A. A. Jackson

Orbital evolution of dust particles from comets and asteroids

Abstract In a computer simulation, dust grains of radius 10, 30, and 100 μm were released at perihelion passage from each of 35 different celestial bodies: 15 main belt asteroids, 15 short period comets with perihelion greater than 1 AU, and 5 short period comets with perihelion less than 1 AU. The evolving orbit of each of the 105 released dust grains was then continuosly computed with the Everhart numerical integrator until the orbit aphelion passed inside of 0.387 AU, or the dust grain had been ejected from the Solar System. The forces due to the gravity of the Sun and the planets as well as radiation pressure, Poynting-Robertson drag, and solar wind drag were all included in these numerical simulations. It is found that when dust grains evolve to intersection with the Earths orbit, they nearly always retain orbital characteristics indicative of their origins; grains from main belt asteroids differ significantly in orbital characteristics, especially in orbital eccentricity, from grains that evolve from comets. Average intersect velocities with the Earth, before the Earths gravitationa acceleration is taken into account, are about 5 km/sec for asteroidal and in excess of 12 km/ sec for cometary-derived grains. Average orbital eccentricities are about 0.1 for asteroidal grains and usually in excess of 0.4 for cometary grains when their orbits can intersect the Earths orbit. These results mean that accurate trajectory measurements of meteoroids collected with a near-Earth space platform would make it possible to distinguish asteroidal grains from cometary grains.

Analysis of orbital perturbations acting on objects in orbits near geosynchronous earth orbit

Orbital evolution has been numerically simulated for objects started in geosynchronous Earth orbit (GEO) or in orbits near GEO, during a project to study potential orbital debris problems in this region. Perturbations simulated include nonspherical terms in the Earths geopotential field, lunar and solar gravity, and solar radiation pressure. Objects simulated include large satellites, for which solar radiation pressure is insignificant, and small particles (a few microns in diameter), for which solar radiation pressure is an important force. Results for large satellites are largely in agreement with previous GEO studies that used classical perturbation techniques; orbital evolution studies were extended to possible storage orbits slightly above or below GEO. One notes that while the orbit planes of GEO satellites initially placed in equatorial orbits precess, so that those orbits reach inclinations of 14° to 15° to the equator, a “stable plane” exists inclined approximately 7.3° to the equator. The orbit planes of GEO satellites placed in such a stable plane orbit experience very little precession, remaining always within 1.2° of their initial orientation. Solar radiation pressure generates two major effects on small particles. One is an orbital eccentricity oscillation anticipated from previous research. The other is an oscillation in orbital inclination. This orbital inclination pattern is due to a precession of the small particles orbital angular momentum vector about an axis offset from the Earths polar axis. The magnitude of the precession axis offset angle depends on the particles cross-sectional area to mass ratio. The rate for this precession differs greatly from the precession rate predicted in a previous study using perturbation techniques. This difference points up the inadequacy of those perturbation techniques for orbits with large eccentricities. For one sequence of runs with small particles, Poynting-Robertson drag was added to the simulation in order to slowly reduce the orbital semimajor axis and probe for possible orbital period resonances near the GEO distance. A significant resonance was found at the geosynchronous distance, where small grains are trapped into a 1:1 resonance with the Earths daily rotation.

Results in orbital evolution of objects in the geosynchronous region

The orbital evolution of objects at or near geosynchronous orbit (GEO) has been simulated to investigate possible hazards to working geosynchronous satellites. Both large satellites and small particles have been simulated, subject to perturbations by nonspherical geopotential terms, lunar and solar gravity, and solar radiation pressure. Large satellites in initially circular orbits show an expected cycle of inclination change driven by lunar and solar gravity but very little altitude change. They have little chance of colliding with objects at other altitudes, provided that the initial eccentricities of their orbits are small. However, if such a satellite is disrupted, debris can reach thousands of kilometers above or below the initial satellite altitude. Small particles in GEO experience two cycles driven by solar radiation: an expected eccentricity cycle and an unexpected inclination cycle. This inclination cycle results from a precession of the orbit plane driven by asymmetric torque effects of the radiation pressure on an eccentric orbit. Particles generated by GEO insertion stage solid rocket motors typically hit the Earth or escape promptly; a small fraction remain in orbits that persist longer than 10 years.

The Capture of Interstellar Dust: The Pure Poynting-Robertson Case

Abstract Ulysses and Galileo spacecraft have discovered interstellar dust particles entering the solar system. In general, particles trajectories not altered by Lorentz forces or radiation pressure should encounter the sun on open orbits. Under Newtonian forces alone these particles return to the interstellar medium. Dissipative forces, such as Poynting–Robertson (PR) and corpuscular drag and non-dissipative Lorentz forces can modify open orbits to become closed. In particular, it is possible for the orbits of particles that pass close to the sun to become closed due to PR drag. Further, solar irradiation will cause modification of the size of the dust particle by evaporation. The combination of these processes gives rise a class of capture orbits and bound orbits with evaporation. Considering only the case of pure PR drag a minimum impact parameter is derived for initial capture by Poynting–Robertson drag. Orbits in the solar radiation field are computed numerically accounting for evaporation with optical and material properties for ideal interstellar particles modeled. The properties of this kind of particle capture are discussed for the Sun but is applicable to other stars.

The out-of-plane distribution of zodiacal dust near the earth

Analysis of IRAS data of the thermal zodiacal emission reveals an out-of-plane dust distribution near the Earth which is well-represented by a Lorentzian function. We suggest a possible explanation for the similarity as near-Earth gravitational perturbations of dust grains. Such perturbations are expected to be chaotic and will randomize any residual band structure near the Earth.

Infrared brightness of a comet belt beyond Neptune

We consider the infrared brightness of a flattened comet belt beyond the orbit of Neptune using a disk-like model with a power-law density distribution of comets. We compare this spectrum with the emission from a model zodiacal dust cloud in the ecliptic and with published IRAS data and present some consequences of dust in the comet belt.

Numerical simulations of particle orbits around 2060 Chiron

Scattered light from orbiting or coorbiting dust is a primary signature by which Earth-based observers study the activity and atmosphere of the unusual outer solar system object 2060 Chiron. Therefore, it is important to understand the lifetime, dynamics, and loss rates of dust in its coma. We report here dynamical simulations of particles in Chirons collisionless coma. The orbits of 17,920 dust particles were numerically integrated under the gravitational influence of Chiron, the Sun, and solar radiation pressure. These simulations show that particles ejected from Chiron are more likely to follow suborbital trajectories, or to escape altogether, than to enter quasistable orbits. Significant orbital lifetimes can only be achieved for very specific launch conditions. These results call into question models of a long-term, bound coma generated by discrete outbursts, and instead suggest that Chirons coma state is closely coupled to the nearly instantaneous level of Chirons surface activity.

Lommel Functions in Some Drag-Perturbed Problems

Let us consider the orbital problem in which a particle is subject to the force (per unit mass)

Are periodic mass extinctions driven by a distant solar companion

{\rm{F = - }}{\mu \over {{r^3}}}{\rm{r - }}{\alpha over {{r^2}}}(2{\rm{\gamma }}{{\rm{v}}_r} + {{\rm{v}}_t})