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1.
The stability of an imaginary planet located in the present main asteroid belt is studied with a 7-body model (Sun, Mars, Jupiter, Saturn, Uranus, Neptune and the imaginary planet). The fourth-order Hermite algorithm P(EC)3 is used, which has a very small secular energy error for the integration of periodic orbits with a constant time-step. The evolution of orbits is followed up to 108 years. Our numerical results show that the low-order resonances with Jupiter can enhance the stability of the imaginary planet in some cases. The survival probability of the imaginary planet decreases with the planet mass. The upper limit of the imaginary planet's mass that can survive in the main belt is around 1025 kg, i.e., about the Earth's mass.  相似文献   

2.
The influence of recently computed axial magnetic core-mantle coupling torques on the Earth's rotation was investigated. These torques derived from poloidal geomagnetic field within the mantle and at the core-mantle boundary are retarding torques. An accelerating torque due to the action of unknown parts of the core field was estimated by inverse solution of the equation of the mantle rotation for the periodic variations of the quantities of the magnetic field and the length of day. The variations of the drift rate of the Earth's core were compared with those of the mantle rotation velocity for a force-free Earth. The time constants of the coupling process were estimated and discussed in connection with the magnetic coupling of the mantle with an upper core layer. Der Einfluß kürzlich berechneter axialer Kern-Mantel-Kopplungsmomente auf die Erdrotation wurde untersucht. Diese Lorentz-Drehmomente, abgeleitet vom poloidalen geomagnetischen Feld im Mantel und an der Kern-Mantel-Grenze, sind retardierende Momente. Ein beschleunigendes Drehmoment, das der Wirkung unbekannter Feldanteile zugeordnet wird, wurde durch inverse Lösung der Mantelrotationsgleichung für die periodischen Variationen der Magnetfeldgrößen und der Tageslänge abgeschätzt. Die Variationen der Kerndriftgeschwindigkeit wurden mit denen der Mantelrotationsgeschwindigkeit für eine kräftefreie Erde verglichen. Die Zeitkonstanten des Kopplungsprozesses wurden ermittelt und im Zusammenhang mit der magnetischen Kopplung des Mantels mit einer oberen Kernschicht diskutiert.  相似文献   

3.
The Hill stability criterion is applied to analyse the stability of a planet in the binary star system of HD 41004 AB, with the primary and secondary separated by 22 AU, and masses of 0.7 M⊙ and 0.4 M⊙, respectively. The primary hosts one planet in an S‐type orbit, and the secondary hosts a brown dwarf (18.64 MJ) on a relatively close orbit, 0.0177 AU, thereby forming another binary pair within this binary system. This star‐brown dwarf pair (HD 41004 B+Bb) is considered a single body during our numerical calculations, while the dynamics of the planet around the primary, HD 41004 Ab, is studied in different phase‐spaces. HD 41004 Ab is a 2.6 MJ planet orbiting at the distance of 1.7 AU with orbital eccentricity 0.39. For the purpose of this study, the system is reduced to a three‐body problem and is solved numerically as the elliptic restricted three‐body problem (ERTBP). The Hill stability function is used as a chaos indicator to configure and analyse the orbital stability of the planet, HD 41004 Ab. The indicator has been effective in measuring the planet's orbital perturbation due to the secondary star during its periastron passage. The calculated Hill stability time series of the planet for the coplanar case shows the stable and quasi‐periodic orbits for at least ten million years. For the reduced ERTBP the stability of the system is also studied for different values of planet's orbital inclination with the binary plane. Also, by recording the planet's ejection time from the system or collision time with a star during the integration period, stability of the system is analysed in a bigger phase‐space of the planet's orbital inclination, ≤ 90°, and its semimajor axis, 1.65–1.75 AU. Based on our analysis it is found that the system can maintain a stable configuration for the planet's orbital inclination as high as 65° relative to the binary plane. The results from the Hill stability criterion and the planet's dynamical lifetime map are found to be consistent with each other. (© 2016 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

4.
Abstract— The newly discovered asteroid 2003 YN107 is currently a quasi‐satellite of the Earth, making a satellite‐like orbit of high inclination with apparent period of one year. The term quasi‐satellite is used since these large orbits are not completely closed, but rather perturbed portions of the asteroid's orbit around the Sun. Due to its extremely Earth‐like orbit, this asteroid is influenced by Earth's gravity to remain within 0.1 AU of the Earth for approximately 10 years (1997 to 2006). Prior to this, it had been on a horseshoe orbit closely following Earth's orbit for several hundred years. It will re‐enter such an orbit, and make one final libration of 123 years, after which it will have a close interaction with the Earth and transition to a circulating orbit. Chaotic effects limit our ability to determine the origin or fate of this object.  相似文献   

5.
It is shown that with a virial approach to the solution of the many-body problem the integral characteristics of a system (Jacobi's function and total energy), being present in Jacobi's equation, are immanent to its own integrals. Estimating the Lyapunov stability of motion of a system they play the role of Lyapunov functions.Studying Lyapunov stability of the virial oscillations of celestial bodies we used the Duboshin criterion applicable when permanent perturbations are present. In the case of conservative systems the potential energy of the system plays the role of such a perturbation. Thus, the nature of the virial oscillations can be understood as an effect of non-linear resonance between the kinetic and the potential energies.It is shown that the stability of virial oscillations of conservative systems relative to variations of the form-factors product is only a necessary condition in the proof of the hypothesis that =const. for celestial bodies. The sufficient condition for the proof of this equality consists of the given direct derivation of the equation of virial oscillations of celestial bodies from Einstein's equation, as well as of the equivalence of Schwarzschild's solution and the solution of Jacobi's equation at .The stability of virial oscillations for dissipative systems is studied. It is shown that the stability is limited by the period of time of its bifurcation.  相似文献   

6.
The present study deals with numerical modeling of the elliptic restricted three-body problem as well as of the perturbed elliptic restricted three-body (Earth-Moon-Satellite) problem by a fourth body (Sun). Two numerical algorithms are established and investigated. The first is based on the method of the series solution of the differential equations and the second is based on a 5th-order Runge-Kutta method. The applications concern the solution of the equations and integrals of motion of the circular and elliptical restricted three-body problem as well as the search for periodic orbits of the natural satellites of the Moon in the Earth-Moon system in both cases in which the Moon describes circular or elliptical orbit around the Earth before the perturbations induced by the Sun. After the introduction of the perturbations in the Earth-Moon-Satellite system the motions of the Moon and the Satellite are studied with the same initial conditions which give periodic orbits for the unperturbed elliptic problem.  相似文献   

7.
Generalized Jacobi's equation is derived by introducing the friction force into the equations of motion of mass points constituting the system.The exact solution of the equation of virial oscillations of celestial bodies written for non-conservative systems is obtained using non-linear time scale in the course of the change of variables for a particular friction force law.The nature of the undamped virial oscillations of celestial bodies is though to be related to the system unstability near the state determined by the virial theorem. Thus, the friction force changes its sign near the unstable equilibrium state and due to dissipation of energy during evolution of the system the undamped virial oscillations can be described as self-exited oscillations.  相似文献   

8.
Interpretations of current and past results from ground-based solar diameter measurements, as well as the planning of scientific programs for the 1980's, are strongly dependent on the perceived level of the degrading effects of the Earth's atmosphere. One of the more effective approaches has been to design the observing program and the subsequent data analysis such that the solar diameter measurements themselves could provide an evaluation of atmospheric effects. Many important results have been obtained in studies of this type and these results are collected here to help in appraising the current situation. This evidence all points in one direction: the Earth's atmosphere, while complicating the design of observational programs, is not the source of the oscillations observed in solar diameter measurements. Further, this same evidence indicates that the Earth's atmosphere will not pose any serious limitations in ground-based solar diameter studies during the 1980's.  相似文献   

9.
In this paper we compute the rate of solar EUV heating in the upper atmosphere by photo-dissociation and photo-ionization, taking care to include properly the effects of oblique incidence of solar flux, sphericity of the atmosphere and ellipticity of the Earth's orbit. The time and latitudinal variations of the computed heat function are revealed by numerical Fourier analysis of the heat function into harmonics of the yearly cycle. It is shown that EUV absorption contains a ‘latitude independent’ semi-annual component of heating with the ‘proper phase’ to account for the semi-annual density variations. Further, the annual component of the heat function predicts the existence of ‘summer polar’ density increases in the northern and southern hemispheres.  相似文献   

10.
By means of spectral analysis, oscillations have been detected in many-year time series of deviations in the duration of days from the standard that cannot be explained within the framework of existing gravitational theory. The solution of the problem of the origin and structure of these oscillations is associated with the essence of the phenomena taking place inside the Earth and the mechanisms of energy transfer by external fields and the Sun. The effect of the Sun on the Earth’s rotation also leads to the formation of a unified cyclic background, resulting in correlated oscillations in all shells of the Earth, as well as in its atmosphere and its nucleus. Ground magnetic fields of the Earth and the Sun play the leading role in the abovementioned unified cyclic process. The results of spectral autoregressive and wavelet analyses of experimental data concerning deviations in the duration of days from the standard in the years 1832–2006, ground geomagnetic field intensities in 1832–2006, and the mean magnetic field of the Sun during the period from 1975 to 2005 have been discussed in this paper to reveal and compare correlating oscillations. To analyze a short-period (31-yr-long) series of daily data on the mean magnetic field of the Sun, the results of wavelet transformations (the Morlet wavelet) of the detected amplitude of a burst envelope with a carrier frequency of 13 cycles/yr have been obtained.  相似文献   

11.
In order to study the apparent ‘super-rotation’ of the Earth's upper atmosphere, we examine a non-linear solution to the continuity, momentum conservation and state equations of gasdynamics for the steady state motion of a gravitationally stratified, cylindrical, inviscid atmosphere under the influence of a steady state, local time dependent temperature distribution. The resultant flow field can be understood in terms of angular momentum conservation of air masses: heated, rising air decreases its rotation rate and cooled, falling air increases its rotation rate. The local-time average of the differential rotation rate may given rise to an apparent altitude dependent ‘super-rotation’. Comparison with observations is presented.  相似文献   

12.
Adding the angular velocity of sidereal solar rotation and the apparent rotational effect of the Earth's revolution vectorially, a new synodic solar rotation vector has been obtained. The sidereal and synodic solar rotation axes (and equators) are separated. Using the known parameters of the Earth's orbital motion, the synodic rotation angular velocity and the inclination of the synodic equator, the corresponding sidereal rotation parameters have been calculated (ω1 = 2.915 × 10#X2212;6 rad s#X2212;1 and i 1 = 6.076). Various linear rotational velocities at the solar globe are briefly described.  相似文献   

13.
A relationship between the potential energy and the moment of the inertia for celestial bodies is heuristically discovered. This relationship consists in the constancy of the product of formfactors for the potential energy and the moment of the inertia. The product is independent of the body mass and its radial mass distribution.We find the exact solution of Jacobi's virial equation for a gravitating spherical body based on the relationship obtained. This solution represents the unharmonic radial oscillations of the body. The solution is valid for a wide class of celestial bodies including variable stars and relativistic objects for which a relativistic analog of Jacob's equation is derived.The period of the radial oscillations of the planets is estimated with the help of the solution found. We note the coincidence of the experimental data and our theoretical calculations for the Sun.We show the important role of the Coulomb forces in the formation of the planets. It is demonstrated that the Coulomb forces result in the relation between the planet masses and their average molecular weight.  相似文献   

14.
We study two and three-dimensional resonant periodic orbits, usingthe model of the restricted three-body problem with the Sun andNeptune as primaries. The position and the stability character ofthe periodic orbits determine the structure of the phase space andthis will provide useful information on the stability and longterm evolution of trans-Neptunian objects. The circular planarmodel is used as the starting point. Families of periodic orbitsare computed at the exterior resonances 1/2, 2/3 and 3/4 withNeptune and these are used as a guide to select the energy levelsfor the computation of the Poincaré maps, so that all basicresonances are included in the study. Using the circular planarmodel as the basic model, we extend our study to more realisticmodels by considering an elliptic orbit of Neptune and introducingthe inclination of the orbit. Families of symmetric periodicorbits of the planar elliptic restricted three-body problem andthe three-dimensional problem are found. All these orbitsbifurcate from the families of periodic orbits of the planarcircular problem. The stability of all orbits is studied. Althoughthe resonant structure in the circular problem is similar for allresonances, the situation changes if the eccentricity of Neptuneor the inclination of the orbit is taken into account. All theseresults are combined to explain why in some resonances there aremany bodies and other resonances are empty.  相似文献   

15.
We investigate the expected performance of a wide-angle camera in Martian orbit, which, unlike previous cameras that have flown to Mars, is capable of recording meteor activity in that planet's atmosphere. We show that, based on our current understanding of meteor physics and the interplanetary meteoroid population, several meteors will be detected by this instrument during a single nightside pass on a low Martian orbit. The instrument will also record the signatures of meteor showers expected to occur every Martian year (1.88 Earth years). The results of this investigation will test models of the flux of “large” (mm-cm) meteoroids at the orbit of Mars and their interaction with the Martian atmosphere.  相似文献   

16.
We have studied the 27-day variations and their harmonics in Galactic cosmic ray (GCR) intensity, solar wind velocity, and interplanetary magnetic field (IMF) components during the recent prolonged solar minimum 23/24. The time evolution of the quasi-periodicity in these parameters connected with the Sun’s rotation reveals that the synodic period of these variations is ≈?26?–?27 days and is stable. This means that the changes in the solar wind speed and the IMF are related to the Sun’s near-equatorial regions in considering the differential rotation of the Sun. However, the solar wind parameters observed near the Earth’s orbit provide only the conditions in the limited local vicinity of the equatorial region in the heliosphere (within ±?7° in latitude). We also demonstrate that the observed period of the GCR intensity connected with the Sun’s rotation increased up to ≈?33?–?36 days in 2009. This means that the process that drives the 27-day GCR intensity variations takes place not only in the limited local surroundings of the equatorial region but in the global 3-D space of the heliosphere, covering also higher latitude regions. A relatively long period (≈?34 days) found for 2009 in the GCR intensity gives possible evidence of the onset of cycle 24 due to active regions at higher latitudes and rotating slowly because of the Sun’s differential rotation. We also discuss the effect of differential rotation on the theoretical model of the 27-day GCR intensity variations.  相似文献   

17.
《Icarus》1987,69(3):557-565
Standing acoustic waves, with periods between about 4.5 and 9 min, may be trapped in a wave duct beneath Jupiter's tropopause. Detection of these oscillations by observations of Doppler shifting of infrared and ultraviolet absorption lines would offer a new important method for probing the giant planet's deep atmosphere and interior. Information would be revealed on Jupiter's thermal and density structure and the depth to which its zonal winds penetrate. Standing oscillations in the molecular hydrogen envelope are modeled and their theoretical eigenfrequencies are presented as they might appear in actual data analysis. Several forcing functions for wave generation are considered. These include coupling with turbulent and convective motions, thermal overstability due to radiative transfer, effects of wave propagation in a saturated atmosphere, and consequences of ortho- to parahydrogen conversion. Altjough the forcing mechanisms couple well with the acoustic waves, allowing for possible maintenance of the oscillations, the contribution they make to velocity amplitudes is very small, between 1.0 and 0.1 m sec−1. This implies that the Doppler shifting caused by the waves may be unresolvable except, perhaps, by methods of superposing time records of oscillations to enhance acoustic signals and diminish random noise.  相似文献   

18.
A general approach to the solution of the perturbed oscillation problem for celestial bodies is considered. The solution sought describes unperturbed virial oscillations (zero approximation) affected by external perturbing effects. In the general case, these perturbations can be expressed by an arbitrary given function of time, Jacobi's function and its first derivative. Standard methods and modes of perturbation theory are used for solution of the problem.It is shown that while studying the evolution of a celestial body as a dissipative system in the framework of perturbed virial oscillations, the analytical expression for perturbing function can be derived, assuming the celestial body to be an oscillating electrical dipole emitting electromagnetic energy.The general covariant form of Jacobi's equation is derived and its spur is examined. It is shown that the scalar form of Jacobi's equation appears to be more universal than Newton's laws of motion from which it is derived.  相似文献   

19.
A detailed derivation of the effect of solar radiation pressure on the orbit of a body about a primary orbiting the Sun is given. The result is a set of secular equations that can be used for long-term predictions of changes in the orbit. Solar radiation pressure is modeled as a Fourier series in the body’s rotation state, where the coefficients are based on the shape and radiation properties of the body as parameters. In this work, the assumption is made that the body is in a synchronous orbit about the primary and rotates at a constant rate. This model is used to write explicit variational equations of the energy, eccentricity vector, and angular momentum vector for an orbiting body. Given that the effect of the solar radiation pressure and the orbit are periodic functions, they are readily averaged over an orbit. Furthermore, the equations can be averaged again over the orbit of the primary about the Sun to give secular equations for long-term prediction. This methodology is applied to both circular and elliptical orbits, and the full equations for secular changes to the orbit in both cases are presented. These results can be applied to natural systems, such as the binary asteroid system 1999 KW4, to predict their evolution due to the Binary YORP effect, or to artificial Earth orbiting, nadir-pointing satellites to enable more precise models for their orbital evolution.  相似文献   

20.
A New Ionosphere Monitoring Technology Based on GPS   总被引：1，自引：0，他引：1  
Although global positioning system (GPS) was originally planned as a satellite-based radio-navigation system for military purposes, civilian users have significantly increased their access to the system for both, commercial and scientific applications. Almost 400 permanent GPS tracking stations have been stablished around the globe with the main purpose of supporting scientific research. In addition, several GPS receivers on board of low Earth orbit satellites fitted with special antennas that focus on Earth's horizon, are tracking the radio signals broadcasted by the high-orbiting GPS satellites, as they rise and set on Earth horizon. The data of these ground and space-born GPS receivers, readily accessible through Internet in a ‘virtual observatory’ managed by the International GPS Service, are extensively used for many researches and might possibly ignite a revolution in Earth remote sensing. By measuring the changes in the time it takes for the GPS signals to arrive at the receiver as they travel through Earth's atmosphere, scientists can derive a surprising amount of information about the Earth's ionosphere, a turbulent shroud of charged particles that, when stimulated by solar flares, can disrupt communications around the world. This contribution presents a methodology to obtain high temporal resolution images of the ionospheric electron content that lead to two-dimensional vertical total electron content maps and three-dimensional electron density distribution. Some exemplifying results are shown at the end of the paper.  相似文献   

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