AS-508 S-4B postflight lunar impact trajectory analysis
As-508 S-4B post flight lunar impact trajectory analysis
Mc Fadden, W. D.↗
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The Impact Trajectory of Asteroid 2008 TC3
Asteroid 2008 TC3 was the rst asteroid ever discovered before reaching Earth. By using the almost 900 astrometric observations acquired prior to impact we estimate the trajectory of 2008 TC3 and the ground-track of the impact location as a function of altitude. For a reference altitude of 100 km the impact location 3- formal uncertainty is a 1.4 km 0.15 km ellipse with a semimajor axis azimuth of 105. We analyze the contribution of modeling errors and nd that the second-order zonal harmonics of the Earth gravity eld moves the ground-track by more than 1 km and the location along the ground-track by more than 2 km. Non-zonal and higher order harmonics only change the impact prediction by less than 20 m. The contribution of the atmospheric drag to the trajectory of 2008 TC3 is at the numerical integration error level, a few meters, down to an altitude of 50 km. Integrating forward to lower altitudes and ignoring the break-up of 2008 TC3, the atmospheric drag causes an along-track error that can be as large as a few kilometers at sea level. The locations of the recovered meteorites is consistent with the computed ground-track.
Trajectory↗
Apollo/Saturn 5 postflight lunar impact trajectory - AS-511 S-4B/IU
The postflight trajectory is presented for the Apollo/Saturn V AS-511 spent S-IVB/IU stage from CSM separation to lunar impact. The lunar impact coordinates and conditions are included. Some combinations of small S-IVB/IU stage related forces are hypothesized to account for a significant angular momentum increase and small translational perturbations. Trajectory dependent parameters in geocentric and selenocentric inertial coordinates (PACSS4, reference epoch at mean nearest Besselian year) module separation to lunar impact. Data relating to the tracking residuals (observed minus model calculated (O-C)) are also given for the best-estimate trajectory.
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Orbit Determination Accuracy for Comets on Earth-Impacting Trajectories
The results presented show the level of orbit determination accuracy obtainable for long-period comets discovered approximately one year before collision with Earth. Preliminary orbits are determined from simulated observations using Gauss' method. Additional measurements are incorporated to improve the solution through the use of a Kalman filter, and include non-gravitational perturbations due to outgassing. Comparisons between observatories in several different circular heliocentric orbits show that observatories in orbits with radii less than 1 AU result in increased orbit determination accuracy for short tracking durations due to increased parallax per unit time. However, an observatory at 1 AU will perform similarly if the tracking duration is increased, and accuracy is significantly improved if additional observatories are positioned at the Sun-Earth Lagrange points L3, L4, or L5. A single observatory at 1 AU capable of both optical and range measurements yields the highest orbit determination accuracy in the shortest amount of time when compared to other systems of observatories.
Kay-Bunnell, Linda↗
Warning Time for Long-Period Comets on Earth Impact Trajectories
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collision hazard orbital eccentricities star catal↗
Methodology for multiaircraft minimum noise impact landing trajectories
The problem of optimizing landing trajectories with respect to noise impact index is addressed. In contrast with previous work, multilandings are considered. In order to make the problem tractable the trajectories are specified in functional form with certain parameters left free for selection by the optimization methods. Constraint of aircraft dynamic behavior, trajectory separation, pilot workload, passenger comfort, and maximum noise intensity all enter into the determination of what is an allowable trajectory. A version of the quasi-Newton iterative procedure is used to determine the optimum parameter values. The results show improvement in noise impact to the airport considered and the potential for even greater improvement at many airports.
Cook, G.↗
An analytic study of impact ejecta trajectories in the atmospheres of Venus, Mars, and earth
Calculations have been made to determine the effects of atmospheric drag and gravity on impact ejecta trajectories on Venus, Mars, and earth. The equations of motion were numerically integrated for a broad range of body sizes, initial velocities, and initial elevation angles. A dimensionless parameter was found from approximate analytic solutions which correlated the ejecta range, final impact angle, and final impact velocity for all three planets.
Tauber, M. E.↗
Deflection and Fragmentation of Near-Earth Asteroids
Collisions by near-earth asteroids or the nuclei of comets pose varying levels of threat to man. A relatively small object, approximately 100 m diameter, which might be found on an impact trajectory with a populated region of the Earth, could potentially be diverted with a velocity of approximately1 cm/sec from an Earth impacting trajectory by impact (at 12 km/sec) by a rocket launched, 10^2 to 10^3 Kg impactor. For larger bodies, the use of kinetic energy impactors appear impractical because of the larger mass requirement. For any size object, nuclear explosions appear to be more efficient, using either the prompt blow-off from neutron radiation, the impulse from ejecta of a near-surface explosion for deflection, or, least efficiently, as a fragmenting charge.
Harris, Alan W.↗
The Impact of Trajectory Prediction Uncertainty on Air Traffic Controller Performance and Acceptability
A Human-In-The-Loop air traffic control simulation investigated the impact of uncertainties in trajectory predictions on NextGen Trajectory-Based Operations concepts, seeking to understand when the automation would become unacceptable to controllers or when performance targets could no longer be met. Retired air traffic controllers staffed two en route transition sectors, delivering arrival traffic to the northwest corner-post of Atlanta approach control under time-based metering operations. Using trajectory-based decision-support tools, the participants worked the traffic under varying levels of wind forecast error and aircraft performance model error, impacting the ground automations ability to make accurate predictions. Results suggest that the controllers were able to maintain high levels of performance, despite even the highest levels of trajectory prediction errors.
trajectory prediction uncertainty↗
Spray Cooling Trajectory Angle Impact Upon Heat Flux Using a Straight Finned Enhanced Surface
Experiments were conducted to study the effects of spray trajectory angles upon heat flux for flat and enhanced surface spray cooling. The surface enhancement consisted of straight fins machined on the top surface of a copper heater block. Spray cooling curves were obtained with the straight fin surface aligned both parallel (axial) and perpendicular (transverse) to the spray axis. Measurements were also obtained on a flat surface heater block for comparison purposes. Each copper block had a cross-sectional area of 2.0 sq cm. A 2x2 nozzle array was used with PF-5060 as the working fluid. Thermal performance data was obtained under nominally degassed (chamber pressure of 41.4 kPa) conditions. Results show that the maximum CHF in all cases was attained for a trajectory angle of 30' from the surface normal. Furthermore, trajectory angles applied to straight finned surfaces can have a critical heat flux (CHF) enhancement as much as 75% (heat flux value of 140 W/sq cm) relative to the vertical spray orientation for the analogous flat surface case under nominally degassed conditions.
Silk, Eric A.↗
Near Earth asteroid orbit perturbation and fragmentation
Collisions by near earth asteroids or the nuclei of comets pose varying levels of threat to man. A relatively small object, approximately 100 meter diameter, which might be found on an impact trajectory with a populated region of the Earth, could potentially be diverted from an Earth impacting trajectory by mass driver rocket systems. For larger bodies, such systems would appear to be beyond current technology. For any size object, nuclear explosions appear to be more efficient, using either the prompt blow-off from neutron radiation, the impulse from ejecta of near-surface explosion for deflection, or as a fragmenting charge. Practical deflections of bodies with diameters of 0.1, 1, and 10 km require interception, years to decades prior to earth encounter, with explosions a few kilotons, megatons, or gigatons, respectively, of equivalent TNT energy to achieve orbital velocity changes or destruction to a level where fragments are dispersed to harmless spatial densities.
Ahrens, Thomas J.↗
Displaced mass, depth, diameter, and effects of oblique trajectories for impact craters formed in dense crystalline rocks.
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Gault, D. E.↗
Minimum noise impact aircraft trajectories
Numerical optimization is used to compute the optimum flight paths, based upon a parametric form that implicitly includes some of the problem restrictions. The other constraints are formulated as penalties in the cost function. Various aircraft on multiple trajectores (landing and takeoff) can be considered. The modular design employed allows for the substitution of alternate models of the population distribution, aircraft noise, flight paths, and annoyance, or for the addition of other features (e.g., fuel consumption) in the cost function. A reduction in the required amount of searching over local minima was achieved through use of the presence of statistical lateral dispersion in the flight paths.
Jacobson, I. D.↗
Unique Aeolian Transport Mechanisms on Mars: Respective Roles of Percussive and Repercussive Grain Populations in the Sediment Load
Experiments show that when sand-size grains impact a sediment surface with energy levels commensurate for Mars, small craters are formed by the ejection of several hundred grains from the bed. The experiments were conducted with a modified crossbow in which a sand-impelling sabot replaced the bolt-firing mechanism. Individual grains of sand could be fired at loose sand targets to observe ballistic effects unhindered by aerodynamic mobilization of the bed. Impact trajectories simulated the saltation process on dune surfaces. Impact craters were not elongated despite glancing (15 deg.) bed impact; the craters were very close to being circular. High-speed photography showed them to grow in both diameter and depth after the impactor had ricochetted from the crater site. The delayed response of the bed was "explosive" in nature, and created a miniature ejecta curtain spreading upward and outward for many centimeters for impact of 100-300 um-diameter grains into similar material. This behavior is explained by deposition of elastic energy in the bed by the "percussive" grain. Impact creates a subsurface stress regime or "quasi-Boussinesq" compression field. Elastic recovery of the bed occurs by dilatancy; shear stresses suddenly convert the grains to open packing and they consequently become forcefully ejected from the site. Random jostling of the grains causes radial homogenization of stress vectors and a resulting circular crater. A stress model based on repercussive bed dilatancy and interparticle adhesive forces (for smaller grains) predicts, to first order, the observed crater volumes for various impact conditions. On earth, only a few grains are mobilized by a percussive saltating grain; some grains are "knudged" along the ground, and some are partly expelled on short trajectories. These motions constitute reptation transport. On Mars, saltation and reptation become indistinct: secondary or "repercussive" trajectories have sufficient vertical impulse to create a dense saltation population of many tens or hundreds of grains for each single high-speed saltation percussion of the bed. Impact cascading will lead to near-surface distortion of the boundary layer, and choked flow formed by a dense "slurry" of sand, with the majority of grains mobilized by repercussive forces rather than by aerodynamic lift. This proceeds until a fully-matured transport layer imposes self-limitations as grain-population density constrains the free-path motion of individial grains.
Marshall, John R.↗
Unique Aeolian Transport Mechanisms on Mars: Respective Roles of Percussive and Repercussive Grain Populations in the Sediment Load
Experiments show that when sand-size grains impact a sediment surface with energy levels commensurate for Mars, small craters are formed by the ejection of several hundred grains from the bed. The experiments were conducted with a modified crossbow in which a sand-impelling sabot replaced the bolt-firing mechanism. Individual grains of sand could be fired at loose sand targets to observe ballistic effects unhindered by aerodynamic mobilization of the bed. Impact trajectories simulated the saltation process on dune surfaces. Impact craters were not elongated despite glancing (15 deg.) bed impact; the craters were very close to being circular. High-speed photography showed them to grow in both diameter and depth after the impactor had ricochetted from the crater site. The delayed response of the bed was "explosive" in nature, and created a miniature ejecta curtain spreading upward and outward for many centimeters for impact of 100-300 micron-diameter grains into similar material. This behavior is explained by deposition of elastic energy in the bed by the "percussive" grain. Impact creates a subsurface stress regime or "quasi-Boussinesq" compression field. Elastic recovery of the bed occurs by dilatancy; shear stresses suddenly convert the grains to open packing and they consequently become forcefully ejected from the site. Random jostling of the grains causes radial homogenization of stress vectors and a resulting circular crater. A stress model based on repercussive bed dilatancy and interparticle adhesive forces (for smaller grains) predicts, to first order, the observed crater volumes for various impact conditions. On earth, only a few grains are mobilized by a percussive saltating grain; some grains are "knudged" along the ground, and some are partly expelled on short trajectories. These motions constitute reptation transport. On Mars, saltation and reptation become indistinct: secondary or "repercussive" trajectories have sufficient vertical impulse to create a dense saltation population of many tens or hundreds of grains for each single high-speed saltation percussion of the bed. Impact cascading will lead to near-surface distortion of the boundary layer, and choked flow formed by a dense "slurry" of sand, with the majority of grains mobilized by repercussive forces rather than by aerodynamic lift. This proceeds until a fully-matured transport layer imposes self- limitations as grain-population density constrains the free-path motion of individual grains.
Marshall, John R.↗
A numerical investigation of planetesimal collision trajectories with a Moon accumulating in Earth orbit
In the scenario of lunar origin in which the Moon is assumed to have accreted most of its mass while in orbit about the Earth, ismals on the accrea knowledge of the relative impact rates of heliocentric planetting Earth and Moon is essential for any attempt to establish dynamical constraints on lunar origin. Numerical integrations of the regularized equations of motion for four bodies (Sun, Earth, Moon, planetismal) were done. A planetismal impact trajectory was calculated by assuming that the planetismal has hit the surface of the Moon at an assumed location, traveling in an assumed direction, and with an assumed impact speed. Next, the equations of motion were numerically integrated backward in time in order to determine from where the planetismal has come. In this way those volumes in heliocentric orbital element space which contribute trajectories that directly impact the Moon.
Cox, L. P.↗
Apollo/Saturn 5 Postflight Trajectory - SA-513 Skylab 1 Mission. Tracking and Flight Reconstruction
The postflight trajectory for the Apollo/Saturn V SA-513 Skylab I flight is presented. An analysis is included of the orbital and powered flight trajectories of the launch vehicle, the orbital trajectory of the spent S-II stage, and the free flight impact trajectory of the expended S-IC stage. Launch vehicle trajectory dependent parameters are provided in earth-fixed launch site, launch vehicle navigation, and geographic polar coordinate systems. The time history of the trajectory parameters for the launch vehicle is presented from guidance reference release to the transfer to ATM control. Tables of significant launch vehicle parameters at engine cutoff, stage separation, and workshop orbit insertion are included. Figures of such parameters as altitude, surface and cross range, and the magnitude of total velocity and acceleration as a function of range time for the powered flight trajectory are given.
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