Engineering topics

Jackson, A. A.

Publications and source records attributed to Jackson, A. A..

18 records

NASA NTRS2015

Further Development of Verification Check-Cases for Six- Degree-of-Freedom Flight Vehicle Simulations

This follow-on paper describes the principal methods of implementing, and documents the results of exercising, a set of six-degree-of-freedom rigid-body equations of motion and planetary geodetic, gravitation and atmospheric models for simple vehicles in a variety of endo- and exo-atmospheric conditions with various NASA, and one popular open-source, engineering simulation tools. This effort is intended to provide an additional means of verification of flight simulations. The models used in this comparison, as well as the resulting time-history trajectory data, are available electronically for persons and organizations wishing to compare their flight simulation implementations of the same models.

Jackson, E. Bruce↗

NASA NTRS2001

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

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.

Jackson, A. A.↗

NASA NTRS1995

Radiation Pressure, Poynting-Robertson Drag, and Solar Wind Drag in the Restricted Three-Body Problem

In this paper, we examine the effects of radiation pressure, Poynting-Robertson (PR) drag, and solar wind drag on dust grains trapped in mean motion resonances with the Sun and Jupiter in the restricted (negligible dust mass) three-body Problem. We especially examine the evolution of dust grains in the 1:1 resonance. As a first step, the Sun and Jupiter are idealized to both be in circular orbit about a common center of mass (circular restricted three-body problem). From the equation of motion of the dust particle in the rotating reference frame, the drag-induced time rate of change of its Jacobi "constant," C, is then derived and expressed in spherical coordinates. This new mathematical expression in spherical coordinates shows that C, in the 1:1 resonance, both oscillates and secularly increases with increasing time. The new expression gives rise to an easy understanding of how an orbit evolves when the radiation force and solar wind drag are included. All dust grain orbits are unstable in time when PR and solar wind drag are included in the Sun-Jupiter-dust system. Tadpole orbits evolve into horseshoe orbits; and these orbits continuously expand in size to lead to close encounters with Jupiter. Permanent trapping is impossible. Orbital evolutions of a dust grain trapped in the 1:1 resonance in the planar circular, an inclined case, an eccentric case, and the actual Sun-Jupiter case are numerically simulated and compared with each other and show grossly similar time behavior. Resonances other than 1:1 are also explored with the new expression. Stable exterior resonance trapping may be possible under certain conditions. One necessary condition for such a trap is derived. Trapping in interior resonances is shown to be always unstable.

Liou, Jer-Chyi↗

NASA NTRS1994

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 Chiron's 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 Chiron's coma state is closely coupled to the nearly instantaneous level of Chiron's surface activity.

Stern, S. A.↗

NASA NTRS1994

Dust evolution from comets and asteroids: Their velocities at Earth orbit intersection

In this study on the evolution of dust particles from comets and asteroids, the effects of accurate many-body planetary motion on the gravitational perturbations of the dust grains are computed. In a computer simulation, dust grains of radius 10, 30, and 100 micron were released at perihelion passage from each of 36 different celestial bodies: 16 main asteroids, 15 short period comets with perihelion greater than 1 AU, and 5 short period comets with perihelion less than 1 AU. It is found that when dust grains evolve to intersection with the earth's orbit, they nearly always retain orbital characteristics indicative of their origins. Grains from main belt asteroids differ significantly in orbital characteristics, especially orbital eccentricity, from grains that evolve from comets.

Jackson, A. A.↗

NASA NTRS1994

Some considerations on velocity vector accuracy in dust trajectory analysis

Jackson, A. A.↗

NASA NTRS1994

Some considerations on velocity vector accuracy in dust trajectory analysis

The relative contributions of comets and asteroids to the reservoir of dust in the interplanetary medium is not known. There are direct observations of dust released from comets and there is evidence to associate the IRAS dust bands with possible collisions of asteroids in the main belt. A means towards sorting out the parent sources has been proposed in the establishment of a dust collector in orbit about the Earth. The purpose of such a facility would be to collect not only cosmic dust particles intact but also the state vectors, as they arrive at the detector, the idea being that one may combine analytical laboratory analysis of the physics and chemistry of the captured particles with orbital data in order to help distinguish between bodies and identify parent bodies. The theoretical study of dust particle orbits in the solar system takes on greatly more importance if we use collected trajectory data. The orbital motion of dust when radiation and forces alone are acting is well understood. When gravitational forces due to the planets are included, the motion can become quite complex. In order to characterize the orbits of particles as they crossed the Earth's orbits, a study of the long-time dust orbital evolution was undertaken. We have considered various parameters associated with these dust orbits to see if one may in a general way discriminate between particles evolved from comets and asteroids. We proceed in this study as we have done previously. That is, we considered the dust particles as ideal black bodies, of density 1 gm/cc, spherical, with radii 10-100 microns. Particles of this size are affected by radiation forces, photon pressure, and Poynting-Robertson drag. Account was also taken of solar wind drag, which amounts to about 30 percent of the Poynting-Robertson drag negligible. The gravitational forces due to the planets are included, unlike in our previous study; the planetary orbits are those of true n-body interaction so that the possibility of secular resonance is included. Our method was to calculate explicitly by a numerical procedure the orbits of dust particles after they left their parent bodies. The motion is determined numerically with the implicit Runge-Kutta integrator using Gauss-Radau spacings.

Jackson, A. A.↗

NASA NTRS1993

Orbital resonances and Poynting-Robertson drag

The phenomenon of resonance trapping with Poynting-Robertson drag in the simplest case - the circular restricted three-body problem - is elucidated. Attention is given to what determines whether a grain of a given size passes through a given resonance or is trapped there, to how and why a trapped particle's orbit evolves with time, and to why Poynting-Robertson drag resonances are only temporary, while gas-drag resonances appear to be stable. The possibility of trapping a grain into resonance with a planet depends on the combination of the following parameters: the ratio of radiation pressure force to solar gravity, the mass of the perturbing planet normalized to the solar mass, an integer, and eccentricity. In general, the peak eccentricity and sometimes the threshold value are large enough so that crossing orbits and close approaches to the planet can inhibit capture and aid escape from resonance.

Weidenschilling, S. J.↗

NASA NTRS1993

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.

Clark, F. O.↗

NASA NTRS1993

Orbital evolution of dust from comet Schwassmann-Wachmann 1: A case of one-to-one resonance trapping

In a recent study we have modeled the orbital evolution of dust particles released from comets and asteroids in the solar system. The source bodies were either asteroids inside Jupiter's orbit or comets from the Jupiter family of comets. However there are other dust producing parent bodies in the solar system of interest, one of these is comet P/Schwassman-Wachmann 1. Since comet Schwassman-Wachmann 1, which has an orbit outside of Jupiter's orbit, is an active dust producer and has low eccentricity, dust particle evolution from it is of interest. We report on a particular 2 micron radius particle that captured into a 1 to 1 mean motion resonance orbit with Saturn.

Jackson, A. A.↗

NASA NTRS1992

Orbital evolution of dust particles from comets and asteroids

Results are presented from a computer simulation in which dust grains of three different sizes were released at perihelion passage from each of (1) 15 main belt asteroids, (2) 15 short-period comets with perihelion greater than 1 AU, and (3) 5 such comets with perihelion less than 1 AU. The evolving-orbit calculations for each of the dust rains include the effects of solar and planetary gravity, radiation pressure, Poynting-Robertson drag, and solar wind drag. It is noted that when dust grains evolve to intersection with the earth's orbit, they retain orbital characteristics indicative of their origins.

Jackson, A. A.↗

NASA NTRS1991

Dust particles from comets and asteroids collected at the Earth's orbit: Parent-daughter relationships

The relative contributions of comets and asteroids to the reservoir of dust in the interplanetary medium is not well known. There are direct observations of dust released from comets and there is evidence to associate the IRAS dust bands with possible collisions of Asteroids in the main belt. It is believed that one may combine lab analysis of the physics and chemistry of captured particles with orbital data in order to identify comet and asteroid parent bodies. It is possible to use the collected orbits of the dust to connect with its source in two ways. One is to consider the long time orbit evolution of the dust under Poynting-Robertson drag. The other is to look at the prompt orbit change of dust from comets onto trajectories that intersect the earth's orbit. In order to characterize the orbits of dust particles evolved over a long period of time, a study of its orbital evolution was undertaken. Various parameters associated with these dust orbits as they cross the Earth's orbit were considered in order to see if one may discriminate between particles evolved from comets and asteroids. The method was to calculate by a numerical procedure the orbits of dust particles after they left their parent bodies. It appears that as the particles pass the Earth's orbit, asteroidal grains and cometary grains can be differentiated on the basis of their measured orbital eccentricities even after much planetary perturbation. Broad parent daughter associations can be made on this basis from measurement of their trajectories intercepted in earth orbit.

Jackson, A. A.↗

NASA NTRS1989

A solar system dust ring with earth as its shepherd

Numerical integrations are used here to show that small dust grains can be temporarily captured into exterior orbit-orbit resonances with the earth, lasting from less than 10,000 years to more than 100,000 years. Grains with radii of 30-100 microns, orbiting in planes less than 10 deg from the plane of the solar system and with orbital eccentricities of less than 0.3, are captured most easily. It is argued that there should be an approximately toroidal cloud of particles, derived mostly from the asteroid belt, trapped into a variety of these exterior resonances. The cloud is mostly beyond the earth's orbit, but includes it.

Jackson, A. A.↗

NASA NTRS1988

Planet X and the stability of resonances in the Neptune-Pluto system

Four test orbits of a trans-Plutonian planet have been integrated forward for four million years in order to determine the effects of such a body on the stability of the Neptune-Pluto 3:2 resonance. Planets beyond Pluto with masses of 0.1 M and 1.0 Earth masses in orbits at 48.3 and 75.5 AU, respectively, do not disturb the 3:2 resonance. Test planets of 5 Earth masses with semimajor axes of 52.5 and 62.5 AU disrupt the four million year libration of Pluto's argument of perihelion.

Jackson, A. A.↗

NASA NTRS1988

Infrared brightness of a comet belt beyond Neptune

The infrared brightness of a flattened comet belt beyond the orbit of Neptune is considered using a disk-like model with a power-law density distribution of comets. This spectrum is compared with the emission from a model zodiacal dust cloud in the ecliptic and with published IRAS data and some consequences of dust in the comet belt are presented.

Jackson, A. A.↗

NASA NTRS1983

Some applications of Lie groups in astrodynamics

Differential equations that arise in astrodynamics are examined from the standpoint of Lie group theory. A summary of the Lie method is given for first degree differential equations. The Kepler problem in Hamiltonian form is treated by this method. Extension of the Lie method to optimal trajectories is outlined.

Jackson, A. A.↗

NASA NTRS1976

Natural resources research and development in Lesotho using LANDSAT imagery

The author has identified the following significant results. A map of the drainage of the whole country to include at least third order streams was constructed from LANDSAT imagery. This was digitized and can be plotted at any required scale to provide base maps for other cartographic projects. A suite of programs for the interpretation of digital LANDSAT data is under development for a low cost programmable calculator. Initial output from these programs has proved to have better resolution and detail than the standard photographic products, and was to update the standard topographic map of a particular region.

Jackson, A. A.↗

NASA NTRS1974

Use of ERTS imagery for natural resources research and development in Lesotho

The author has identified the following significant results. As far as the geological aspects of the project were concerned, the project was a success. It was concluded that: (1) It is possible to trace the lithological boundaries between sedimentary rocks and basaltic rocks, both extrusive and intrusive. (2) It was possible to localize sponges in the mountain areas, some of which may conceal undiscovered diamond pipes. (3) Possible main structural axes were localized within the framework of lineaments. Due to drought which occured at the time the images were gathered by ERTS-1, the usefulness of the data was limited for agricultural purposes.

Nixon, P. H.↗