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1.
The Radio Science Experiment is one of the on board experiments of the Mercury ESA mission BepiColombo that will be launched in 2014. The goals of the experiment are to determine the gravity field of Mercury and its rotation state, to determine the orbit of Mercury, to constrain the possible theories of gravitation (for example by determining the post-Newtonian parameters), to provide the spacecraft position for geodesy experiments and to contribute to planetary ephemerides improvement. This is possible thanks to a new technology which allows to reach great accuracies in the observables range and range rate; it is well known that a similar level of accuracy requires studying a suitable model taking into account numerous relativistic effects. In this paper we deal with the modelling of the space-time coordinate transformations needed for the light-time computations and the numerical methods adopted to avoid rounding-off errors in such computations.  相似文献   

2.
The ESA mission BepiColombo will include a Mercury Planetary Orbiter equipped with a full complement of instruments to perform Radio Science Experiments. Very precise range and range-rate tracking from Earth, on-board accelerometry, altimetry and accurate angular measurements with optical instruments will provide large data sets. From these it will be possible to study (1) the global gravity field of Mercury and its temporal variations due to tides, (2) the medium to short scale (down do 300400 km) gravity anomalies, (3) the rotation state of the planet, in particular the obliquity and the libration with respect to the 3/2 spin orbit resonance and (4) the orbit of the center of mass of the planet.With the global gravity field and the rotation state it is possible to tightly constrain the internal structure of the planet, in particular to determine whether the solid surface of the planet is decoupled from the inner core by some liquid layer, as postulated by dynamo theories of Mercury's magnetic field. With the gravity anomalies and altimetry it is possible to study the geophysics of the planet's crust, mantle and impact basins. With the orbit of the planet closest to the Sun it is possible to constrain relativistic theories of gravitation.The possibility of achieving these scientific goals has been tested with a full cycle numerical simulation of the Radio Science Experiments. It includes the generation of simulated tracking and accelerometer data, and the determination, by least squares fit, of a long list of variables including the initial conditions for each observed arc, calibration parameters, gravity field harmonic coefficients, and corrections to the orbit of Mercury. An error budget has been deduced both from the formal covariance matrices and from the actual difference between the nominal values used in the data simulation and the solution. Thus the most complete error budget contains the effect of systematic measurement errors and is by far more reliable than a formal one. For the rotation experiment an error budget has been computed on the basis of dedicated studies on each separate error source.The results of the full cycle simulation are positive, that is the experiments are feasible at the required level of accuracy. However, the extraction of the full accuracy results from the data will be by no means trivial, and there are a number of open problems, both in the data processing (e.g., the selection of the orbital arc length) and in the mission scheduling (e.g., the selection of the target areas for the rotation experiment).  相似文献   

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

4.
《Planetary and Space Science》2007,55(10):1398-1413
The BepiColombo Laser Altimeter (BELA) has been selected for flight on board the European Space Agency's BepiColombo Mercury Planetary Orbiter (MPO). The experiment is intended to be Europe's first planetary laser altimeter system. Although the proposed system has similarities to the Mercury Laser Altimeter (MLA) currently flying on board NASA's MESSENGER mission to Mercury, the specific orbit and construction of the MPO force the use of novel concepts for BELA. Furthermore, the base-lined range-finding approach is novel. In this paper, we describe the BELA system and show preliminary results from some prototype testing.  相似文献   

5.
The BepiColombo space mission is one of the European Space Agency's cornerstone projects; it is planned for launch in 2013 to study the planet Mercury. One of the imaging instruments of BepiColombo is a STereo Camera (STC), whose main scientific objective is the global stereo mapping of the entire surface of Mercury. STC will permit the generation of a Digital Terrain Model (DTM) of Mercury's surface, improving the interpretation of morphological features at different scales and clarifying the stratigraphic relationships between different geological units.To evaluate the effectiveness of the STC-derived DTM for geological purposes, a series of simulations has been performed to find out to what extent the errors expected in the DTM may prevent the correct classification and interpretation of geological features. To meet this objective, Earth analogues (a crater, a lava cone and an endogenous dome) of likely components of the Hermean surface, small enough to be near the detection limit of the STC, were selected and a photorealistic three-dimensional (3D) model of each feature was generated using Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) stereo images. Stereoscopic pairs of synthetic images of each feature were then generated from the 3D model at different locations along the BepiColombo orbit. For each stereo pair, the corresponding Hermean DTM was computed using image correlation and compared to the reference data to assess the loss of detail and interpretability. Results show that interpretation and quantitative analysis of simple craters morphologies and small volcanic features should be possible all along the periherm orbit arc. At the apoherm only the larger features can be unequivocally distinguished, but they will be reconstructed to a poor approximation.  相似文献   

6.
Several versions of a Mercury surface element, part of the ESA BepiColombo Mercury Cornerstone mission to be launched in 2009, have been studied. The major constraint on system design has been the need to maximise the useful system mass on the surface of Mercury. The absence of atmosphere on the planet forces the adoption of a purely propulsive descent and landing system. The need to maintain the shock level at landing below limits which are acceptable to the payload imposes the adoption of a precise guidance, navigation & control system, which allows a drastic reduction of the landing speed, and therefore the adoption of an airbag landing system. Surface mobility is an obvious requirement for the purpose of geochemical exploration, since selected rocks have a much higher scientific yield than the average regolith. Geophysical investigations require that thermal, accelerometric, and densitometric probes be brought in contact with subsurface regions, to a depth of several metres. Magnetometric measurements may need deployment of sensors to some distance from the bulk of the lander body. The thermal environment on the surface of Mercury is extreme, even in the polar regions that will be targeted by the BepiColombo lander, while the solar flux rises seasonally to 10 times the one experienced in Earth orbit. The need to provide a low-temperature heat sink to sensors is particularly critical, if these are installed on a small-size, small-mass mobile deployment device. A consequence of the landing in a polar region will be the extremely variable lighting conditions, with extended portions of the surface shrouded in darkness by any small surface obstacle. Limitations on communications between Earth and the deployed payload will be caused by the low available data rate and by visibility windows (contact may be restricted to as little as <10 min every 9.5 h). This will impose a high degree of autonomy to be built into the payload systems.  相似文献   

7.
We studied the stability of aromatic compounds in low Earth orbit environment and describe the scientific results and successful flight of the ORGANICS experiment on-board the BIOPAN V space exposure facility. This experiment investigated the photo stability of large organic molecules in low Earth orbit. Thin films of selected organic molecules, such as polycyclic aromatic hydrocarbons (PAHs) and the fullerene C60 were subjected to the low Earth orbit environment and the samples were monitored before and after flight. PAHs and fullerenes have been proposed as carriers for a number of astronomical absorption and emission features and are also identified in meteorites. Our experiment on BIOPAN V was exposed to a total fluence of 602.45 kJ m−2 for photons in the range 170–280 nm. The experiment was also intended as a hardware test-flight for a long-term exposure experiment (Survival of organics in space) on the EXPOSE facility on the International Space Station (ISS). For the small fluence that was collected during the BIOPAN V experiment we found little evidence of photo-destruction. The results confirm that PAH molecules are very stable compounds in space. The small differences in destruction rates that are expected to arise among the PAH samples as a function of molecular size and structure will only show after the longer irradiation fluences that are expected in the exposure experiment on the ISS.  相似文献   

8.
We have estimated a preliminary error budget for the Italian Spring Accelerometer (ISA) that will be allocated onboard the Mercury Planetary Orbiter (MPO) of the European Space Agency (ESA) space mission to Mercury named BepiColombo. The role of the accelerometer is to remove from the list of unknowns the non-gravitational accelerations that perturb the gravitational trajectory followed by the MPO in the strong radiation environment that characterises the orbit of Mercury around the Sun. Such a role is of fundamental importance in the context of the very ambitious goals of the Radio Science Experiments (RSE) of the BepiColombo mission. We have subdivided the errors on the accelerometer measurements into two main families: (i) the pseudo-sinusoidal errors and (ii) the random errors. The former are characterised by a periodic behaviour with the frequency of the satellite mean anomaly and its higher order harmonic components, i.e., they are deterministic errors. The latter are characterised by an unknown frequency distribution and we assumed for them a noise-like spectrum, i.e., they are stochastic errors. Among the pseudo-sinusoidal errors, the main contribution is due to the effects of the gravity gradients and the inertial forces, while among the random-like errors the main disturbing effect is due to the MPO centre-of-mass displacements produced by the onboard High Gain Antenna (HGA) movements and by the fuel consumption and sloshing. Very subtle to be considered are also the random errors produced by the MPO attitude corrections necessary to guarantee the nadir pointing of the spacecraft. We have therefore formulated the ISA error budget and the requirements for the satellite in order to guarantee an orbit reconstruction for the MPO spacecraft with an along-track accuracy of about 1 m over the orbital period of the satellite around Mercury in such a way to satisfy the RSE requirements.  相似文献   

9.
This paper presents a definition study of a laser altimeter for the topographic exploration of Mercury. The reference scenario is the BepiColombo mission, a cornerstone mission of European Space Agency (ESA) planned for 2012. BepiColombo will offer the chance to make a remarkable new contribution to our knowledge of the Solar System, by venturing into the hot region near the Sun and exploring Mercury, the most enigmatic of the earth's sisters among the terrestrial planets. First images of Mercury surface were acquired by Mariner 10 in 1974 and 1975 offering a coverage and resolution comparable to Earth-based telescopic coverage of the Moon before spaceflight. BepiColombo mission can be very beneficial by using an optical rangefinder for Mercury exploration. In fact starting from the first missions in 1970s until today, laser altimeters have been demonstrating to be particularly appropriate as part of the scientific payload whenever the topography of earth, lunar and planetary surface is the scientific objective of a space mission.Our system design is compliant to Mercury Polar Orbiter (MPO) of the mission. System performance analysis is carried out simulating main hermean topographic features and the potential targets on the planet by means of analytical models and computer codes and several plot are presented to analyse the performance of the instrument.  相似文献   

10.
The magnetic field of Mercury and the structure and dynamics of Mercury's magnetosphere, which will be studied by the spacecraft orbiting Mercury, are strongly influenced by the interaction of the solar wind with Mercury. In order to understand the internal magnetic field, it will be necessary to correct the observations of the external field for the distortions produced by the solar wind. Understanding of the solar wind interaction with Mercury is essential for understanding the structure and dynamics of the magnetosphere and phenomena such as magnetic storms. Helios 1 and 2 made a number of passes in the region traversed by the orbit of Mercury, and each pass provided a sample of the solar wind environment of Mercury. This paper reviews the plasma and magnetic field observations from Helios that provide a general basis for interpreting the observations of Mercury that will be made by orbiting spacecraft. The variables that govern the structure and dynamics of the magnetospheres of Mercury and Earth are approximately 5–10 times larger at Mercury than at Earth. Thus, the solar wind interaction with Mercury will be much stronger than the interaction with Earth. Moreover, the solar wind at Mercury is probably more variable than that at Earth. There is a clear need for measurements of the solar wind during the approach of spacecraft to Mercury and while they are in orbit around Mercury.  相似文献   

11.
A major goal of the BepiColombo mission to Mercury is the determination of the structure and state of Mercury's interior. Here the BepiColombo rotation experiment has been simulated in order to assess the ability to attain the mission goals and to help lay out a series of constraints on the experiment's possible progress. In the rotation experiment pairs of images of identical surface regions taken at different epochs are used to retrieve information on Mercury's rotation and orientation. The idea is that from observations of the same patch of Mercury's surface at two different solar longitudes of Mercury the orientation of Mercury can be determined, and therefore also the obliquity and rotation variations with respect to the uniform rotation.The estimation of the libration amplitude and obliquity through pattern matching of observed surface landmarks is challenging. The main problem arises from the difficulty to observe the same landmark on the planetary surface repeatedly over the MPO mission lifetime, due to the combination of Mercury's 3:2 spin-orbit resonance, the absence of a drift of the MPO polar orbital plane and the need to combine data from different instruments with their own measurement restrictions.By assuming that Mercury occupies a Cassini state and that the spacecraft operates nominally we show that under worst case assumptions the annual libration amplitude and obliquity can be measured with a precision of, respectively, 1.4 arcseconds (as) and 1.0 as over the nominal BepiColombo MPO lifetime with about 25 landmarks for rather stringent illumination restrictions. The outcome of the experiment cannot be easily improved by simply relaxing the observational constraints, or increasing the data volume.  相似文献   

12.
The motion of a satellite with negligible mass in the Schwarzschild metric is treated as a problem in Newtonian physics. The relativistic equations of motion are formally identical with those of the Newtonian case of a particle moving in the ordinary inverse-square law field acted upon by a disturbing function which varies asr ?3. Accordingly, the relativistic motion is treated with the methods of celestial mechanics. The disturbing function is expressed in terms of the Keplerian elements of the orbit and substituted into Lagrange's planetary equations. Integration of the equations shows that a typical Earth satellite with small orbital eccentricity is displaced by about 17 cm from its unperturbed position after a single orbit, while the periodic displacement over the orbit reaches a maximum of about 3 cm. Application of the equations to the planet Mercury gives the advance of the perihelion and a total displacement of about 85 km after one orbit, with a maximum periodic displacement of about 13 km.  相似文献   

13.
目前,越来越多的低轨卫星上都搭载了用于精密定轨的星载GPs接收机,星载GPS已成为低轨卫星精密定轨的主要手段之一.星载GPS精密定轨精度依赖于GPS星历及钟差精度.基于SHORDE-Ⅲ非差动力学定轨功能,以2005年8月1日至8月7日一周的GRACE卫星实测数据为例,采用事后精密轨道(igs)、快速轨道(igr)和超快速轨道(igu)三种GPS星历在同等条件下定轨,估计GPS星历精度对低轨卫星定轨精度的影响,实际计算结果表明igs和igr两类GPS星历定轨精度相当,约为9.5 cm,igu星历定轨精度略低于igs和igr星历,约为10.5cm:高频GPS卫星钟差数据对定轨精度会产生1-6cm影响.  相似文献   

14.
The basic geochemical model of the structure of the Moon proposed by Anderson, in which the Moon is formed by differentiation of the calcium, aluminium, titanium-rich inclusions in the Allende meteorite, is accepted, and the conditions for formation of this Moon within the solar nebula models of Cameron and Pine are discussed. The basic material condenses while iron remains in the gaseous phase, which places the formation of the Moon slightly inside the orbit of Mercury. Some condensed metallic iron is likely to enter the Moon in this position, and since the Moon is assembled at a very high temperature, it is likely to have been fully molten, so that the iron can remove the iridium from the silicate material and carry it down to form a small core. Interactions between the Moon and Mercury lead to the present rather eccentric Mercury orbit and to a much more eccentric orbit for the Moon, reaching past the orbit of the Earth, establishing conditions which are necessary for capture of the Moon by the Earth. In this orbit the Moon, no longer fully molten, will sweep up additional material containing iron oxide. This history accounts in principle for the two major ways in which the bulk composition of the Moon differs from that of the Allende inclusions.Paper dedicated to Professor Harold C. Urey on the occasion of his 80th birthday on 29 April 1973.  相似文献   

15.
Because of its proximity to the Sun and its small size, Mercury has not been able to retain its atmosphere and only a thin exosphere surrounds the planet. The exospheric pressure at the planetary surface is approximately 10−10 mbar, set by the Mariner 10 occultation experiment. The existence of gaseous species H, He, and O has been established by Mariner 10. In addition Na, K, and Ca have been observed by ground based instrumentation. Other elements are expected to be found in Mercury's exosphere since the total pressure of the known species is almost two orders of magnitude less than the exospheric pressure.It is intended to measure these exospheric particle densities in situ with an instrument on board of ESA's BepiColombo Mercury Planetary Orbiter (MPO) spacecraft. Since the expected exospheric densities are very small we developed a Monte-Carlo computer model to investigate if such a measurement is feasible along the MPO spacecraft orbit. We model energy and ejection angle distributions of the particles at the surface, with the emission process determining the actual distribution functions. Our model follows the trajectory of each particle by numerical integration until the particle hits Mercury's surface again or escapes from the calculation domain. Using a large set of these trajectories bulk parameters of the exospheric gas are derived, e.g., particle densities for various atomic and molecular species. Our study suggests that a mass spectrometric measurement is feasible and, at least at MPO's periherm, all species that are released from the surface will be observed.  相似文献   

16.
For numerical integration of the geocentric equations of motion of Earth satellites in the general relativity framework one may choose now between rather simple equations involving in their relativistic dynamical part only the Earth-induced terms and very complicated equations taking into account the relativistic third-body action. However, it is possible quite easily to take into account the relativistic indirect third-body perturbations and to neglect much lesser direct third-body perturbations. Such approach is based on the use of the Newtonian third-body perturbations in geocentric variables with expressing them in the relativistic manner in terms of the barycentric arguments. Together with it, to extend the known results for the spheroid model of the Earth, the Earth-induced terms are treated in great detail by including the non-spin part of the Earth vector-potential and the Earth triaxial non-sphericity.This revised version was published online in October 2005 with corrections to the Cover Date.  相似文献   

17.
Two space missions dedicated to Mercury (MESSENGER and BepiColombo) aim at understanding its rotation and confirming the existence of a liquid core. This double challenge requires much more accurate models for the spin-orbit resonant rotation of Mercury. The purpose of this paper is to introduce planetary perturbations on Mercury’s rotation using an analytical method and to analyse the influence of the perturbations on the libration in longitude. Applying a perturbation theory based on the Lie triangle, we were able to re-introduce short periodic terms into the averaged Hamiltonian and to compute the evolution of the rotational variables. The perturbations on Mercury’s forced libration in longitude mainly come from the orbital motion of Mercury (with an amplitude around 41 arcsec that depends on the momenta of inertia). It is completed by various effects from Jupiter (11.86 and 5.93 year-periods), Venus (with a 5.66 year-period), Saturn (14.73 year-period), and the Earth (6.58 year-period). The amplitudes of the oscillations due to Jupiter and Venus are approximately 33% and 10% of those from the orbital motion of Mercury and the amplitudes of the oscillations due to Saturn and the Earth are approximately 3% and 2%. We compare the analytical results with the solution obtained from the spin-orbit numerical model SONYR.  相似文献   

18.
This paper provides a method for finding initial conditions of frozen orbits for a probe around Mercury. Frozen orbits are those whose orbital elements remain constant on average. Thus, at the same point in each orbit, the satellite always passes at the same altitude. This is very interesting for scientific missions that require close inspection of any celestial body. The orbital dynamics of an artificial satellite about Mercury is governed by the potential attraction of the main body. Besides the Keplerian attraction, we consider the inhomogeneities of the potential of the central body. We include secondary terms of Mercury gravity field from \(J_2\) up to \(J_6\), and the tesseral harmonics \(\overline{C}_{22}\) that is of the same magnitude than zonal \(J_2\). In the case of science missions about Mercury, it is also important to consider third-body perturbation (Sun). Circular restricted three body problem can not be applied to Mercury–Sun system due to its non-negligible orbital eccentricity. Besides the harmonics coefficients of Mercury’s gravitational potential, and the Sun gravitational perturbation, our average model also includes Solar acceleration pressure. This simplified model captures the majority of the dynamics of low and high orbits about Mercury. In order to capture the dominant characteristics of the dynamics, short-period terms of the system are removed applying a double-averaging technique. This algorithm is a two-fold process which firstly averages over the period of the satellite, and secondly averages with respect to the period of the third body. This simplified Hamiltonian model is introduced in the Lagrange Planetary equations. Thus, frozen orbits are characterized by a surface depending on three variables: the orbital semimajor axis, eccentricity and inclination. We find frozen orbits for an average altitude of 400 and 1000 km, which are the predicted values for the BepiColombo mission. Finally, the paper delves into the orbital stability of frozen orbits and the temporal evolution of the eccentricity of these orbits.  相似文献   

19.
The great strengthening the material undergoes under high confining pressure, and jet pattern of matter outflowing from large impact craters make possible the ejection of asteroid-size bodies from the Earth into space. The ejected bodies, after gaining energy in planetary perturbations, may fall back with a velocity higher than that of their ejection. This solves, in particular, the problem of shower bombardments with ~ 25 Myr interval (Drobyshevski, Sov. Astron. Let. 16(3), 193, 1990), and a question arises whether this process could become self-sustained, like a chain reaction, when secondary impacts release an energy higher than that of primary impact. Estimates show that such a possibility could have been realized for Mercury (Drobyshevski, Lunar Planet. Sci. Conf. Abstr. 23(1), 317, 1992) due to its low escape and high orbital velocities. Self-sustained bombardment can account for the loss of the silicate mantle from Mercury. The energy and angular momentum conservation laws imply that its orbit contracted toward the Sun in the course of ejection of the mantle fragments by Mercury's perturbations beyond its orbit. Straight-forward calculations show the initial orbit to have practically coincided with the Venusian orbit. This puts the old hypothesis of Mercury being a lost satellite of Venus on a solid ground and provides an explanation for many facts from the origin of the Imbrium bombardment to the observed locks in the axial and orbital rotation of Mercury, Venus, and the Earth.  相似文献   

20.
The great strengthening the material undergoes under high confining pressure, and jet pattern of matter outflowing from large impact craters make possible the ejection of asteroid-size bodies from the Earth into space. The ejected bodies, after gaining energy in planetary perturbations, may fall back with a velocity higher than that of their ejection. This solves, in particular, the problem of shower bombardments with ~ 25 Myr interval (Drobyshevski, Sov. Astron. Let. 16(3), 193, 1990), and a question arises whether this process could become self-sustained, like a chain reaction, when secondary impacts release an energy higher than that of primary impact. Estimates show that such a possibility could have been realized for Mercury (Drobyshevski, Lunar Planet. Sci. Conf. Abstr. 23(1), 317, 1992) due to its low escape and high orbital velocities. Self-sustained bombardment can account for the loss of the silicate mantle from Mercury. The energy and angular momentum conservation laws imply that its orbit contracted toward the Sun in the course of ejection of the mantle fragments by Mercury's perturbations beyond its orbit. Straight-forward calculations show the initial orbit to have practically coincided with the Venusian orbit. This puts the old hypothesis of Mercury being a lost satellite of Venus on a solid ground and provides an explanation for many facts from the origin of the Imbrium bombardment to the observed locks in the axial and orbital rotation of Mercury, Venus, and the Earth.  相似文献   

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