On the model of the accumulation of the moon compatible with the data on the composition and the age of lunar rocks

It is suggested that the overall early melting of the lunar surface is not necessary for the explanation of facts and that the structure of highlands is more complicated than a solidified anorthositic ‘plot’. The early heating of the interior of the Moon up to 1000K is really needed for the subsequent thermal history with the maximum melting 3.5 × 10⁹ yr ago, to give the observed ages for mare basalts. This may be considered as an indication that the Moon during the accumulation retained a portion of its gravitational energy converted into heat, which may occur only at rapid processes. A rapid (t < 10³ yr) accretion of the Moon from the circumterrestrial swarm of small particles would give necessary temperature, but it is not compatible with the characteristic time 10⁸ yr of the replenishment of this swarm which is the same as the time-scale of the accumulation of the Earth. It is shown that there were conditions in the circumterrestial swarm for the formation at a first stage of a few large protomoons. Their number and position is evaluated from the simple formal laws of the growth of satellites in the vicinity of a planet. Such ‘systems’ of protomoons are compared with the observed multiple systems, and the conclusion is reached that there could have been not more than 2–3 large protomoons with the Earth. The tidal evolution of protomoon orbits was short not only for the present value of the tidal phase-lag but also for a considerably smaller value. The coalescence of protomoons into a single Moon had to occur before the formation of the observed relief on the Moon. If we accept the age 3.9 × 10⁹ yr for the excavation of the Imbrium basin and ascribe the latter to the impact of an Earth satellite, this collision had to be roughly at 30R, whereR is the radius of the Earth, because the Moon at that time had to be somewhere at this distance. Therefore, the protomoons had to be orbiting inside 20–25R, and their coalescence had to occur more than 4.0x10⁹ yr ago. The energy release at coalescence is equivalent to several hundred degrees and even 1000 K. The process is very rapid (of the order of one hour). Therefore, the model is valid for the initial conditions of the Moon.     

Rotation of the elastic Earth: the role of the angular-velocity-dependence of the elasticity-caused perturbation

We calculate the so-called convective term, which shows up in the expression for the angular velocity of the elastic Earth, within the Andoyer formalism. The term emerges due to the fact that the elasticity-caused perturbation depends not only on the instantaneous orientation of the Earth but also on its instantaneous angular velocity. We demonstrate that this term makes a considerable contribution into the overall angular velocity. At the same time the convective term turns out to be automatically included into the correction to the nutation series due to the elasticity, if the series is defined by the perturbation of the figure axis (and not of the rotational axis) in accordance with the current IAU resolution. Hence it is not necessary to take the effect of the convective term into consideration in the perturbation of the elastic Earth as far as the nutation is related to the motion of the figure axis.     

On the origin of the solar system and the exceptional position of the Sun in the Galaxy

The solar system's position in the Galaxy is an exclusive one, since the Sun is close to the corotation circle, which is the place where the angular velocity of the galactic differential rotation is equal to that of density waves displaying as spiral arms. Each galaxy contains only one corotation circle; therefore, it is an exceptional place. In the Galaxy, the deviation of the Sun from the corotation is very small — it is equal to ΔR/R _⊙≈0.03, where ΔR=R _c ?R _⊙,R _c is the corotation distance from the galactic center andR _⊙ is the Sun's distance from the galactic center. The special conditions of the Sun's position in the Galaxy explain the origin of the fundamental cosmogony timescalesT ₁≈4.6×10⁹ yr,T ₂?10⁸ yr,T ₃?10⁶ yr detected by the radioactive decay of various nuclides. The timescaleT ₁ (the solar system's ‘lifetime’) is the protosolar cloud lifetime in a space between the galactic spiral arms. The timescaleT ₂ is the presolar cloud lifetime in a spiral arm.T ₃ is a timescale of hydrodynamical processes of a cloud-wave interaction. The possibility of the natural explanation of the cosmogony timescales by the unified process (on condition that the Sun is near the state of corotation) can become an argument in favour of the fact that the nearness to the corotation is necessary for the formation of systems similar to the Solar system. If the special position of the Sun is not incidental, then the corotation circles of our Galaxy, as well as those of other galaxies, are just regions where situations similar to ours are likely to be found.     

低纬子午环的电水准器与水平差测定

本文介绍了低纬子午环上电水准器的工作原理；讨论了电水准器在测定定位盘上盘的水平差时，其Ｄｅｔｉｃｏｎ的比例尺的测定方法及其测量精度；讨论了电水准器中狭缝倾斜量的测量方法；最后给出了水平差的测量范围以及可达到的精度，证明低纬子午环对轴系的要求是比较低的，而水平差的测量精度是相当高的。     

On the stability of the solutions of the general problem of three bodies

The following question is investigated: By how much may the initial conditions of a given three-body system be varied before the subsequent evolution of the new system completely differs from that of the original? Stated somewhat differently, how big is the ‘island’ in the phase space of initial conditions throughout which the parameters describing the evolution of the systems are continuous functions of the initial conditions? The extent of one such island is determined numerically and found to be surprisingly large. It is conjectured, however, that this result is due to the fact that the corresponding systems have very short disintegration times, so that the total motion is not very complex.     

Accounting for the viscosity of the fluid core in the problem of the physical libration of the moon

A two-component theoretical model of the physical libration of the Moon in longitude is constructed with account taken of the viscosity of the core. In the new version, a hydrodynamic problem of motion of a fluid filling a solid rotating shell is solved. It is found that surfaces of equal angular velocity are spherical, and a velocity field of the fluid core of the Moon is described by elementary functions. A distribution of the internal pressure in the core is found. An angular momentum exchange between the fluid core and solid mantle is described by a third-order differential equation with a right-hand side. The roots of a characteristic equation are studied and the stability of rotation is proved. A libration angle as a function of time is found using the derived solution of the differential equation. Limiting cases of infinitely large and infinitely small viscosity are considered and an effect of lag of a libration phase from a phase of action of an external moment of forces is ascertained. This makes it possible to estimate the viscosity and sizes of the lunar fluid core from data of observations.     

On the role of the motion of the photospheric footpoints of the magnetic field lines

By means of a simple relation between the velocity v of the fluid particle and the velocity v_f of the photospheric footpoint of the magnetic field line v_z and B_z being respectively the components of v and the magnetic field B normal to the photospheric surface, it is shown formally that through the phtospheric surface the transport of all the quantities attributed to the magnetic field, such as the magnetic flux, the magnetic energy and the helicity, is independent of v_z, and v_f is the only kinematical quantity on which the transport depends. In addition, in the neighborhood of the neutral line the velocity v_l of the moving curve of constant B_z is found to be equal approximately to the component of v or v_f in the direction of v_l. Since v_l can be measured or extimated, so can the components of v and v_f near the neutral line.     

Properties of the solar nebula and the origin of the moon

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.     

On the election of the flat metric in the bimetric theory of gravitation

The problem of the form of the flat metric in the Rosen bimetric theory is examined in the following work.It is shown, on concrete examples, how necessary it is to write down the flat metric and solve the problem of finding the gravitational field in arbitrary non-inertial frame. It is shown also how to separate the pure gravitational effects from those connected with non-inertiality of the frame by way of comparing both metrics.     

1m红外太阳望远镜光电导行系统中像场旋转的分析

云南天文台1m红外太阳望远镜(YNST)光电导行系统是基于检测太阳像在面阵CMOS图像传感器上的偏移量作为反馈控制信号的高精度闭环跟踪系统[1]。由于YNST是一个地平式装置,在太阳像偏移检测量中存在着像场旋转量,为了获取稳定清晰的太阳像,必须对检测量进行消旋[2]才能达到光电导行系统的跟踪要求。根据球面天文学及天体测量学的知识并结合导行镜的光学系统,推导了光电导行系统中像场旋转的变化规律并对其进行模拟分析。     

A new approach to evaluation of the effect of the two half-Lambert surfaces composed of different albedoes on the emergent radiation at the top of the atmosphere

A new way is adopted for the evaluation of the upwelling radiation from atmosphere bounded by two half-Lambert surfaces. The atmosphere is assumed to be homogeneous, and is composed of aerosol, molecules, and absorbent gases, where the model aerosol is of the oceanic and water soluble types.In the computational procedure, an iterative doubling-adding equation is expanded into a series of the radiative interaction modes between atmosphere and surface. Next, a probability of radiation interacting with respective half surfaces is calculated based on the assumption of single-scattering in the atmosphere. On the basis of this probability, the emergent radiation at the top of the atmosphere is approximately calculated by considering the radiative intractions to be twice as large. The effect of the multiple-scattering is fully taken into account. A numerical simulation exhibits the extraordinary effect near the two half-surface boundary of different albedoes. The effect of the other half-surface on the radiance decreases monotonically with the distance from the boundary. The present new version enable us to quantitatively discuss radiative transfer near the boundary of two half-surfaces even if the optical thickness is large and (or) surface albedo is great.     

On the origin of the Kirkwood Gaps

It is proposed that the Kirkwood Gaps are primordial, representing regions where asteroids failed to form by accretion. A brief scenario is presented to indicate the main features of a model for the early history of the asteroids. An analytical treatment is given for the effects of a solar nebula upon the eccentricity-pumping of asteroids, due to secular perturbations and to commensurability-type resonances associated with Jupiter. It is shown that nebular effects promote growth of main-belt asteroids; but in commensurability regions, growth is inhibited. A discussion is given of two related problems: the origin of asteroidal eccentricities and inclinations, and the likelihood that Jupiter suffered major changes in its semimajor axis during its formation. It is suggested that in view of these problems, the present theory should not be taken as necessarily correct, but should be regarded as illustrative of viewpoints which in time may yield a correct theory.     

低纬子午环的轴准直器与枢轴不规则的测定

本文论述了因枢轴不规则和两个叉臂的温差引起水平轴指向漂移的影响；详细叙述了用轴准直器测定和修正这种影响的方法；并且给出了测定轴准直器参数的方法。精度估计表明，在低纬子午环上使用了电水准器和轴准直器后，对枢轴的加工精度降低了一个数量级，并且降低了对轴系稳定性的要求，然而测量和修正这些误差的精度却是很高的。     

A model of the motion of the Nneuschwanstein bolide in the atmosphere

A new model of the atmospheric entry of the Neuschwanstein fireball has been developed. The fireball was photographed in Germany on April 6, 2002, and three fragments of it were found during a subsequent search in the territory predicted according to observations. In this study, the form of the meteoric body is assumed to be a cube with rounded vertices and edges. The estimated mass of the meteoric body at its entry into the atmosphere is close to the literature data obtained using seismic, acoustic, and infrasonic analysis. It is noted that the analysis of this fireball was for the first time made without using the photometric approach.     

Stabilization of the spectrum position in the main stellar spectrograph of the 6-m telescope of the Special Astrophysical Observatory of the Russian Academy of Sciences

New results on the stability analysis study of the Main Stellar Spectrograph of the 6-m telescope of the Special Astrophysical Observatory of the Russian Academy of Sciences when it operated jointly with the CCD detection system on a laboratory source are reported. The spectrum is found to drift along the dispersion direction for several tenths of a pixel (several hundredths of angstrom) over a one-hour time scale. To prevent this drift (i.e., the spectrum shift)—a plane parallel glass plate is mounted; tilt angle of this plate varies as a function of the misalignment between the current and reference spectra of a hollow-cathode tube laboratory source. Operation of the spectrum stabilizer is described. The correction time is of about 1 minute, allowing the position of the spectrum to be maintained to within ±0.0006Å.     

On some problems concerning the calculation of the form of the magnetopause and the electric field on the magnetopause in the framework of the continuum medium model

In order to understand the reason of the existence of the electric field in the magnetosphere, and for the theoretical evaluation of its value, it is necessary to find the solution of the problem of determination of the magnetosphere boundary form in the frameworks of the continuum medium model which takes into account part of the magnetospheric plasma movement in supporting the magnetospheric boundary equilibrium. A number of problems for finding the distribution of the pressure, the density, the magnetic field and the electric field on the particular tangential discontinuity is considered in the case when the form of discontinuity is set (the direct problem) and a number of problems for finding the form of the discontinuity and the distribution of the above-mentioned physical quantities on the discontinuity is considered when the law of the change of the external pressure along the boundary is set (for example, with the help of the approximate Newton equation). The problem which is considered here, which deals with the calculation of the boundary form and with the calculation of the distribution of the corresponding physical quantities on the discontinuity of the 1st kind for the compressible fluid with the magnetic field with field lines which are perpendicular to the plane of the flow in question, concerns the last sort of problems. The comparison of the results of the calculation with the data in the equatorial cross-section of the magnetosphere demonstrates that the calculated form of the boundary, the value of the velocity of the return flow and the value of the electric field on the magnetopause, agree satisfactorily with the observational data.     

On the influence of nonlinearities on the eigenfrequencies of five-minute oscillations of the Sun

Fitting the results of linear normal-mode analysis of the solar five-minute oscillations to the observed k - ω diagram selects a class of models of the Sun's envelope. It is a property of all the models in this class that their convection zones are too deep to permit substantial transmission of internal g modes of degree 20 or more. This is in apparent conflict with Hill and Caudell's (1979) claim to have detected such modes in the photosphere. A proposal to resolve the conflict was made by Rosenwald and Hill (1980). They pointed out that despite the impressive agreement between linearized theory and observation, nonlinear phenomena in the solar atmosphere might influence the eigenfrequencies considerably. In particular, they suggested that a correct nonlinear analysis could predict a shallow convection zone. This paper is an enquiry into whether their hypothesis is plausible. We construct k - ω diagrams assuming that the modes suffer local nonlinear distortions in the atmosphere that are insensitive to the amplitude of oscillation over the range of amplitudes that are observed. The effect of the nonlinearities on the eigenfrequencies is parameterized in a simple way. Taking a class of simple analytical models of the Sun's envelope, we compute the linear eigenfrequencies of one model and show that no other model can be found whose nonlinear eigenfrequencies agree with them. We show also that the nonlinear eigenfrequencies of a particular solar model with a shallow convective zone, computed with more realistic physics, cannot be made to agree with observation. We conclude, therefore, that the hypothesis of Rosenwald and Hill is unlikely to be correct.     

A new variant of the large-impact hypothesis for the origin of the Moon

The hypothesis is advanced that after collision of a Mars-sized impact with the Earth, collisions between debris particles themselves are able to place enough material into Earth orbit, to form the Moon. Collision probability estimates show that the collision frequency is high enough to place about one lunar mass into Earth orbit, if the average semimajor axis is of order of the Earth's Roche limit of 18 500 km.