The distant retrograde orbits (DROs) can serve as the parking orbits for a long-term cis-lunar space station. This paper gives a comprehensive study on the transfer problem from DROs to Earth orbits, including low Earth orbits (LEOs), medium Earth orbits (MEOs), and geosynchronous orbits (GSOs), in the bicircular restricted four-body problem (BR4BP) via optimizations within a large solution space. The planar transfer problem is firstly solved by grid search and optimization techniques, and two types of transfer orbits, direct ones and low-energy ones, are both constructed. Then, the nonplanar transfer problem to Earth orbits with inclinations between 0 and 90 degrees are solved via sequential optimizations based on the planar transfers. The transfer characteristics in the cases of different destination orbit inclinations are discussed for both the direct and the low-energy transfer orbits. The important role of the lunar gravity in the low-energy transfers is also discussed, which can overcome the increase of transfer cost caused by the high inclination of Earth orbits. The distinct features of different transfer scenarios, including multiple revolutions around the Earth and Moon, the exterior phase, and the lunar flyby, are discovered. The energy of transfer orbits is exploited to discuss the effects of close lunar flybys. The results will be helpful for the transfer design in future manned or unmanned return missions, and can also provide valuable information for selecting proper parking DROs for cis-lunar space stations.
The structure, dynamical equilibrium, and evolution of Saturn’s moon Iapetus are studied. It has been shown that, in the current epoch, the oblateness of the satellite ε2 ≈ 0.046 does not correspond to its angular velocity of rotation, which causes the secular spherization behavior of the ice shell of Iapetus. To study this evolution, we apply a spheroidal model, containing a rock core and an ice shell with an external surface ε2, to Iapetus. The model is based on the equilibrium finite-difference equation of the Clairaut theory, while the model parameters are taken from observations. The mean radius of the rock core and the oblateness of its level surface, ε1 ≈ 0.028, were determined. It was found that Iapetus is covered with a thick ice shell, which is 56.6% of the mean radius of the figure. We analyze a role of the core in the evolution of the shape of a gravitating figure. It was determined that the rock core plays a key part in the settling of the ice masses of the equatorial bulge, which finally results in the formation of a large circular equatorial ridge on the surface of the satellite. From the known mean altitude of this ice ridge, it was found that, in the epoch of its formation, the rotation period of Iapetus was 166 times shorter than that at present, as little as T ≈ 11h27m. This is consistent with the fact that a driving force of the evolution of the satellite in our model was its substantial despinning. The model also predicts that the ice ridge should be formed more intensively in the leading (dark and, consequently, warmer) hemisphere of the satellite, where the ice is softer. This inference agrees with the observations: in the leading hemisphere of Iapetus, the ridge is actually high and continuous everywhere, while it degenerates into individual ice peaks in the opposite colder hemisphere. 相似文献
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. 相似文献
We investigate the angular-momentum distribution in a classical homogeneous Maclaurin spheroid. An exact formula for the distribution as a function of the mass of a cylindrical column in the spheroid is obtained in both integral and differential forms. This expression is used to calculate the angular-velocity distributions in galaxies evolving from initially spheroidal configurations to steady-state configurations with observed density distributions. 相似文献
The climatic impact of volcanic activity on the Earth and Mars is considered and a comparative analysis is made. The effect of gaseous components and of aerosols, formed in the process of the evolution of volcanic cloud, on the greenhouse effect and climate on the Earth and Mars is analyzed. A numerical modelling has shown that the climatic impact of volcanic activity depends on the optical properties (the extent of opacity of the atmospheric gaseous components and on the intensity of volcanic activity). In connection with sporadic variations in the intensity of volcanic activity, a temporal modulation of climate takes place with alternating periods of warming and cooling. An important role of SO2 and volcanic aerosols in the formation of climate in the presence of evolution of the Earth and Mars is revealed. 相似文献
It is known that the center of mass (CM) of the Moon does not coincide with its geometrical center of figure (CF), and that the CF–CMline deviates to the Southeast of the direction toward the center of the Earth. An investigation of this phenomenon, which has remained incompletely understood, has been carried out in two stages. One mechanism can explain part of the eastward shift of the lunar CM as being due to tidal evolution of the lunar orbit. A second mechanism is considered here, which relates this shift of the lunar CM with evolution of the shape of the Moon. A differential equation describing the shift of the lunar CMto the East in the course of the physically inevitable rounding of its shape as it moves away from the Earth is derived and solved. This mechanism not only explains the eastward shift of the lunar CM, but also predicts that the oblateness of the Moon could have been appreciable at earlier epochs, reaching values ε ≈ 0.31. The theory of figures of equilibrium in a tidal gravitational field is used to determine how close to the Earth the Moon could have formed. 相似文献
Models for 12 elliptical galaxies are constructed based on the second-order tensor virial theorem. This method takes into account the spatial shape and structure of the internal density layers for each galaxy. New data for the surface brightness and isophote structure of the E galaxies derived from deep photometric observations are used. A system of equations is used to find the components of the gravitational-energy, rotational-energy, and velocity-dispersion tensors. This makes it possible to calculate the anisotropy index β of the velocity dispersion of each galaxy. The values for the entire sample lie in the range 0.012 ? β ? 0.246. It is shown that taking into account variations in the mass-to-light ratio M/L (for the stellar component) can reduce the value of β by roughly 20%. The results are compared with those from other studies. Our values of β for small E galaxies (rapid rotators) agree with those found in the ATLAS3D project based on Jeans anisotropy models. However, our models for giant E galaxies (slow rotators) taking into account the triaxial shape and realistic structure of the density layers provide a much better agreement with observations than the simple axially symmetrical models from the SAURON project.
Astronomy Reports - A new approach to the study of long-period and secular perturbations in celestial mechanics is developed. In contrast to the traditional use of the apparatus of the perturbing... 相似文献
From the observations of the gravitational field and the figure of the Moon, it is known that its center of mass (briefly COM) does not coincide with the center of figure (COF), and the line “COF/COM” is not directed to the center of the Earth, but deviates from it to the South–East. Here we study the deviation of the lunar COM to the East from the mean direction to Earth.At first, we consider the optical libration of a satellite with synchronous rotation around the planet for an observer at a point on second (empty) orbit focus. It is found that the main axis of inertia of the satellite has asymmetric nonlinear oscillations with amplitude proportional to the square of the orbit eccentricity. Given this effect, a mechanism of tidal secular evolution of the Moon’s orbit is offered that explains up to \(20\%\) of the known displacement of the lunar COM to the East. It is concluded that from the alternative—evolution of the Moon’s orbit with a decrease or increase in eccentricity—only the scenario of evolution with a monotonous increase in orbit eccentricity agrees with the displacement of lunar COM to the East. The precise calculations available confirm that now the eccentricity of the lunar orbit is actually increasing and therefore in the past it was less than its modern value, \(e = 0.0549\).To fully explain the displacement of the Moon’s COM to the East was deduced a second mechanism, which is based on the reliable effect of tidal changes in the shape of the Moon. For this purpose the differential equation which governs the process of displacement of the Moon’s COM to the East with inevitable rounding off its form in the tidal increase process of the distance between the Earth and the Moon is derived. The second mechanism not only explains the Moon’s COM displacement to the East, but it also predicts that the elongation of the lunar figure in the early epoch was significant and could reach the value \(\varepsilon\approx0.31\). Applying the theory of tidal equilibrium figures, we can estimate how close to the Earth the Moon could have formed. 相似文献
Astronomy Reports - The new analytical R-toroid method is applied to study the apsidal and nodal precession of test orbits in the circumbinary exo-systems Kepler-16, Kepler-35, Kepler-38,... 相似文献
