On the Substantial Spatial Spread of the Quadrantid Meteoroid Stream

We explored the substantial spatial spread of the Quadrantid stream, based on the backward integration of orbital motions of the Quadrantids, impulsively perturbed by Jupiter. We found that the Jovian impulses can widely spread out them in the early twentieth century, especially their perihelia extended by a factor of ∼90 than those at the observed epoch. We regarded the spread as the intrinsic one of the Quadrantid stream itself.     

The parent of the Quadrantid meteoroid stream

The Quadrantid meteor shower is one of the major showers that produces reliable displays every January. However, it is unique amongst the major showers in still not having its parent uniquely identified. One of the reasons for this may be because the stream, and presumably the parent, lies in a region of the Solar system where near-resonant motion with Jupiter, coupled with potential close encounters, is possible. Such a combination can lead to a rapid dynamical evolution of an orbit. In particular, it may be possible that the orbit of the parent both satisfies the condition for a close encounter and is in resonant motion, while most of the meteoroids cannot satisfy both conditions. This results in the parent evolving away from the bulk of the stream.
To date, two suggestions have been made regarding possible parents for the Quadrantid stream, these being Comet 1491 I and Comet 96P/Machholz. The argument in favour of the first named being the parent is because of the general similarity between the orbits around 1491. The argument for comet 96P/Machholz being the parent is based on the similarity in orbital evolution coupled with a similarity in orbits phase-shifted by 2000 yr. In this paper we suggest that on both counts asteroid 5496 (1973 NA) is more similar to the Quadrantids, and that even if 5496 is not the actual parent in the strict sense that meteoroids are currently being ejected, it is either likely to be a fragment of the parent or the dormant remains of the parent.     

The Quadrantid meteoroid complex

The Quadrantids, one of the more active of the annual meteor showers, is unusual for its strong but brief maximum within a broader background of activity. It is also notable for its recent onset, the first observation having been likely made in 1835. Until recently, no parent with a similar orbit had been observed and previous investigators concluded that the stream was quite old, with the stream's recent appearance and sharp peak attributed to a fortuitous convergence of meteoroid orbits. The discovery of the near-Earth Asteroid 2003 EH1 on an orbit very similar to that of the Quadrantids has probably unveiled the parent body of this stream [Jenniskens and Marsden, 2003. 2003 EH1 and the Quadrantids. IAU Circ. 8252]. From simulations of the orbit of this body and of meteoroids released from it at different intervals in the past, we find that both the sharp peak and recent appearance of the Quadrantids can most easily be explained by a release of meteoroids from 2003 EH1 near 1800 AD. This is supported by three lines of evidence. First, the evolution of the observed solar longitude of the Quadrantids over time is consistent with release from 2003 EH1 approximately 200 years ago. Second, numerical simulations of meteoroids released from this parent body at this time match the basic orbital characteristics of the Quadrantid stream well. Finally, these simulations also reveal that the Quadrantid core is well reproduced by a single outburst at perihelion circa 1800, whereas earlier releases result in the shower's appearance in our skies significantly prior to 1835. These results apply to the concentrated central core of the stream: the extended background was likely produced at earlier times. In fact, we find that 2003 EH1 is in a state of Kozai circulation along with a number of other comets and NEAs which may form a larger Quadrantid complex. Using the current total duration of the broader background Quadrantid activity compared to our simulations, we suggest a minimum age of ∼3500 years for the stream as a whole. This also represents the approximate lower limit for the age of the complex. We have further identified five comets as well as nine additional NEAs which may be part of the aforementioned complex, the latter all having Tisserand parameters less than three, further suggesting that the are extinct comet nuclei.     

Meteoroid streams that trace to candidate dormant comets

In an effort to identify space mission targets of interest, the association of known meteoroid streams with Near-Earth Objects (NEOs) was investigated. In addition to updating previous searches to include NEOs discovered up to January 1, 2007, a new dissimilarity criterion based on dynamical arguments was applied to evaluate the likelihood of each candidate association. The new criterion is based on the fact that the few established cases, such as 2003 EH1 and the Quadrantid stream, involve parent bodies that fragmented in the most recent nutation cycle of their secular orbital evolution. In established cases, the statistics speak strongly of an association due to the lack of NEOs in the a, e, i phase space occupied by these showers. The newly proposed associations are much more uncertain, because the odds of chance associations greatly increase as orbital inclination of the showers decreases. Forty-two plausible candidate dormant comets were identified, that deserve further scrutiny. Both comet and stream typically lack sufficient data to prove the association. Most candidate parent bodies pertain to NEOs with an aphelion distance just short of Jupiter's orbit, a perihelion distance near Earth orbit, and an eccentricity in the range 0.5-0.8. Surprisingly many have , which means that most candidate parent bodies are dormant Jupiter family comets that have not yet fully decoupled from Jupiter. Establishing these associations can provide further evidence that (mostly) dormant comets break frequently, making this the dominant mechanism for replenishing the zodiacal cloud.     

ARE ASTEROID 2003 EH1 AND COMET C/1490 Y1 DYNAMICALLY RELATED?

The orbit of asteroid 2003 EH1 is very similar to the mean orbit of the Quadrantid meteoroid stream so that a close relationship between the two is very likely. It has already been suggested that Comet C/1490 Y1 could be the parent of the Quadrantids. If this is the case, then some relationship between the comet and the asteroid might be expected. The orbit of C/1490 Y1 is based on a short observing arc of about 6 weeks and all the observations were with the naked eye, so that its elements are very poorly determined. Hence, forward integration to determine whether asteroid 2003 EH1 represents the re-discovery of the dormant nucleus of C/1490 Y1 is not feasible. Instead we choose to integrate back in time the orbit of 2003 EH1, which is far better determined, and a family of 3500 clones, all of which are moving on an orbit that is consistent with the present known orbit of 2003EH1. We compare the results primarily with the recorded observations of the comet rather than the orbit of the comet derived by Hasegawa. We find that one clone is consistent with these observations.     

Models for the Origin of the Quadrantids

We present two scenarios for production of the Quadrantid stream based on two different models for its origin: the extinct model in which 2003EH1 was an active comet that released the dust particles during past 5000 years, stopping its activity abruptly in AD 1488; and the split model; in which a catastrophic disruption of an asteroid at AD 1488 released a large number of dust particles in a single event. We calculate the orbital evolution of test particles released in both cases and derive the resulting size distribution of surviving meteoroids in the current Quadrantid stream in the form of s ^−α ds, where s denotes the radius of a meteoroid. We find α = 3.1 in the extinct model and 2.0 in the split model. In addition, the radius of the surviving meteoroids is derived as s >10 μm in the both models. We propose, based on our estimation of the infrared color ratio for the Quadrantid stream derived from both models, that infrared observations of the Quadrantid stream may determine which origin model is more reasonable.     

P/2010 TO20 LINEAR-Grauer: A comet in transition from Centaurs to the Jupiter family

The object P/2010 TO20 LINEAR-Grauer, discovered at a heliocentric distance of over 5 AU, and at first classified as a Trojan, is now believed to be a comet. This paper reports special observations of the object that have allowed a significant refinement of its orbit and investigation of its dynamic evolution. It is shown that P/2010 TO20 LINEAR-Grauer is not a Trojan yet demonstrates unusual dynamic features. In particular, the object moves in a temporary satellite orbit relative to Jupiter over the observation interval. The comet has been in the Hill sphere for about two years and has made one revolution around the planet. The jovicentric distance function has two minima, and the smallest distance is 0.075 AU. Our estimates show that, with a probability of 0.76, the comet is likely to move in a Jupiter family orbit with a perihelion distance of less than 2.5 AU. The average time for such a transition is around forty thousand years.     

On the mechanisms leading to orphan meteoroid streams

We analyse several mechanisms capable of creating orphan meteoroid streams (OMSs) for which a parent has not been identified. OMSs have been observed as meteor showers since the XIXth century and by the IRAS satellite in the 1980s. We find that the process of close encounters with giant planets (particularly Jupiter) is the most efficient mechanism to create them: only a limited section of the stream is perturbed and follows the parent body on its new orbit, while the majority of the meteoroids remain in their pre-encounter orbit or in an intermediate state, breaking the link with their parent body. Cometary non-gravitational forces can also contribute to the process since they cause the comet to drift away from its stream. However, they are not sufficient by themselves to produce an OMS. Resonances can either split or confine a stream over a long time (>1000 yr). Some meteoroid streams may look like OMSs since their parent comet is dormant or not observable (e.g. long period). Even if new techniques succeed in linking minor objects to meteoroid streams, OMSs will still exist simply because cometary nuclei are subject to complete disruption leading to their disappearance.     

An iterative method of general perturbations programmed for a computer

Hansen's classical method of general perturbations was revised from its basis on a Taylor Series expansion in the masses of the disturbing planets to an iterative method, which can start with the best theory known, or with only the mean, or osculating, orbit of the planet. The article describes the iterative Hansen's method together with some of the necessary subroutines which have been programmed to handle the series on a digital computer.The method has been tested by generating the theory of a major planet and the theory of a minor planet having a near commensurability with Jupiter and some of the results have been described in the last section of the paper.This paper is a summary of dissertation presented to the University of Cincinnati in candidacy for the degree of Doctor of Philosophy.     

The influence of the great inequality on the secular disturbing function of the planetary system

This paper derives the contributionF ₂ ^* by the great inequality to the secular disturbing function of the principal planets. Andoyer's expansion of the planetary disturbing function and von Zeipel's method of eliminating the periodic terms is employed; thereby, the corrected secular disturbing function for the planetary system is derived. An earlier solution suggested by Hill is based on Leverrier's equations for the variation of elements of Jupiter and Saturn and on the semi-empirical adjustment of the coefficients in the secular disturbing function. Nowadays there are several modern methods of eliminating periodic terms from the Hamiltonian and deriving a purely secular disturbing function. Von Zeipel's method is especially suitable. The conclusion is drawn that the canonicity of the equations for the secular variation of the heliocentric elements can be preserved if there be retained, in the secular disturbing function, terms only of the second and fourth order relative to the eccentricity and inclinations.The Krylov-Bogolubov method is suggested for eliminating periodic terms, if it is desired to include the secular perturbations of the fifth and higher order in the heliocentric elements. The additional part of the secular disturbing functionF ₂ ^* derived in this paper can be included in existing theories of the secular effects of principal planets. A better approach would be to preserve the homogeneity of the theory and rederive all the secular perturbations of principal planets using Andoyer's symbolism, including the part produced by the great inequality.     

Temporary satellite capture of comets by Jupiter

This paper studies the dynamical evolution of 97 Jupiter-family comets over an 800-year time period. More than two hundred encounters with Jupiter are investigated, with the observed comets moving during a certain period of time in an elliptic jovicentric orbit. In most cases this is an ordinary temporary satellite capture of a comet in Everhart??s sense, not associated with a transition of the small body into Jupiter??s family of satellites. The phenomenon occurs outside the Hill sphere with comets with a high Tisserand constant relative to Jupiter; the comets?? orbits have a small inclination to the ecliptic plane. An analysis of 236 encounters has allowed the determination within the planar pair two-body problem of a region of orbits in the plane (a, e) whose semimajor axes and eccentricities contribute to the phenomenon under study. Comets with orbits belonging to this region experience a temporary satellite capture during some of their encounters; the jovicentric distance function has several minima; and the encounters are characterized by reversions of the line of apsides and some others features of their combination that are intrinsic to comets in this region. Therefore, this region is called a region of comets with specific features in their encounters with Jupiter. Twenty encounters (out of 236), whereby the comet enters an elliptic jovicentric orbit in the Hill sphere, are identified and investigated. The size and shape of the elliptic heliocentric orbits enabling this transition are determined. It is found that in 11 encounters the motion of small bodies in the Hill sphere has features the most important of which is multiple minima of the jovicentric distance function. The study of these 20 encounters has allowed the introduction of the concept of temporary gravitational capture of a small body into the Hill sphere. An analysis of variations in the Tisserand constant in these (20) encounters of the observable comets shows that their motion is unstable in Hill??s sense.     

Analytical Proper Elements for the Hilda Asteroids I: Construction of a Formal Solution

In this paper, we present the mathematical basis for the calculation of proper elements for asteroids in 3:2 mean-motion resonance with Jupiter from their osculating Keplerian elements. The method is based on a new resonant Lie-series perturbation theory (Ferraz-Mello, 1997, 2002), which allows the construction of formal solutions in cases where resonant and long-period angles appear simultaneously. For the disturbing function, we used the Beaugé’s expansion (Beaugé, 1996), adapted to include short period terms. In this paper, the theory is restricted to the planar case and only the perturbations due to Jupiter are considered.     

General relativity and satellite orbits: The motion of a test particle in the Schwarzschild metric

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.     

Interplanetary dust particles near Jupiter

We calculate the expected counting rate of a flat micrometeoroid detector of finite sensitivity passing in hyperbolic orbit near a planet. We assume that the distribution of particle sizes, s, can be expressed as a power law spectrum of index p, i.e. dN(s) = Cs^?pds, and also that the particles encounter the sphere of influence of the planet with a certain speed v_∞. The results of the calculations are then compared with the results returned by Pioneer 10 in its flyby of Jupiter. The observed increase in impact rate near Jupiter can be completely explained in terms of gravitational “focusing” of particles which are in heliocentric orbits; i.e., they are not in orbit about Jupiter. The absolute concentration of particles near the orbit of Jupiter is of the same order as at 1 AU: the exact ratio being a function of particle speed and spectral index. Data from one flyby are insufficient to determine a unique value for both the spectral index, p, and the particle velocity, v_∞, but limits can be set. For reasonable encounter speeds (corresponding to eccentricities and inclinations of dust particles experienced near the Earth), the particles near Jupiter are characterized by a spectrum of index p ～ 3. The spectral index which best fits the data increases with increasing encounter speeds.     

Multiple-satellite-aided capture trajectories at Jupiter using the Laplace resonance

Satellite-aided capture is a mission design concept used to reduce the delta-v required to capture into a planetary orbit. The technique employs close flybys of a massive moon to reduce the energy of the planet-centered orbit. A sequence of close flybys of two or more of the Galilean moons of Jupiter may further decrease the delta-v cost of Jupiter orbit insertion. A Ganymede-Io sequence can save 207 m/s of delta-v over a single Io flyby. A phase angle analysis based on the Laplace resonance is used to find triple-satellite-aided capture sequences involving Io, Europa, and Ganymede. Additionally, the near-resonance of Callisto and Ganymede is used to find triple-satellite-aided capture sequences involving Callisto, Ganymede, and another moon. A combination of these techniques is used to find quadruple-satellite-aided capture sequences that involve gravity-assists of all four Galilean moons. These sequences can save a significant amount of delta-v and have the potential to benefit both NASA’s Jupiter Europa orbiter mission and ESA’s Jupiter Ganymede orbiter mission.     

On the unusual activity of the Perseid meteor shower (1989–96) and the dust trail of comet 109P/Swift–Tuttle

We present the first measurements of the radiant and orbit of meteoroids that are part of the unusual Perseid activity called the 'Perseid Filament'. This filament was encountered by Earth in the years before and after the return of the comet to perihelion in December of 1992. Between 1989 and 1996, there were brief meteor outbursts of near-constant duration with a symmetric activity profile. In 1993, however, rates increased more gradually to the peak. That gradual increase is identified here as a separate dust component, which we call the 'Nodal Blanket'. We find that the Nodal Blanket has a very small radiant dispersion. On the other hand, the Perseid Filament has a radiant that is significantly dispersed and systematically displaced by 0.3°. This dispersion implies that unusually high ejection velocities or planetary perturbations must have had time to disperse the stream. In both cases, one would expect a rapid dispersion of matter along the comet orbit. In order to explain the concentration of dust near the comet position, we propose a novel scenario involving long-term accumulation in combination with protection of the region near the comet against close encounters with Jupiter due to librations of the comet orbit around the 1:11 mean-motion resonance.     

Resonance and Capture of Jupiter Comets

A number of Jupiter family comets such as Otermaand Gehrels 3make a rapid transition from heliocentric orbits outside the orbit of Jupiter to heliocentric orbits inside the orbit of Jupiter and vice versa. During this transition, the comet can be captured temporarily by Jupiter for one to several orbits around Jupiter. The interior heliocentric orbit is typically close to the 3:2 resonance while the exterior heliocentric orbit is near the 2:3 resonance. An important feature of the dynamics of these comets is that during the transition, the orbit passes close to the libration points L ₁and L ₂, two of the equilibrium points for the restricted three-body problem for the Sun-Jupiter system. Studying the libration point invariant manifold structures for L ₁and L ₂is a starting point for understanding the capture and resonance transition of these comets. For example, the recently discovered heteroclinic connection between pairs of unstable periodic orbits (one around the L ₁and the other around L ₂) implies a complicated dynamics for comets in a certain energy range. Furthermore, the stable and unstable invariant manifold tubes associated to libration point periodic orbits, of which the heteroclinic connections are a part, are phase space conduits transporting material to and from Jupiter and between the interior and exterior of Jupiter's orbit.     

Statistics of the variations of the high-energy electron population between 7 and 28 jovian radii as measured by the Galileo spacecraft

Recent measurements of the high-energy, omni-directional electron environment by the Galileo spacecraft Energetic Particle Detector (EPD) have been analyzed in the range from 7 to 28 Jupiter radii. 10-min averages of these data between Jupiter orbit insertion in 1995 to the end of the mission have been analyzed to provide estimates of the electron differential fluxes at 1.5, 2, and 11 MeV in the jovian equatorial plane as a function of radial distance. These data provide a long term picture of the variations in the high-energy electron environment over the ∼8 years of the Galileo mission. This paper reviews those measurements and the statistics associated with them for the 8 year period. In general, the data variations are well behaved with variations being within a factor of ∼2 of a median value at a given distance from Jupiter. These results are analyzed in detail and the orbit variations discussed in the context of the overall data set. The results of this analysis of the long-term statistical variations in high-energy electron fluxes are directly applicable to models that estimate the effects of the radiation environment on Jupiter's moons and their atmospheres as they permit estimates of the possible range of radiation effects that might be expected.     

木星探测轨道分析与设计

研究了与木星探测相关的轨道设计问题.重点关注木星探测轨道与火星、金星等类地行星探测轨道的不同及由此带来的轨道设计难点.首先分析了绕木星探测任务轨道的选择.建立近似模型讨论了向木星飞行需要借助多颗行星的多次引力辅助,对地木转移的多种行星引力辅助序列,使用粒子群算法搜索了2020年至2025年之间的燃料最省飞行方案并对比得到了向木星飞行较好的引力辅助方式为金星-地球-地球引力辅助.结合多任务探测,研究了航天器在飞向木星途中穿越主小行星带飞越探测小行星的轨道设计.最后,给出2023年发射完整的结合引力辅助与小行星多次飞越的木星探测轨道设计算例.     

Precession of the orbital nodes of Jupiter and Saturn triggered by the mutual perturbation: A model of two rings

The problem of the precession of the orbital planes of Jupiter and Saturn under the influence of mutual gravitational perturbations was formulated and solved using a simple dynamical model. Using the Gauss method, the planetary orbits are modeled by material circular rings, intersecting along the diameter at a small angle α. The planet masses, semimajor axes and inclination angles of orbits correspond to the rings. What is new is that each ring has an angular momentum equal to the orbital angular momentum of the planet. Contrary to popular belief, it was proved that the orbital resonance 5: 2 does not preclude the use of the ring model. Moreover, the period of averaging of the disturbing force (T ≈ 1332 yr) proves to be appreciably greater than a conventionally used period (≈900 yr). The mutual potential energy of rings and the torque of gravitational forces between the rings were calculated. We compiled and solved the system of differential equations for the spatial motion of rings. It was established that a perturbing torque causes the precession and simultaneous rotation of the orbital planes of Jupiter and Saturn. Moreover, the opposite orbit nodes on the Laplace plane coincide and perform a secular movement in retrograde direction with the same velocity of 25.6″/yr and the period T _J = T _S ≈ 50687 yr. These results are close to those obtained in the general theory (25.93″/yr), which confirms the adequacy of the developed model. It was found that the vectors of the angular velocity of orbital rings move counterclockwise over circular cones and describe circles on the celestial sphere with radii β₁ ≈ 0.8403504° (Saturn) and β₂ ≈ 0.3409296° (Jupiter) around the point which is located at an angular distance of 1.647607° from the ecliptic pole.