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The dynamics of a particle moving near a classical ring is studied under a Hill-type approximation. A classical ring is comprised of particles of equal mass arranged symmetrically about a massive central body, the particles having a uniform rotation rate.
We have developed a lidar technique for measuring the tropospheric C02 concentrations as a candidate for NASA's planned ASCENDS mission. Our technique uses two pulsed laser transmitters allowing simultaneous measurement of a C02 absorption line in the 1570 nm band, 02 extinction in the Oxygen A-band and surface height and backscatter. The lidar measures the energy and time of flight of the laser echoes reflected from the atmosphere and surface. The lasers are stepped in wavelength across the C02 line and an 02 line region during the measurement. The receiver uses a telescope and photon counting detectors, and measures the background light and energies of the laser echoes from the surface along with scattering from any aerosols in the path. The gas extinction and column densities for the C02 and 02 gases are estimated from the ratio of the on- and off- line signals via the DIAL technique. Pulsed laser signals and a time gated receiver are used to isolate the laser echo signals from the surface, to reject laser photons scattered in the atmosphere, and measure the surface height and scattering profile in the path. We have recently completed a second design study for the space instrument. For the study, we selected a nominal sun-synchronous orbit with an altitude of 400 km and equator crossing time of 1:30 pm, and a receiver telescope with 1.5 m diameter.
Comets and asteroids have been altered from their original "pristine" state by impacts occurring throughout their 4.5 billion year lives: [1]. Proof of shock deformation has been detected in the crystal structure of several Stardust samples from Comet Wild 2 [2, 3]. Analyses indicated that the planar dislocations in the crystal structure of the minerals had been imparted by impacts sustained during their lives, and not due to the aerogel capture process. Distortions to crystal structure also affect the ideal absorption spectra in the infrared, and [4], thus providing indirect evidence of its impact history and a means of remotely investigating the impact history of small bodies through comparing laboratory spectra with spectra observed by telescopes or spacecraft. -The effects of impacts propagating shock waves through minerals were investigated through laboratory impact experiments. Utilizing NASA Johnson Space Center's Experimental Impact Laboratory, projectiles were fired from the vertical gun at velocities ranging from 2.0 to 2.8 km/sec, projected impact velocities between Kuiper Belt Objects. Two types of projectiles were used, including spherical alumina ceramic, whose density mimics that of rock, and cylinders made from the same material that they impacted. The target materials chosen for testing included: OLIVINES forsterite (Mg2SiO4) and fayalite, Fe2SiO4); PYROXENES enstatite (Mg2Si2O6) and diopside (MgCaSi2O6); and CARBONATES magnesite (MgCO3) and siderite (FeCO3). Targets were impacted at either 25 C or cooled to -20 C to examine the effects of temperature, if any, on lattice distortions during the shock propagation. As comets and asteroids can undergo a wide range of temperatures in their orbital lifetimes, the effect of temperature on the equation of state of minerals being shocked needs to be examined for interpreting the results of these experiments. The porosity of the target mineral is varied by either grinding it into a powder/granular texture or as whole mineral rocks to investigate the differences in shock propagation when voids are present. By varying velocity, ambient temperature, and porosity, we can investigate different variables affecting impacts in the solar system. -Data indicates that there is a non-linear relationship between peak shock pressure and the variation in infrared spectral absorbances by the distorted crystal structure. The maximum variability occurs around 37 GPa in enstatite and forsterite. The particle size distribution of the impacted material similarly changes with velocity/peak shock pressure. -The experiments described above are designed to measure the near- to mid-IR effects from these changes to the mineral structure. See Lederer et al., this meeting for additional experimental results.
The Atmospheric Science Data Center (ASDC) is in the Science Directorate located at the NASA Langley Research Center (LaRC), in Hampton, Virginia. The ASDC is one of NASA’s Distributed Active Archive Centers (DAAC) and supports over 60 projects and provides access to more than 1,000 archived collections. These datasets were created from satellite measurements, field experiments, and modeled data products. ASDC projects focus on the following Earth science disciplines: Radiation Budget, Clouds, Aerosols, and Tropospheric Composition. The ASDC is the official Distributed Active Archive Center (DAAC) of record for the upcoming Tropospheric Emissions: Monitoring of Pollution (TEMPO) instrument.. The instrument will share a ride on a commercial satellite as a hosted payload and will be launched to an orbit about 22,000 miles above Earth's equator. The investigation will, for the first time, use a space-based instrument to make accurate observations of tropospheric pollution concentrations of ozone, nitrogen dioxide, formaldehyde, and aerosols with high resolution and frequency over the U.S, Canada, and Mexico.
The Atmospheric Science Data Center (ASDC) is in the Science Directorate located at the NASA Langley Research Center (LaRC), in Hampton, Virginia. The ASDC is one of NASA’s Distributed Active Archive Centers (DAAC) and supports over 60 projects and provides access to more than 1,000 archived collections. These datasets were created from satellite measurements, field experiments, and modeled data products. ASDC projects focus on the following Earth science disciplines: Radiation Budget, Clouds, Aerosols, and Tropospheric Composition. The ASDC is the official Distributed Active Archive Center (DAAC) of record for the upcoming Tropospheric Emissions: Monitoring of Pollution (TEMPO) instrument.. The instrument will share a ride on a commercial satellite as a hosted payload and will be launched to an orbit about 22,000 miles above Earth's equator. The investigation will, for the first time, use a space-based instrument to make accurate observations of tropospheric pollution concentrations of ozone, nitrogen dioxide, formaldehyde, and aerosols with high resolution and frequency over the U.S, Canada, and Mexico.
NASA's Tropospheric Emissions: Monitoring of Pollution (TEMPO) mission is the first space-based instrument to monitor major air pollutants across the North American continent every daylight hour at high spatial resolution. TEMPO is an ultraviolet and visible spectrometer that sits on a commercial satellite in a geostationary orbit about 22,000 miles above Earth's equator. This vantage point enables TEMPO to monitor daily variations in ozone, nitrogen dioxide, and other key elements of air pollution from the Atlantic to the Pacific, and from Mexico City and the Yucatan Peninsula to the Canadian oil sands. This webinar will provide an overview of the TEMPO mission and its data products and will show you how to discover and access TEMPO data products using NASA's Earthdata Search. This includes finding documentation, performing searches and filtering, using subsetting/concatenation services in Earthdata Search, and utilizing the Earthdata Forum.
Space agencies are planning missions to the vicinity of the Sun-Earth L sub 2 point, some involving a distributed system of telescope spacecraft, configured in a plane about a hub. An improved understanding is developed of their relative motion. First, the telescope equations of motion are written relative to L sub 2 in the context of the classical circular restricted three-body problem, and expanded in terms of the distance from L sub 2. A basic examination is presented of the spacecraft configuration requirements and effects of small orbit insertion errors. Next, the telescope equations of motion relative to the hub are written and further expanded in terms of the hub-L sub 2 and hub-telescope distances. An analytical solution is developed and a halo telescope orbit investigated, with appropriate initial conditions. Then, the force model is extended to include perturbations to an accuracy of 10 to 20 m, east as additive contributions to the circular restricted problem. Perturbations include Earth's orbital eccentricity, lunar motion, solar radiation pressure, and small thrusting forces. Simulations are presented, along with solution sensitivity to errors in hub position knowledge.
The dynamics and stability of large orbiting flexible beams and platforms oriented along the local horizontal are treated both analytically and numerically. It is assumed that such structures could be gravitationally stabilized by attaching a rigid lightweight dumbbell at the center of mass by a spring loaded hinge which also could provide viscous damping. For the beam it is seen that the small amplitude inplane pitch motion, dumbbell librational motion, and the anti-symmetric elastic modes are all coupled. The three dimensional equations of motion for a circular flat plate in orbit with a two-degree-of-freedom gimballed dumbbell are also developed and show that only those elastic modes described by a single nodal diameter line are influenced by the dumbbell motion. Stability criteria are developed for both examples and a parametric study of the least damped mode characteristics together with numerically simulated transient responses are carried out.
The concept of employing osculating reference position and velocity vectors in the numerical integration of the equations of motion of a satellite is examined. The choice of the reference point is shown to have a significant effect upon numerical efficiency and the class of trajectories described by the differential equations of motion. For example, when the position and velocity vectors on the osculating orbit at a fixed reference time are chosen, a universal formulation is yielded. For elliptical orbits, however, this formulation is unattractive for numerical integration purposes due to Poisson terms (mixed secular) appearing in the equations of motion. Other choices for the reference point eliminate this problem but usually at the expense of universality. A number of these formulations, including a universal one, are considered here. Comparisons of the numerical characteristics of these techniques with those of the Encke method are presented.
This report compares seven double-plate penetration predictor equations for accuracy and effectiveness of a shield design. Three of the seven are the Johnson Space Center original, modified, and new Cour-Palais equations. The other four are the Nysmith, Lundeberg-Stern-Bristow, Burch, and Wilkinson equations. These equations, except the Wilkinson equation, were derived from test results, with the velocities ranging up to 8 km/sec. Spreadsheet software calculated the projectile diameters for various velocities for the different equations. The results were plotted on projectile diameter versus velocity graphs for the expected orbital debris impact velocities ranging from 2 to 15 km/sec. The new Cour-Palais double-plate penetration equation was compared to the modified Cour-Palais single-plate penetration equation. Then the predictions from each of the seven double-plate penetration equations were compared to each other for a chosen shield design. Finally, these results from the equations were compared with test results performed at the NASA Marshall Space Flight Center. Because the different equations predict a wide range of projectile diameters at any given velocity, it is very difficult to choose the "right" prediction equation for shield configurations other than those exactly used in the equations' development. Although developed for various materials, the penetration equations alone cannot be relied upon to accurately predict the effectiveness of a shield without using hypervelocity impact tests to verify the design.
Spacecraft are shielded from micrometeoroids and orbital debris (MMOD) impacts to meet requirements for crew safety and/or mission success. In the past, orbital debris particles have been considered to be composed entirely of aluminum (medium-density material) for the purposes of MMOD shielding design and verification. Meteoroids have been considered to be low-density porous materials, with an average density of 1 g/cu cm. Recently, NASA released a new orbital debris environment model, referred to as ORDEM 3.0, that indicates orbital debris contains a substantial fraction of high-density material for which steel is used in MMOD risk assessments [Ref.1]. Similarly, an update to the meteoroid environment model is also under consideration to include a high-density component of that environment. This paper provides results of hypervelocity impact tests and hydrocode simulations on typical spacecraft MMOD shields using steel projectiles. It was found that previous ballistic limit equations (BLEs) that define the protection capability of the MMOD shields did not predict the results from the steel impact tests and hydrocode simulations (typically, the predictions from these equations were too optimistic). The ballistic limit equations required updates to more accurately represent shield protection capability from the range of densities in the orbital debris environment. Ballistic limit equations were derived from the results of the work and are provided in the paper.
Aerodynamic torque equations for axis motion of spinning spherical satellite
We consider a charged dust grain whose orbital motion is dominated by a planet's point-source gravity, but perturbed by higher-order terms in the planet's gravity field as well as by the Lorentz force arising from an asymmetric planetary magnetic field. Perturbations to Keplerian orbits due to a nonspherical gravity field are expressed in the traditional way: in terms of a disturbing function which can be expanded in a series of spherical harmonics (W. M. Kaula, 1966). In order to calculate the electromagnetic perturbation, we first write the Lorentz force in terms of the orbital elements and then substitute it into Gauss' perturbation equations. We use our result to derive strengths of Lorentz resonances and elucidate their properties. In particular, we compare Lorentz resonances to two types of gravitational resonances: those arising from periodic tugs of a satellite and those due to the attraction of an arbitrarily shaped planet. We find that Lorentz resonances share numerous properties with their gravitational counterparts and show, using simple physical arguments, that several of these patterns are fundamental, applying not only to our expansions, but to all quantities expressed in terms of orbital elements. Some of these patterns have been previously called 'd'Alembert rules' for satellite resonances. Other similarities arise because, to first-order in the perturbing force, the three problems share an integral of the motion. Yet there are also differences; for example, first-order inclination resonances exist for perturbations arising from planetary gravity and from the Lorentz force, but not for those due to an orbiting satellite. Finally, we provide a heuristic treatment of a particle's orbital evolution under the influence of drag and resonant forces. Particles brought into mean-motion resonances experience either trapping or resonant 'jumps,' depending on the direction from which the resonance is approached. We show that this behavior does not depend on the details of the perturbing force but rather is fundamental to all mean-motion resonances.
The nonhomogeneous Clohessy-Wiltshire (C-W) equations are formulated and solved as an initial value problem in the form structure of linear systems theory. The state transition matrix (STM) and its inverse are obtained explicitly in both Newtonian and Hamiltonian form. It is shown that the STM for the C-2 equations possesses a special property making its inverse easily obtainable. Since solutions to the C-W equations are needed in two-point boundary value form to construct a good mission design tool for orbit transfer, the Lambert problem is solved in the context of the C-W equations.
We consider a restricted six-body problem. The Galilean satellites' orbits are circular and coplanar; Io, Europa, and Ganymede are in exact resonance; their mean longitudes obey the Laplace relation. We seek periodic orbits which avoid close approaches to any satellite; such orbits are of interest for mission planning. They are approximated as fixed points of sets of variational equations associated with time-averaged disturbing functions. Stability of the solutions is also determined. The orbits of greatest interest are: planar - twice Callisto's period, eccentricity less than or equal to 0.6; planar - four times Callisto's period, eccentricity less than or equal to 0.75; slightly inclined - twice Callisto's period, eccentricity arbitrary; and planar - 4/5 or 5/4 Europa's period.
In a static magnetic field, some well-known guiding-center equations maintain their form when extended to next order in gyroradius. In these cases, it is only necessary to include the next order term in the magnetic moment series. The differential equation for guiding-center motion which describes both the parallel and perpendicular velocities correctly through first order in gyroradius is given. The question of how to define the guiding center position through second order arises and is discussed, and second order drifts are derived for one usual definition. The toroidal canonical angular momentum, P-phi, of the guiding center in an axisymmetric field is shown to be conserved using the guiding center velocity correct through first order. When second-order motion is included, P-phi is no longer a constant. The above extensions of guiding-center theory help to resolve the different tokamak orbits obtained either by using the guiding-center equations of motion or by using conservation of P-phi.
A zonal geopotential is presented to degree 21 from evaluation of mean elements for 21 satellites, including two of low (less than 20 deg) inclination. Each satellite is represented by an arc of at least one apsidal rotation. The lengths range from 50 to 660 days. Differential correction of the initial elements in all of the arcs, together with radiation pressure and atmospheric drag coefficients, is accomplished simultaneously with the correction for the zonal harmonics. The satellite orbits and their variations are generated by numerical integration of the Lagrange equations for mean elements. Disturbances due to precession and nutation, atmospheric drag, radiation pressure, and lunisolar gravity are added at 1- to 8-day intervals in the integrated orbits.
Formation flying systems can range from global constellations offering extended service coverage to clusters of highly coordinated vehicles that perform distributed sensing. Recently, the use of groups of micro-satellites in the areas of near Earth explorations, deep space explorations, and military applications has received considerable attention by researchers and practitioners. To date, most proposed control strategies are based on linear models (e.g., Hill-Clohessy-Wiltshire equations) or nonlinear models that are restricted to circular reference orbits. Also, all models in the literature are uncoupled between relative position and relative attitude. In this paper, a generalized dynamic model is proposed. The reference orbit is not restricted to the circular case. In this formulation, the leader or follower satellite can be in either a circular or an elliptic orbit. In addition to maintaining a specified relative position, the satellites are also required to maintain specified relative attitudes. Thus the model presented couples vehicle attitude and orbit requirements. Orbit perturbations are also included. In particular, the J(sub 2) effects are accounted in the model. Finally, a sliding mode controller is developed and used to control the relative attitude of the formation and the simulation results are presented.