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NASA NTRS2011

Dynamical Evolution of Meteoroid Streams, Developments Over the Last 30 Years

As soon as reliable methods for observationally determining the heliocentric orbits of meteoroids and hence the mean orbit of a meteoroid stream in the 1950s and 60s, astronomers strived to investigate the evolution of the orbit under the effects of gravitational perturbations from the planets. At first, the limitations in the capabilities of computers, both in terms of speed and memory, placed severe restrictions on what was possible to do. As a consequence, secular perturbation methods, where the perturbations are averaged over one orbit became the norm. The most popular of these is the Halphen- Goryachev method which was used extensively until the early 1980s. The main disadvantage of these methods lies in the fact that close encounter can be missed, however they remain useful for performing very long-term integrations. Direct integration methods determine the effects of the perturbing forces at many points on an orbit. This give a better picture of the orbital evolution of an individual meteoroid, but many meteoroids have to be integrated in order to obtain a realistic picture of the evolution of a meteoroid stream. The notion of generating a family of hypothetical meteoroids to represent a stream and directly integrate the motion of each was probably first used by Williams Murray & Hughes (1979), to investigate the Quadrantids. Because of computing limitations, only 10 test meteoroids were used. Only two years later, Hughes et. al. (1981) had increased the number of particles 20-fold to 200 while after a further year, Fox Williams and Hughes used 500 000 test meteoroids to model the Geminid stream. With such a number of meteoroids it was possible for the first time to produce a realistic cross-section of the stream on the ecliptic. From that point on there has been a continued increase in the number of meteoroids, the length of time over which integration is carried out and the frequency with which results can be plotted so that it is now possible to produce moving images of the stream. As a consequence, over recent years, emphasis has moved to considering stream formation and the role fragmentation plays in this.

Williams, I. P.↗
NASA NTRS2000

Terrestrial planet and asteroid formation in the presence of giant planets. I. Relative velocities of planetesimals subject to Jupiter and Saturn perturbations

We investigate the orbital evolution of 10(13)- to 10(25) -g planetesimals near 1 AU and in the asteroid belt (near 2.6 AU) prior to the stage of evolution when the mutual perturbations between the planetesimals become important. We include nebular gas drag and the effects of Jupiter and Saturn at their present masses and in their present orbits. Gas drag introduces a size-dependent phasing of the secular perturbations, which leads to a pronounced dip in encounter velocities (Venc) between bodies of similar mass. Plantesimals of identical mass have Venc approximately 1 and approximately 10 m s-1 (near 1 and 2.6 AU, respectively) while bodies differing by approximately 10 in mass have Venc approximately 10 and approximately 100 m s-1 (near 1 and 2.6 AU, respectively). Under these conditions, growth, rather than erosion, will occur only by collisions of bodies of nearly the same mass. There will be essentially no gravitational focusing between bodies less than 10(22) to 10(25) g, allowing growth of planetary embryos in the terrestrial planet region to proceed in a slower nonrunaway fashion. The environment in the asteroid belt will be even more forbidding and it is uncertain whether even the severely depleted present asteroid belt could form under these conditions. The perturbations of Jupiter and Saturn are quite sensitive to their semi-major axes and decrease when the planets' heliocentric distances are increased to allow for protoplanet migration. It is possible, though not clearly demonstrated, that this could produce a depleted asteroid belt but permit formation of a system of terrestrial planet embryos on a approximately 10(6)-year timescale, initially by nonrunaway growth and transitioning to runaway growth after approximately 10(5) years. The calculations reported here are valid under the condition that the relative velocities of the bodies are determined only by Jupiter and Saturn perturbations and by gas drag, with no mutual perturbations between planetesimals. If, while subject to these conditions, the bodies become large enough for their mutual perturbations to influence their velocity and size evolution significantly, the problem becomes much more complex. This problem is under investigation.

NASA Discipline Exobiology↗
NASA NTRS1972

Tidal evolution in close binary systems. II.

The aim of the present investigation is to determine the explicit forms of differential equations which govern secular perturbations of the orbital elements of close binary systems in the plane of the orbit (i.e., of the semi-major axis, eccentricity, and longitude of the periastron) arising from the lag of dynamical tides due to viscosity of stellar material. The results obtained are exact for any value of orbital eccentricity comprised between zero and unity, and include the effects produced by the second, third and fourth-harmonic dynamical tides, as well as by axial rotation with arbitrary inclination of the equator to the orbital plane.

Kopal, Z.↗
NASA NTRS1976

On the detection of a cometary mass distribution

The problem of detecting a possible cometary distribution on the fringes of the solar system is examined. The acceleration of a space probe due to a hypothetical cometary mass distribution with the surface density rising to a maximum and subsequently falling off with increasing distance from the sun is analyzed. The total minimum detectable cometary mass for the Pioneer and Mariner spacecraft is estimated on the basis of this model to be on the order of 1000 earth masses. Precision tracking of deep space probes is less sensitive by three orders of magnitude for the detection of an unseen cometary mass distribution at the fringes of the solar system than are the secular perturbations of long-period comets.

Boss, A. P.↗
NASA NTRS1977

Origin of asteroids and the missing planet

Consideration is given to Ovenden's (1972) theory concerning the existence of a planet of 90 earth masses which existed from the beginning of the solar system and then disappeared 16 million years ago, leaving only asteroids. His model for secular perturbations is reviewed along with the principle of least interaction action (1972, 1973, 1975) on which the model is based. It is suggested that the structure of the asteroid belt and the origin of meteorites are associated with the vanished planet. A figure of 0.001 earth masses is proposed as a close estimate of the mass of the asteroidal belt. The hypothesis that the planet was removed through an explosion is discussed, noting the possible origin of asteroids in such a manner. Various effects of the explosion are postulated, including the direct impact of fragments on the earth, their impact on the sun and its decreased radiation, and the direct radiation of the explosion. A model for the disappearance of the planet by ejection in a gravitational encounter with a passing mass is also described.

Opik, E. J.↗
NASA NTRS1979

Long-term risk analysis associated with nuclear waste disposal in space

An assessment and verification of previous analytic results on the long term risk of earth reentry for hazardous payloads is presented. The two areas were studied: (1) stability of nominal, near-circular storage orbits in the regions between Venus and earth and between earth and Mars, and (2) probability of earth reentry for off-nominal planet-crossing orbits resulting from deployment system failures. In the first area, numerical integrations of the equations of motion are compared with stability predications based on secular perturbation theory. The agreement is good in terms of the heliocentric distances covered and the general behavior of the orbital history, although certain near-resonance situations can lead to difficulty. In the second area, a Monte Carlo simulation of orbital evolution is used and the results compared with Opik's analytic theory of planetary encounters and collision statistics, with data verified to within a close order-of-magnitude.

Friedlander, A. L.↗
NASA NTRS1981

Pole and prime meridian expressions for Phobos and Deimos

Simple trigonometric expressions are derived for the right ascensions and declinations of the spin axes of Phobos and Deimos as well as for their prime meridians. Simple expressions are possible since both satellites are in synchronous rotation about Mars and since the orbits of both satellites are accurately modeled as precessing ellipses. Spin axis expressions reflect the offset and precession of the orbit pole about the Laplacian pole. Prime meridian expressions include orbital mean motion, long-period solar perturbations, secular acceleration, and short-period, tidally induced forced libration. These simple expressions agree with rigorous expressions to + or - 0.2 deg.

Duxbury, T. C.↗
NASA NTRS1982

Orbital interactions - A new geometrical formalism

The geometry of encounters between two bodies on independent Keplerian orbits around a third body is considered by a novel analysis, which avoids approximations made in previous studies. For the case of most of the applications considered, the formulas for collision frequencies and orbital element rates of change due to close approaches which comprise the method agree with past results. It is shown that the method can be extended to such other applications as the consideration of oscillations in orbital elements due to secular perturbations, and the computation of probabilities of escape from the system.

Greenberg, R.↗
NASA NTRS1982

Earth-crossing asteroids - New discoveries

An earth-crossing asteroid is an asteroid whose orbit will intersect the orbit of the earth as a result of secular perturbations. Astronomical observations have led to the discovery of 43 earth-crossing asteroids during the last fifty years. Nearly sixty percent of these were found in the decade 1971-1981. Noteworthy results of the last decade are discussed, taking into account the Aten asteroids, accidental rediscoveries, asteroids of possible cometary origin, candidates for rendezvous and sample return missions, and populations and collision rates with earth. The observed earth-crossing asteroids are listed in a table, and the orbits of earth, Mars, and four Atens projected on ecliptic plane are shown.

Helin, E. F.↗
NASA NTRS1983

Precession of inclined rings

It is proposed that node alignment across an inclined ring is maintained by the self-gravity of the ring, which cancels the tendency for differential node precession due to the planet's multiple moments. The analysis is confined to circular rings, which is a self-consistent approximation because the interactions among circular and inclined ringlets do not generate secular perturbations of eccentricity.

Borderies, N.↗
NASA NTRS1984

The asteroidal source region of ordinary chondrites

The final, Earth-impacting orbits of ordinary chondritic meteorites have a very special distribution. By use of visual radiant and time of fall data, as well as photographic fireball orbits (1) it is inferred that chondrite perihelia are concentrated near 1 A.U., eccentricities are usually rather high (approximately 0.5), and inclinations are low (approximately 10 deg). Velocity selection resulting from atmospheric ablation plays a significant role in determining this orbital distribution, but by no means suffices to explain it. The observed distribution is a fragile one, and can easily be destroyed by Earth and Venus perturbations. This places severe constraints on the location of the original source bodies, of which these meteorites are fragments. New calculations were made of the expected distribution of final orbits from a range of initial sources, taking into consideration close encounter planetary perturbations, secular resonance, destruction by collision in space, and atmospheric ablation.

Wetherill, G. W.↗
NASA NTRS1985

Questions about Mercury's role in comparative planetary geophysics

Problems which have arisen in formulating a mutually consistent picture of Mercury's evolution are outlined. It appears that one or more of the following widely adopted assumptions are wrong about Mercury: (1) its original composition at least approximately resulted from equilibrium condensation; (2) its magnetic field arises from a still-active dynamo; (3) its thermal evolution should have yielded early core formation followed by cooling and a global contraction approaching 20 km in the planet's radius; (4) Mercury's surface is basaltic and the intercrater plains are of volcanic origin. It is suggested that Mercury's role in comparative planetology be reevaluated in the context of an alternative timescale based on the possibility that Mercury was subjected to a continuing source of cratering projectiles over recent aeons, which have not impacted the other terrestrial planets. Although such vulcanoids have not yet been discovered, the evolution of Mercury's orbit due to secular perturbations could well have led to a prolonged period of sweeping out any intra-Mercurian planetesimals that were originally present. Mercury's surface could be younger than previously believed, which explains why Mercury's core is still molten.

Chapman, C. R.↗
NASA NTRS1985

The polar caps and the climatic evolution of Mars

Mars and Earth experience quasiperiodic variations in the distribution of incident solar radiation due to secular perturbations in their orbital and axial elements. On Mars, the potential climatic effects of these perturbations are large because the mass of the Martian atmosphere may be determined by the vapor pressures of semipermanent CO2 frost deposits at the poles. The Viking Orbiter observations of the Martian polar caps suggest that the sensitivity of the Martian climate system to the variations in the polar insolation may be considerably reduced by the tendency for polar frost deposits to become brighter with increasing rates of incident solar radiation. This phenomenon can be explained by the tendency for dust particles to sink into CO2 frost at rates that depend on the magnitude of the incident solar flux.

Paige, D. A.↗
NASA NTRS1987

The chronology of Mercury's geological and geophysical evolution - The Vulcanoid hypothesis

The possibility that constraints on Mercury's chronology can be relaxed through reference to a Mercury-specific bombarding population of planetesimals interior to its orbit, and therefore only occasionally encountering the planet at times of secular perturbations, is investigated. While such vulcanoids may have been a significant source of early cratering, those in the pertinent orbits are depleted by mutual collisions and can therefore only furnish a modest extension of the heavy bombardment period. A search is conducted for vulcanoids further within Mercury's orbit; evidence that Mercury's intercrater plains are of volcanic origin is discussed.

Leake, Martha A.↗
NASA NTRS1989

Identification of asteroid dynamical families

Problems involved in the identification of asteroid dynamical families are discussed, and some methodological guidelines are presented. Asteroid family classifications are reviewed, and differences in the existing classifications are examined with special attention given to the effects of observational selection on the classification of family membership. The paper also discusses various theories of secular perturbations, including the classical linear theory, the theory of Williams (1969), and the higher order/degree theory of Yuasa (1973).

Valsecchi, G. B.↗
NASA NTRS1992

Long-term evolution of 1991 DA: A dynamically evolved extinct Halley-type comet

The long-term dynamical evolution of 21 variational orbits for the intermediate-period asteroid 1991 DA was followed for up to +/-10(exp 5) years from the present. 1991 DA is close to the 2:7 resonance with Jupiter; it has avoided close encounters, within 1 AU, with this planet for at least the past 30,000 years, even at the node crossing. The future evolution typically shows no close encounters with Jupiter within at least 50,000 years. This corresponds to the mean time between node crossings with either Jupiter or Saturn. Close encounters with Saturn and Jupiter lead to a chaotic evolution for the whole ensemble, while secular perturbations cause large-amplitude swings in eccentricity and inclination (the latter covering the range 15 deg approximately less than i approximately less than 85 deg) which correlate with deep excursions of the perihelion distance to values much less than 1 AU. These variations are similar to those found in P/Machholz and a variety of other high-inclination orbits, e.g., P/Hartley-IRAS. We emphasize the connection between the orbital evolution of 1991 DA and that of Halley-type comets. If 1991 DA was once a comet, it is not surprising that it is now extinct.

Hahn, Gerhard↗
NASA NTRS1993

On the stability of irradiated accretion disks

The effects of external heating on the stability of hot accretion disks are studied in some detail. It is known that geometrically thin, optically thick, nonirradiated accretion disks have two distinct branches in the surface density mass-accretion rate plane: the upper branch is radiation pressure-dominated and is unstable against thermal and secular perturbations, while the lower one is gas-pressure-dominated and is stable. We show quite generally that, even when disks are strongly irradiated, the upper branch remains unstable and the lower branch remains stable; the lower branch, however, can become radiation pressure dominated, if the irradiating flux, F(irr), is kept constant. A stable, radiation pressure dominated state thus appears. If F(irr) changes in proportion to the mass-accretion rate through the disk, the instabilities associated with radiation pressure dominated disks cannot be removed. Some observational implications are discussed in the context of long-term variations of low-mass X-ray binaries.

Mineshige, Shin↗
NASA NTRS1993

Non-stationary and non-linear dispersive medium as external field which generates the squeezed states

The theory of quantum effects in nonlinear dielectric media is developed. The nonlinear dielectric media is influenced by an external pumping field. The diagonalization of the Hamiltonian of a quantized field is obtained by the canonical Bogoliubov transformations. The transformations allow us to obtain the general expressions for the number of created photons and for the degree of squeezing. In the case of a plane pumping wave, for example, the results are calculated by using the zero order of the secular perturbation theory, with small parameters characterizing the medium nonlinearity. The Heisenberg equations of motion are obtained for non-stationary case and a commonly used Hamiltonian is derived from the first principles of quantum electrodynamics.

Lobashov, A. A.↗