Low-eccentricity Orbits Research Articles

Dust particles beyond the asteroid belt—a study based on recent results of the Ulysses dust experiment

Dust fluxes detected by the Ulysses dust experiment beyond the asteroid belt, their possible sources and the possibilities of comparing them to observations of dust in the Zodiacal light are discussed. The dust fluxes detected at solar distances about r < 2.5 AU are compatible with a population of interplanetary dust particles moving on low eccentricity and low inclination orbits. However, different orbital parameters are required in order to explain the data obtained beyond this region. The analysis of impact directions and related inclinations of orbits points to the existence of an interstellar dust stream (see Grün et al., Nature 362, 428–430, 1993) that makes up about 50% of the particles detected in the outer solar system. Further components of the dust flux seem to be randomly oriented and on high eccentricity or unbound orbits. The activity of long period comets yields a possible source: from the analysis of radiation pressure particles of submicron size are expected to be in unbound orbits, whereas larger particles stay coupled to the solar system. Comparison to the out-of-ecliptic distribution of dust derived from Zodiacal cloud models, shows that this outer dust cloud has only a small influence on the Zodiacal light brightness. However, it is shown, that detailed observations of the spectral variation in the infrared brightness could help for a better understanding. Also the compatibility of submicron dust, predominant in flux data, and larger particles, predominant in brightness data, is shown to be not as clear in the outer dust cloud as in the inner solar system dust cloud.

Dynamical and Observational Constraints on Satellites in the Inner Pluto-Charon System

It is not known if Pluto has other satellites besides its massive partner Charon. In the past, searches for additional satellites in the Pluto-Charon system have extended from the Solar-tidal stability boundary (≈90 arcsec from Pluto) inward to about 1 arcsec from Pluto. Here we further explore the inner (i.e., <10 arcsec) region of the Pluto-Charon system to determine where additional satellites might lie. In particular, we report on (i) dynamical simulations to delineate the region where unstable orbits lie around Charon, (ii) dynamical simulations which use the low orbital eccentricity of Charon to constrain the mass of any third body near Pluto, and (iii) analysis of HST archival images to search for satellites in the inner Pluto-Charon system. Although no objects were found, significant new constraints on bodies orbiting in the inner Pluto-Charon system were obtained.

Zodiacal Dust Bands

One of the outstanding problems in solar system science is the source of the particles that constitute the zodiacal cloud. The zodiacal dust bands discovered by IRAS have a pivotal role in this debate because, without doubt, they are the small, tail end products of asteroidal collisions. Geometrical arguments are probably the strongest and the plane of symmetry of the dust bands places their source firmly in the asteroid belt. A cometary source, Comet Encke for example, could exist at the distance of the mainbelt, but the dynamics of cometary orbits makes the formation of cometary dust bands impossible, unless, of course, there is a significant (comparable in volume to the asteroidal families) source of comets interior to the orbit of Jupiter with low (asteroidal) orbital eccentricities. We have suggested that the dust bands are associated with the prominent asteroidal families. The link with the Themis and Koronis families is good but the link with Eos remains to be proved. We show here by detailed modeling that even though the filtered infrared flux in the 25μm waveband associated with the dust bands is only ~1% of the total signal, this is only the “tip of the iceberg” and that asteroidal dust associated with the bands constitutes ~10% of the zodiacal cloud. This result, plus the observed size-frequency distribution of mainbelt asteroids and the observed ratio of the number of family to non-family asteroids allows us to estimate that asteroidal dust accounts for about one third of the zodiacal cloud. The discovery of the “leading-trailing” asymmetry of the zodiacal cloud in the IRAS data and our interpretation of this asymmetry in terms of a ring of asteroidal particles in resonant lock with the Earth is important for two reasons. (1) The existence of the ring strongly suggests that large (diameter ≥ 12μm) asteroidal particles (or particles with low orbital eccentricities) are transported to the inner solar system by drag forces. (2) The observed ratio of the trailing-leading asymmetry allows an independent estimate of the contribution of asteroidal particles to the zodiacal cloud. These new results have important implications for the source of the interplanetary dust particles (IDPs) collected at the Earth. Because asteroidal particles constitute about one third of the zodiacal cloud and are transported to the inner solar system by drag forces, gravitational focussing by the Earth that results in the preferential capture of particles from orbits with low inclinations and low eccentricities and the possible “funneling” effect of the ring itself, imply that nearly all of the unmelted IDPs collected at the Earth are asteroidal.

Dust Measurements in the Outer Solar System

In-situ measurements of micrometeoroids provide information on the spatial distribution of interplanetary dust and its dynamical properties. Pioneers 10 and 11, Galileo and Ulysses spaceprobes took measurements of interplanetary dust from 0.7 to 18 AU distance from the sun. Distinctly different populations of dust particles exist in the inner and outer solar system. In the inner solar system, out to about 3 AU, zodiacal dust particles are recognized by their scattered light, their thermal emission and by in-situ detection from spaceprobes. These particles orbit the sun on low inclination (i ≤ 30°) and moderate eccentricity (e ≤ 0.6) orbits. Their spatial density falls off with approximately the inverse of the solar distance. Dust particles on high inclination or even retrograde trajectories dominate the dust population outside about 3 AU. The dust detector on board the Ulysses spaceprobe identified interstellar dust sweeping through the outer solar system on hyperbolic trajectories. Within about 2 AU from Jupiter Ulysses discovered periodic streams of dust particles originating from within the jovian system.

The gravitational sculpting of the Kuiper belt

Results are presented of numerical integrations over billion year time scales of the orbital evolution of more than one thousand test particles on initially low-inclination, low-eccentricity orbits within the proposed Kuiper belt beyond Neptune. Particles which eventually crossed Neptune's orbit often showed long periods (up to several billion years) of relatively low-eccentricity oscillations punctuated by a very rapid jump to Neptune-crossing eccentricity. This flux may be the ultimate source of present-day short-period comets. It is found here that there exists a correlation between Liapunov and crossing times in the Kuiper belt. None of the particles in the study with Liapunov time scales greater than about 1 Myr actually became a Neptune-crosser in 4 Gyr. An intricate structure to the region between 35 and 45 AU is found at the end of the billion year simulation. Implications for the origins of short-period comets and the detectability of objects currently in the Kuiper belt are discussed.

Air drag correction for satellite orbits of low eccentricity

A method is derived for removing the perturbations in eccentricity due to the effects of air drag, on satellite orbits of low eccentricity and, in particular, for those lying in planes inclined at angles close to the critical angle of inclination of 63.4°, for which the oscillation in eccentricity due to the Earth’s gravity field is significantly large.

The contraction of satellite orbits under the influence of air drag. VII. Orbits of high eccentricity, with scale height dependent on altitude

Part III of this series of papers developed the theory of high-eccentricity orbits ( e &gt; 0.2) in an atmosphere having an exponential variation of air density with height, that is, with the density scale height H taken as constant. Part IV derived the appropriate theory for low-eccentricity orbits ( e &lt; 0.2) in a more realistic atmosphere where H varies linearly with height y (and μ = d H /d y &lt; 0.2). The present paper treats the orbits of part III when they meet the air drag specified by the atmospheric model of part IV. Equations are derived showing how the perigee height varies with eccentricity, and the eccentricity varies with time, over the major part of the satellite’s life. It is shown that the theory of part III remains valid, to order μ 2 , if H is evaluated at a specific height above perigee.

The frequency and intensity of comet showers from the Oort cloud

We simulate the Oort comet cloud to study the rate and properties of new comets and the intensity and frequency of comet showers. An ensemble of ∼10 6 comets is perturbed at random times by a population of main sequence stars and white dwarfs that is described by the Bahcall-Soneira Galaxy model. A cloning procedure allows us to model a large ensemble of comets efficiently, without wasting computer time following a large number of low eccentricity orbits. For comets at semimajor axis a = 20,000 AU, about every 100 myr a star with mass in the range 1 M ⊙−2 M ⊙ passes within ∼10,000 AU of the Sun and triggers a shower that enhances the flux of new comets by more than a factor of 10. The time-integrated flux is dominated by the showers for comets with semimajor axes less than ∼30,000 AU. For semimajor axes greater than ∼30,000 AU the comet loss rate is roughly constant and strong showers do not occur. In some of our simulations, comets are also perturbed by the Galactic tidal field. The inclusion of tidal effects increases the loss rate of comets with semimajor axes between 10,000 and 20,000 AU by about a factor of 4. Thus the Galactic tide, rather than individual stellar perturbations, is the dominant mechanism which drives the evolution of the Oort cloud.

A Cowell-based semi-analytical procedure for generating orbits of low eccentricity

A new approach to the semi-analytical modelling of Earth-satellite motion is proposed. It is based on the standard Cowell procedure in which the satellite's equations of motions are integrated numerically, but it uses analytical formulae for the high-frequency perturbations associated with geopotential harmonics of high degree; this avoids the need for very short integration steps. As the integration procedure dominates in the new approach, it differs fundamentally from the author's earlier method in which all the short-period perturbations are analytically represented and a minimal Euler integration operates on a set of mean orbital elements. Thus much less mathematical development is now necessary and it should be possible to produce operational software in a relatively short timescale.

A New Approach to Evaluate Planetary Perturbations on a Cloud of Dust in Low Eccentricity Heliocentric Orbits

AbstractDynamical perturbations on ensembles of particles in heliocentric orbits of low eccentricity are integrated over time. The dust is perturbed by radiation pressure, Poynting-Robertson drag, their corpuscular counterparts, and by gravitation due to any number of planets. A dust cloud is represented by a set of centroids and orbital dispersions (about the centroids). Gravitational perturbations on the centroid are derived from a single matrix, valid for any planet, in the appropriate frame of reference. After transformation of the time derivatives to a common coordinate system, the perturbation rates are summed up and integrated. The time dependence of the planets’ orbital elements are evaluated inside the time integral.

Intercept probability of satellites in circular orbits

An analytical and computational approach is provided to calculate the probability that a designated transmitter satellite in circular orbit will intercept a particular receiver satellite also in circular orbit. The term intercept implies that the transmitter satellite passes within some minimum distance of the receiver satellite for a minimum period of time. The probability calculated is the probability of interception within some maximum time interval. This paper discusses the dynamics and definitions leading to intercept probability calculations and compares the predicted intercept probabilities to estimates determined through Monte Carlo techniques. HE problem posed in this paper can be defined as a form of communication s problem. Assume that one satellite in a circular orbit must transmit information to another satellite in circular orbit within some specified period of time, 7}. Furthermore, assume that a transmission time of at least tt s must be allowed, and the transmitter must be within a range R of the receiver for the communication to take place. Then, an important parameter of this communications problem is the probability that the transmitter will be within R for at least tt within 7} starting from some random initial time. Throughout the remainder of this paper the transmitter will be called a platform and the receiver will be called the target. An intercept will be defined to be the event of the platform passing within the distance R of the target for at least tt s. Therefore, the problem can be restated to be the calculation of the probability of interception within the interval 7} assuming a random starting time. An obvious solution to this problem is to simply simulate the trajectories of the platform and target and, using random initial positions of the satellites, estimate the probability of intercept using a Monte Carlo technique. However, Monte Carlo techniques, although effective, provide little insight into the understanding of the problem. A similar problem involving the collision of satellites has been studied by several authors.13 A simplified collision problem treats essentially the same types of parameters: the probability that two orbiting objects will pass within some specified distance within some specified time. However, the distance is typically on the order of meters in the collision problem and kilometers in the intercept problem, and the time is on the order of months and years in the collision problem and hours in the intercept problem. Perhaps a more significant difference is that an intercept is an event that occurs over a time interval, whereas a collision is essentially a point event. Despite these differences both problems share many areas of common interest. The primary purpose of this paper is to provide an analytical model for understanding and calculating the probability of intercept. It will be assumed throughout this paper that the platform and target are both in circular orbits. Although this assumption appears rather restrictive, it does lead to a tractable problem and provides a close approximation for low eccentricity orbits. Furthermore, the solution also provides some interesting and potentially valuable insights into the variation of intercept probability. It should be noted at this point that the probability calculations also ignore the effects of precession. The error introduced by this omission will be

Direct determination of gravitational harmonics from low‐low GRAVSAT data

An efficient method is developed to compute gravitational harmonics from low‐low satellite‐satellite range rate measurements. The satellites are assumed to be in nearly the same low eccentricity orbits. The residual range rate signal is modeled with frequencies derived from linear perturbation theory to an accuracy of about 99%. Significant nonlinear effects involving J2, not currently modeled, require both J2 and J3 to be known in the reference trajectories. Each harmonic (l, m) generates l+ 1 principal frequencies, but they are not unique. Yet it appears possible to design a low‐altitude mission which keeps the pair at nearly constant separation and where the frequencies for all terms to (180,180) are separable after only about 4 weeks. A simple demonstration of the method is shown to recover (in two iterations) a complete (4,4) model (less J2 and J3) from 1 day of “perfect” measurements (every 7 min) generated by numerical integration. In this result, the effects of orbit determination are included in a crude way, but no other gravitational effects (of higher degree or from luni‐solar attraction) are present. Nevertheless, the method is easily extended to high degree with rapid new techniques (which are described) for calculating the required inclination functions of the orbits.

Brunhes-Matuyama magnetic reversal dated at 790,000 yr B.P. by marine-astronomical correlations

The presence of the Brunhes-Matuyama magnetic reversal in deep-sea core sediments makes possible an alternative to the usual K/Ar radioistope method of dating the reversal as found in rocks. The alternative method uses correlations of Northern Hemisphere summer insolation with oxygen-isotope ratios from tropical cores. The latitude-dependent insolation variations are calculated from planetary mechanics and thus provide a highly accurate astronomical time scale. The insolation variations strongly influence glacial-ice volume fluctuations that dominate the oxygenisotope ratio changes recorded in core sediments. The summer half-year insolation variations are identified with corresponding isotope-ratio changes in cores from the present through glacial Stage 20. Misleading effects of discontinuities or major nonuniformities of sediment deposition are avoided by an analysis of the uniformity of V28-238 and V28-239, the principal cores studied, and by comparisons with other cores. The top section (Stages 1 to 10) of V28-238 is uniformly deposited, and for this section an isotope-ratio time scale is chosen that agrees with the thorium-uranium date for the high sea stand of the last interglacial extreme. Over this interval, major glacial extremes (strong isotope-ratio minima) coincide consistently with major insolation minima at times of low orbital eccentricity. In addition interstadials are directly associated with precessional insolation peaks, and the envelope of isotope-ratio peaks resembles the envelope of precessionally dominated insolation peaks. The assumption that the glacial extremes depended similarly on insolation minima during Stages 10 to 20 permits minor age shifts of strong isotope-ratio minima in the two cores (relative to ages based on uniform overal deposition) to match the ages of low-eccentricity insolation minima. The age shifts reflect residual nonuniformities of deposition. The validity of this matching procedure is supported by a resulting consistent identification of principal isotope-ratio peaks with high- and low-latitude coincident insolation maxima. The Brunhes-Matuyama reversal is found intinterglacial Stage 19, and is dated on the astronomical time scale at 790,000 ± 5000 yr B.P.

A second-order satellite orbit theory, with compact results in cylindrical coordinates

First-order perturbations of a low-eccentricity satellite orbit due to the general harmonic coefficientJ1mof the Earth’s gravitational field are derived, and compactly expressed (see equations (92)-(94)) in cylindrical polar coordinates. For the dominant harmonicJ2, the perturbations are taken to second order, and it is shown how formulae for the second-order variation of the orbital elements depend on the definition of the mean elements used for reference. With a particular choice of mean elements, the formulae for perturbations in cylindrical coordinates are again very compact (see equations (297), (315) and (321)). The general approach also yields first-order perturbations due to lunisolar gravity and eclipse-free solar radiation. The paper finishes with a set of untruncated expressions (valid for any eccentricity) forJ2/2 secular and long-periodic perturbations.

THE MASSIVE HOT BINARY 29 CANIS MAJORIS.

ABSTRACT The results are presented from analysis of 16 high- and medium-dispersion spectrograms of the system. Mass loss from the primary has a strong dependence on phase in an orbit of low eccentricity. No change in period is detected but the primary star amplitude shows an 10 % increase over the value derived from observations in 1957. The secondary spectrum is described and the fundamental parameters of the stars and their evolutionary status are discussed. Key words: early-type stars-binaries-mass loss

Paleoclimate, paleomagnetism and the eccentricity of the Earth's orbit

Climatic changes, geomagnetic intensity fluctuations, and variations of the eccentricity of the earth's orbit during the past 0.8 m. y. are compared. In general, warm climate stages are aligned with low magnetic field intensities and high orbital eccentricity. We tentatively conclude that the eccentricity of the earth's orbit may partially modulate both the earth's magnetic field and climate.

Minor planets and comets in libration about the 2:1 resonance with Jupiter

view Abstract Citations (30) References (27) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Minor planets and comets in libration about the 2:1 resonance with Jupiter. Franklin, F. A. ; Marsden, B. G. ; Williams, J. G. ; Bardwell, C. M. Abstract We examine the orbits of minor planets in a search for objects librating about the 2:1 mean-motion resonance with Jupiter. Some 30 candidates are found among the Palomar-Leiden Survey and other unnumbered minor planets. Although almost all the orbits are very uncertain, there does seem to be an indication that librators of low orbital eccentricity do exist, contrary to the hypothesis by Giffen. We also tabulate data describing 12 comets that are temporarily librating about the 2:1 resonance. Finally, we present a discussion of what are apparently 'apocentric' librations. This type of libration, of which we find seven representatives among the numbered minor planets, can occur only for sufficiently small eccentricity. For such bodies, the role of Jupiter's eccentricity is vital; it is associated with a continuing alternation between apocentric libration and an oscillation of the line of apsides. Publication: The Astronomical Journal Pub Date: September 1975 DOI: 10.1086/111806 Bibcode: 1975AJ.....80..729F Keywords: Asteroids; Comets; Jupiter (Planet); Librational Motion; Orbital Elements; Planetary Orbits; Circular Orbits; Eccentric Orbits; Resonance; Saturn (Planet); Tables (Data); Lunar and Planetary Exploration full text sources ADS |

Origin of Cosmic Rays, Atomic Nuclei and Pulsars in Explosions of Massive Stars

Explosions of massive stars (8 ≲ M/M⊙ ≲ 70) are examined as the source of galactic cosmic rays. Detailed nucleosynthetic and evolutionary calculations suggest that these massive stars produce the heavy elements (carbon and above) in their proper relative abundances. This is particularly significant because lower mass stars (in particular the 4–8 M⊙ range) are not able to produce the observed abundances of C and O relative to the iron peak. A small (~ 1.4 M⊙) dense remnant star (a neutron star) left after the explosion may provide a location for an electromagnetic acceleration mechanism. Those abundance ratios which can now be predicted (He, C, O, Ne, Mg) for the material to be accelerated by the pulsar give a reasonable match to the observed cosmic ray data. The conditions at the outer edge of the remnant and the inner edge of the ejected material may be appropriate for an r-process to occur; the high Z cosmic rays seem to show an enrichment of r-process material. It appears that these stars may be the astrophysical source for the galactic cosmic rays. The questions of rotation and black hole formation were discussed. It appears that the most straight-forward result of evolution of a close massive binary is a massive star and a neutron star in a low eccentricity orbit, in agreement with observation.

LR Cen is not Cen X-3.

THE eclipsing variable LR Cen has been suggested1,2 as a candidate for the optical counterpart of Cen X–33 on the basis of the near coincidence of the position and period of LR Cen with those of Cen X–3. My observations4 and those of Kristian et al.1 show that in March, the time of eclipse of the secondary of LR Cen nearly coincided with that of Cen X–3. Also LR Cen and Cen X–3 both have orbits of low eccentricity; thus, LR Cen and Cen X–3 have similar positions, periods, phases and eccentricities.

Interaction between attitude libration and orbital motion of a rigid body in a near keplerian orbit of low eccentricity

Interaction between orbital motion and attitude libration dynamics of an arbitrary rigid body moving in a central Newtonian field is considered to second order. Advantage is taken of the decoupling between inplane-pitch and roll-yaw out-of-plane motion to restrict the motion to the orbital plane by an appropriate choice ofinitial conditions. An averaged solution to the nonlinear inplane-pitch equations whose accuracy is determined by ignoring terms of order {e·G32/a 2, e2,αe2,G32/a 2} and higher is presented. The results show that the near-resonant motion is characterized by a periodic interchange of energy between the attitude and orbital motion.