth. The mass of water delivered to the Moon from beyond Jupiter’s orbit could be less than that for the Earth by a factor not more than 20.  相似文献   

18.
Abstract— In the primordial solar system, the most plausible sources of the water accreted by the Earth were in the outer asteroid belt, in the giant planet regions, and in the Kuiper Belt. We investigate the implications on the origin of Earth's water of dynamical models of primordial evolution of solar system bodies and check them with respect to chemical constraints. We find that it is plausible that the Earth accreted water all along its formation, from the early phases when the solar nebula was still present to the late stages of gas‐free sweepup of scattered planetesimals. Asteroids and the comets from the Jupiter‐Saturn region were the first water deliverers, when the Earth was less than half its present mass. The bulk of the water presently on Earth was carried by a few planetary embryos, originally formed in the outer asteroid belt and accreted by the Earth at the final stage of its formation. Finally, a late veneer, accounting for at most 10% of the present water mass, occurred due to comets from the Uranus‐Neptune region and from the Kuiper Belt. The net result of accretion from these several reservoirs is that the water on Earth had essentially the D/H ratio typical of the water condensed in the outer asteroid belt. This is in agreement with the observation that the D/H ratio in the oceans is very close to the mean value of the D/H ratio of the water inclusions in carbonaceous chondrites.  相似文献   

19.
The origin and evolution of the Earth-Moon system is studied by comparing it to the satellite systems of other planets. The normal structure of a system of secondary bodies orbiting around a central body depends essentially on the mass of the central body. The Earth with a mass intermediate between Uranus and Mars should have a normal satellite system that consists of about half a dozen satellites each with a mass of a fraction of a percent of the lunar mass. Hence, the Moon is not likely to have been generated in the environment of the Earth by a normal accretion process as is claimed by some authors.Capture of satellites is quite a common process as shown by the fact that there are six satellites in the solar system which, because they are retrograde, must have been captured. There is little doubt that the Moon is also a captured satellite, but its capture orbit and tidal evolution are still incompletely understood.The Earth and the Moon are likely to have been formed from planetesimals accreting in particle swarms in Kepler orbits (jet streams). This process leads to the formation of a cool lunar interior with an outer layer accreted at increasingly higher temperatures. The primeval Earth should similarly have formed with a cool inner core surrounded in this case by a very strongly heated outer core and with a mantle accreted slowly and with a low average temperature but with intense transient heating at each individual impact site.  相似文献   

20.
We have for the first time calculated the population characteristics of the Earth’s irregular natural satellites (NESs) that are temporarily captured from the near-Earth-object (NEO) population. The steady-state NES size–frequency and residence-time distributions were determined under the dynamical influence of all the massive bodies in the Solar System (but mainly the Sun, Earth, and Moon) for NEOs of negligible mass. To this end, we compute the NES capture probability from the NEO population as a function of the latter’s heliocentric orbital elements and combine those results with the current best estimates for the NEO size–frequency and orbital distribution. At any given time there should be at least one NES of 1-m diameter orbiting the Earth. The average temporarily-captured orbiter (TCO; an object that makes at least one revolution around the Earth in a co-rotating coordinate system) completes (2.88 ± 0.82) rev around the Earth during a capture event that lasts (286 ± 18) d. We find a small preference for capture events starting in either January or July. Our results are consistent with the single known natural TCO, 2006 RH120, a few-meter diameter object that was captured for about a year starting in June 2006. We estimate that about 0.1% of all meteors impacting the Earth were TCOs.  相似文献   

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