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1.
The Roche Limit     
The role of tides in deforming and possibly disrupting a secondary body orbiting about a primary body has been known for a considerable time. This was first inspired by the observations of ocean tides on Earth and then seen as playing an important role in the formation and evolution of the Earth–Moon system. Finally, in the beginning of the 20th century it was generally thought to have a significant role in the formation of the solar system through the tidal disruption of the Sun. Here, an overview of the historical developments of the ideas concerned with tidal disruption of a secondary body that can lead to mass loss is given. Some discussion of possible extensions to consider more realistic situations where the secondary body may not be moving on a circular orbit and may not rotate so as to maintain the phase-on configuration to the primary body is also given.  相似文献   

2.
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   

3.
The aim of this paper is to analyze the optimal trajectories of a spacecraft subjected to a modulated radial thrust, whose magnitude is inversely proportional to the square of the distance from the primary body. This case is representative of a Sun-facing solar sail with a passive attitude control system. In this study the sailcraft is assumed to perform a finite number of reorientation maneuvers to set the propelling acceleration to zero and generate suitable coasting arcs along the trajectory. Accordingly, the resulting generalized orbit is a sequence of either propelled or ballistic conic arcs, whose main characteristics (in terms of semimajor axis, eccentricity, and perihelion radius) can be calculated in closed form. As a result, the sailcraft optimal performance can be studied using an analytical approach. In particular, some compact relationships are drawn and discussed that allow one to find the optimal sailcraft characteristics required to reach a prescribed final orbit.  相似文献   

4.
We generalize the well‐known Hill's circular restricted three‐body problem by assuming that the primary generates a Schwarzschild‐type field of the form U = A/r + B/r3. The term in B influences the particle, but not the far secondary. Many concrete astronomical situations can be modelled via this problem. For the two‐body problem primary‐particle, a homoclinic orbit is proved to exist for a continuous range of parameters (the constants of energy and angular momentum, and the field parameter B > 0). Within the restricted three‐body system, we prove that, under sufficiently small perturbations from the secondary, the homoclinic orbit persists, but its stable and unstable manifolds intersect transversely. Using a result of symbolic dynamics, this means the existence of a Smale horseshoe, hence chaotic behaviour. Moreover, we find that Hill's generalized problem (in our sense) is nonintegrable. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

5.
Jay McMahon  Daniel Scheeres 《Icarus》2010,209(2):494-509
A previous theory by the authors for detailed modeling of the binary YORP effect is reviewed and expanded to accommodate doubly-synchronous binary systems, as well as a method for non-dimensionalizing the coefficients for application to binary systems where a shape model to compute its own coefficients is not available. The theory is also expanded to account for the effects of primary J2 and the Sun’s 3rd body perturbation on the secular orbit evolution. The newly expanded theory is applied to the binary near-Earth Asteroid 1999 KW4, for which a detailed shape model is available. The result of simulation of the secular evolutionary equations shows that the KW4 orbit will be double in size in approximately 22,000 years, and will reach the Hill radius in approximately 54,000 years. The simulation also shows that the eccentricity will alternate growing and shrinking in magnitude, depending on the location of the solar node in the body-fixed frame. Therefore the eccentricity is not fixed to evolve in the opposite sign as the semi-major axis unless the circulation of the node (with a period of 500 years) is averaged out as well. The current orbit expansion rate for KW4 of 7 cm per year is shown to be detectable with observations of the mean anomaly which grows quadratically in time with an expanding orbit. Finally, the KW4 results are scaled for application to a number of other binary systems for which detailed shape models are not available. This application shows that the orbits considered can expand to their Hill radius in the range of 104-106 years. This implies rapid formation of binary systems is necessary to support the large percentage of binaries observed in the NEA population.  相似文献   

6.
《Planetary and Space Science》2006,54(9-10):988-998
The Cassini radio and plasma wave science (RPWS) instrument is sensitive to few-micron dust grains impacting on the spacecraft at relative speeds of order 10 km/s. Through the first year or so of operations in orbit at Saturn, the RPWS has made a number of both inclined and equatorial crossings of the E ring, particularly near the orbit of Enceladus. Assuming water ice grains, the typical size particle detected by the RPWS has a radius of a few microns. Peak impact rates of about 50 s−1 are found near the orbit of Enceladus corresponding to densities of order 5×10−4 m−3. The variation of dust fluxes as a function of height above or below the equator is well described by a Gaussian distribution with a scale height of about 2800 km although there is usually some non-Gaussian variation near the peak fluxes suggesting some structure in the core of the ring. Offsets of the peak number densities are typically of the order of a few hundred km from the geometric equator. A near-equatorial radial profile through the orbit of Enceladus shows a sharply peaked distribution at the orbit of the moon. A size distribution averaged over several passes through the orbit of Enceladus is determined which varies as m−2.80. The peak in dust number density at the orbit of Enceladus is consistent with previous optical measurements and strongly supports the suggestion that Enceladus is a primary source for E ring particles.  相似文献   

7.
Differential equations are derived for studying the effects of either conservative or nonconservative torques on the attitude motion of a tumbling triaxial rigid satellite. These equations, which are analogous to the Lagrange planetary equations for osculating elements, are then used to study the attitude motions of a rapidly spinning, triaxial, rigid satellite about its center of mass, which, in turn, is constrained to move in an elliptic orbit about an attracting point mass. The only torques considered are the gravity-gradient torques associated with an inverse-square field. The effects of oblateness of the central body on the orbit are included, in that, the apsidal line of the orbit is permitted to rotate at a constant rate while the orbital plane is permitted to precess (either posigrade or retrograde) at a constant rate with constant inclination.A method of averaging is used to obtain an intermediate set of averaged differential equations for the nonresonant, secular behavior of the osculating elements which describe the complete rotational motions of the body about its center of mass. The averaged differential equations are then integrated to obtain long-term secular solutions for the osculating elements. These solutions may be used to predict both the orientation of the body with respect to a nonrotating coordinate system and the motion of the rotational angular momentum about the center of mass. The complete development is valid to first order in (n/w 0)2, wheren is the satellite's orbital mean motion andw 0 its initial rotational angular speed.  相似文献   

8.
The formation of spiral structure in a galaxy, as a result of the gravitational perturbation caused by a permanent companion, is studied. It is found that spiral structure appears only when a resonance exists between the rotational frequency of the stars in the galaxy and the rotational frequency of the companion galaxy. The number of spiral arms depends strongly on the particular resonance. In the case where the companion moves in an elliptic orbit, spiral arms are formed when a resonance, inside the galactic body, exists in almost all the parts of the orbit or, at least, in the largest part of it.  相似文献   

9.
The aim of this paper is to study the dynamical problem of tidal friction in a binary system consisting of deformable components, with the restriction that the angle of lag or advance of the tidal distortion with respect to the direction of the disturbing companion is small. The fractional distortion of the bodies due to rotation and tidal interaction is also treated as a first-order small quantity, and terms up to the fourth harmonic in the tidal potential are retained. In this linear approximation, the time-dependent tidal potential can be Fourier decomposed into a spectrum of simple harmonic terms, each of which is responsible for raising a partial wave in the body; each such partial wave can then be treated independently of the others. This is the method first employed by Darwin.In Section 2, it is assumed that the phase lag in the response of the body (due to dissipation of kinetic energy of deformation) is proportional to the forcing frequency, which is justified for small amplitude oscillations of a viscous fluid or visco-elastic body. A simple expression is then obtained for the potential function for the distortion in terms of the disturbing potential and the structure of the body.In Section 3, the distortion potential function is employed in deriving the componentsR, S andW of the disturbing force which are then substituted in the Gaussian form of the equations for variation of the elements. In Section 4, the Eulerian equations for motion of deformable bodies are derived, using the so-called mean axes of the body as the rotating axes of reference. In Section 5, it is shown that the dynamical effects of rotational distortion occur on a much shorter time scale than those arising from tidal friction, which allows one to consider the two phenomena as acting independently of one another. The collected set of Gaussian (orbital) and Eulerian (body) equations is re-written in terms of dimensionless variables for the tidal friction case, and the stability of the system is examined on the basis of these equations.In Section 6, the tidal friction equations are integrated numerically for the close binary system AG Persei and for the Earth-Moon system. In the former, the integrations were started from a highly elliptical orbit and the system was found to relax into a circular orbit, with synchronous rotation perpendicular to the orbit. In the latter, the integrations were performed backwards in time from the present day, and it was found that the lunar orbit rapidly becomes highly elliptical at the time of closest approach, thus indicating a probable capture of the Moon by the Earth. This result is in agreement with that obtained by other investigators; however, it is shown that the detailed behaviour of the system at the time of capture, in particular the inclination of the lunar orbit to the ecliptic, depends critically on the chosen rate of dissipation in the Moon's interior. A simple argument is presented which allows an estimation for the mean viscosity of a fluid body from the known age of the system: for the components of AG per, the result is 2×1011 g cm–1 s–1, indicating that the stars must have possessed turbulent convective outer regions during some part of their tidal evolution, while for the Earth, the result, is 1.4×1012 g cm–1 s–1. It is shown that the angle of tidal lag in nonsynchronous close binary systems in general is expected to be extremely small, and not observationally detectable.  相似文献   

10.
Within the model of solid-body accumulation of planets (or their nuclei) the accumulation and migration of bodies from the feeding zones of the giant planets are investigated. The investigation is based on results of computer simulation of evolving disks which initially consisted of hundreds of particles moving about the Sun and coagulating under collisions. In some models the disks initially consisted of identical bodies. In other models they included also almost-formed planets. The computer simulation results as well as analytical investigations of the disk evolution depending on the number of particles in the disk allowed some estimates and conclusions on the accumulation process when the number of initial bodies was great (~ 106–1012). In this paper the characteristics of an initial protoplanetary circumsolar cloud, the body migration in the forming solar system, the planet orbit evolution, the formation of the beyond-Neptune belt and asteroid belts between the giant planet orbits are considered. The results obtained confirm many analytical estimates earlier made by V. S. Safronov and his colleagues.  相似文献   

11.
Abstract— Data on the trajectory and orbit of an extremely bright bolide (superbolide) over Greenland on 1997 December 9 are given, and circumstances of the phenomenon and its observations are described. A surveillance video camera and satellite‐based records enabled computing the trajectory and orbit independently of visual sightings of casual observers. The superbolide body of about 36 000 kg penetrated the atmosphere with an initial velocity of 30.5 ± 1.7 km s?1. Its orbit was a long‐period orbit and seems to be at variance with the low value of ablation coefficient (0.017 kg MJ?1) derived from modeling the atmospheric trajectory. However, such an event has been documented previously. Also the intensity and brevity of the satellite‐detected light flares are highly unusual. The impact area of the main hypothetical remnant of the body is given. Search for meteorites was performed. No meteorites were recovered. Also analysis of snow samples gave no hint of meteoritic dust.  相似文献   

12.
The temperatures of electrons and ions in the post-shock accretion region of a magnetic cataclysmic variable (mCV) will be equal at sufficiently high mass flow rates or for sufficiently weak magnetic fields. At lower mass flow rates or in stronger magnetic fields, efficient cyclotron cooling will cool the electrons faster than the electrons can cool the ions and a two-temperature flow will result. Here we investigate the differences in polarized radiation expected from mCV post-shock accretion columns modeled with one- and two-temperature hydrodynamics. In an mCV model with one accretion region, a magnetic field ?30 MG and a specific mass flow rate of ～0.5 g?cm?2?s?1, along with a relatively generic geometric orientation of the system, we find that in the ultraviolet either a single linear polarization pulse per binary orbit or two pulses per binary orbit can be expected, depending on the accretion column hydrodynamic structure (one- or two-temperature) modeled. Under conditions where the physical flow is two-temperature, one pulse per orbit is predicted from a single accretion region where a one-temperature model predicts two pulses. The intensity light curves show similar pulse behavior but there is very little difference between the circular polarization predictions of one- and two-temperature models. Such discrepancies indicate that it is important to model some aspect of two-temperature flow in indirect imaging procedures, like Stokes imaging, especially at the edges of extended accretion regions, were the specific mass flow is low, and especially for ultraviolet data.  相似文献   

13.
The Hill stability of the low mass binary system in the presence of a massive third body moving on a wider inclined orbit is investigated analytically. It is found that, in the case of the third body being on a nearly circular orbit, the region of Hill stability expands as the binary/third body mass ratio increases and the inclination (i) decreases. This i-dependence decreases very quickly with increasing eccentricity (e 2) of the third body relative to the binary barycentre. In fact, if e 2 is not extremely small, the Hill stable region can be approximately expressed in a closed form by setting i = 90°, and it contracts with increasing e 2 as ${e_2^2}$ for sufficiently low mass binary. Our analytic results are then applied to the observed triple star systems and the Kuiper belt binaries.  相似文献   

14.
The equations of motion for a third body of small mass are developed in the problem where the two primary bodies are in hyperbolic orbits about each other. The equations are applied to a hypothetical star-sun-comet system to determine the effect of the stellar encounter on the orbit of the comet.This paper is part of a doctoral thesis completed at the University of Illinois at Urbana-Champaign.  相似文献   

15.
Analytical equations describing the velocity and energy variation of a spacecraft in a Powered Swing-By maneuver in an elliptic system are presented. The spacecraft motion is limited to the orbital plane of the primaries. In addition to gravity, the spacecraft suffers the effect of an impulsive maneuver applied when it passes by the periapsis of its orbit around the secondary body of the system. This impulsive maneuver is defined by its magnitude \(\delta V\) and the angle that defines the direction of the impulse with respect to the velocity of the spacecraft (\(\alpha\)). The maneuver occurs in a system of main bodies that are in elliptical orbits, where the velocity of the secondary body varies according to its position in the orbit following the rules of an elliptical orbit. The equations are dependent on this velocity. The study is done using the “patched-conics approximation”, which is a method of simplifying the calculations of the trajectory of a spacecraft traveling around more than one celestial body. Solutions for the velocity and energy variations as a function of the parameters that define the maneuver are presented. An analysis of the efficiency of the powered Swing-By maneuver is also made, comparing it with the pure gravity Swing-by maneuver with the addition of an impulse applied outside the sphere of influence of the secondary body. After a general study, the techniques developed here are applied to the systems Sun-Mercury and Sun-Mars, which are real and important systems with large eccentricity. This problem is highly nonlinear and the dynamics very complex, but very reach in applications.  相似文献   

16.
This paper studies the stability of Triangular Lagrangian points in the model of elliptical restricted three body problem, under the assumption that both the primaries are radiating. The model proposed is applicable to the well known binary systems Achird, Luyten, αCen AB, Kruger-60, Xi-Bootis. Conditional stability of the motion around the triangular points exists for 0≤μ≤μ ?, where μ is the mass ratio. The method of averaging due to Grebenikov has been exploited throughout the analysis of stability of the system. The critical mass ratio depends on the combined effects of radiation of both the primaries and eccentricity of this orbit. It is found by adopting the simulation technique that the range of stability decreases as the radiation pressure parameter increases.  相似文献   

17.
Binaries in the Kuiper-belt are unlike all other known binaries in the Solar System. Both their physical and orbital properties are highly unusual and, because these objects are thought to be relics dating back to the earliest days of the Solar System, understanding how they formed may provide valuable insight into the conditions which then prevailed. A number of different mechanisms for the formation of Kuiper-belt binaries (KBBs) have been proposed including; two-body collisions inside the Hill sphere of a larger body; strong dynamical friction; exchange reactions; and chaos assisted capture. So far, no clear consensus has emerged as to which of these mechanisms (if any) can best explain the observed population of KBBs. Indeed, the recent characterization of the mutual orbit of the symmetric (i.e., roughly equal mass) KBB 2001 QW322 has only served to complicate the picture because its orbit does not seem readily explicable by any of the available models. The binary 2001 QW322 stands out even among the already unusual population of KBBs for the following reasons: its mutual orbit is extremely large (≈105 km or about 30% of the Hill sphere radius), retrograde, it is inclined ≈120° from the ecliptic and has very low eccentricity, i.e., e ≤ 0.4 (and possibly e ≤ 0.05). Here we propose a hybrid formation mechanism for this object which combines aspects of several of the mechanisms already proposed. Initially two objects are temporarily trapped in a long-living chaotic orbit that lies close to a retrograde periodic orbit in the three-dimensional Hill problem. This is followed by capture through gravitational scattering with a small intruder object. Finally, weak dynamical friction gradually switches the original orbit “adiabatically” into a large, almost circular, retrograde orbit similar to that actually observed.  相似文献   

18.
J. Klinger 《Icarus》1981,47(3):320-324
We consider spheres of water ice of about 1 km in radius moving on three different orbits with a common perihelion distance of 8 AU. As evaporation is negligible in these cases, we call them inactive ice bodies. The surface temperature has been numerically calculated for two extreme situations: (1) The spheres are composed of amorphous ice with a heat conduction to the interior presumed to be negligible. (2) The spheres are composed of compact hexagonal ice with a heat conduction coefficient known from laboratory experiments. Whereas in case 1 the temperature is an unambiguous function of heliocentric distance, in case 2 we observe a thermal “hysteresis” and the maximum temperature has a phase lag with respect to perihelion. The perihelion temperature depends on the eccentricity of the orbit. The case of active ice bodies is also discussed. We come to the conclusion that an ice body moving on the orbit of Tempel 2 must contain crystalline ice and the variations of the surface temperature must be smoothed out in an important way. In the case of Halley's orbit, we suppose that the center of the ice body still contains large amounts of amorphous ice.  相似文献   

19.
We carried out new observations of the binary asteroid 22 Kalliope (S2/2001) with the Shane 3-m telescope of the Lick observatory in October and November 2001. With a FWHM (full width at half maximum) of 0″.2, Kalliope (apparent size of about 0″.15) was not resolved but it was possible to separate the secondary from its primary whose apparent separation was of the order of 0″.7 with a magnitude difference of 3.22±0.20. As each set of observations spanned a few days of time, they are well distributed along the secondary's orbit, enabling us to accurately estimate its orbit.The satellite orbits 22 Kalliope in a prograde manner with respect to Kalliope's rotational spin (which is in a retrograde sense relative to its orbit around the Sun), on a highly inclined (i=19.8±2.0 with respect to the equator of 22 Kalliope) and moderately eccentric orbit (e=0.07±0.02) with an orbital period of 3.58±0.08 days. The semi-major axis is 1020±40 km. Using Kalliope's diameter as determined from IRAS data, the asteroid's bulk density is about 2.03±0.16 g cm−3, suggestive of a highly porous body with a porosity of 70% considering that the grain density of its meteoritic analog is of ∼7.4 g cm−3. This suggests a rubble pile, rather than solid, body. The measured nodal precession rate of the secondary's orbit seems to be much higher than expected from Kalliope's oblateness, assuming a homogeneous body (constant density). This suggests that Kalliope may be 60% more elongated or 35% larger than presently believed or/and that its internal structure is highly inhomogeneous with a denser outer shell.  相似文献   

20.
Two different procedures for analytically modeling the effects of the Moon's direct gravitational force on artificial Earth satellites are discussed from theoretical and numerical viewpoints. One is developed using classical series expansions of inclination and eccentricity for both the satellite and the Moon, and the other employs a method of averaging. Both solutions are seen to have advantages, but it is shown that while the former can be more accurate in special situations, the latter is quicker and more practical for the general orbit determination problem where observed data is used to correct the orbit in near real time.This work was sponsored with the support of the Department of the Air Force under contract F19628-85-C-0002. The views expressed are those of the author and do not reflect the official policy or position of the US Government.  相似文献   

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