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Correction of space trajectories by small midcourse maneuvers governed by impulse which is computed on the ground from radio measurements and sent by radio to the space probe
An analysis was made of the guidance of a space vehicle approaching the earth at supercircular velocity through an entrance corridor containing a desired perigee altitude. Random errors were assumed in the measurement of velocity and flight-path angle and in obtaining the desired thrust impulse. The method described in NASA Technical Note D-191 of scheduling corrections at different values of the angle between perigee and the vehicle's position vector and a slight modification of this method were investigated as a means of correcting perigee altitude when the vehicle's predicted position was at programmed correction points not within a specified deadband about the desired perigee altitude. The study showed that modifying the angular method of NASA Technical Note D-191 by adding another correction near the initial point did not improve the efficiency and accuracy of the angular method. It was found that in some cases the use of a correction procedure which included a deadband could be more costly in total corrective velocity than a procedure which neglected the deadband. This was especially true if a large degree of confidence was required in the total corrective velocity. It was apparent from the results that a correction with a deadband limit in the guidance scheme was more sensitive to the initial conditions, the corrective procedure, the deadband, and the degree of confidence required than a correction without a deadband limit.
An investigation of the amount of velocity or energy required to correct an orbit to a near-perfect, circular, equatorial orbit with a period of one sidereal day. The required velocity is shown to be a function of the satellite position and velocity errors at the time correction is to be performed, as well as certain parameters inherent in the "guidance law." The results in their final form permit computation of the corrective velocity as a function of initial injection cut-off errors and errors arising from perturbative accelerations.
The solution of supersonic flow fields by the method of characteristics requires that starting conditions be known. Ferri, in reference 1, developed a method-of-characteristics solution for axially symmetric bodies of revolution at small angles of attack. With computing machinery that is now available, this has become a feasible method for computing the aerodynamic characteristics of bodies near zero angle of attack. For sharp-nosed bodies of revolution, the required starting line may be obtained by computing the flow field about a cone at a small angle of attack. This calculation is readily performed using Stone's theory in reference 2. Some solutions of this theory are available in reference 3. However, the manner in which these results are presented, namely in a wind-fixed coordinate system, makes their use somewhat cumbersome. Additionally, as pointed out in reference 4, the flow component perpendicular to the meridian planes was computed incorrectly. The results contained herein have been computed in the same basic manner as those of reference 3 with the correct velocity normal to the meridian planes. Also, all results have been transferred into the body-fixed coordinate system. Therefore, the values tabulated herein may be used, in conjunction with the respective zero-angle-of-attack results of reference 5, as starting conditions for the method-of-characteristics solution of the flow field about axially symmetric bodies of revolution at small angles of attack. As in the zero-angle-of-attack case (ref. 5) the present results have been computed using the ideal gas value of 1.4 for the ratio of the specific heats of air. Solutions are given for cone angles from 2.5 deg to 30 deg in increments of 2.5 deg. For each cone angle, results were computed for a constant series of free-stream Mach numbers from 1.5 to 20. In addition, a solution was computed which yielded the minimum free-stream Mach number for a completely supersonic conical flow field. For cone angles of 27.5 deg and 30 deg, this minimum free-stream Mach number was above 1.5. Consequently, solutions at this Mach number were not computed for these two cone angles.
The primary mission is described, which consists of encounters with Venus and Mercury; (a second encounter with Mercury is also possible). The exptected navigation sequences were simulated with a Monte Carlo computer program for the purpose of determining midcourse correction velocity requirements and delivery accuracies. These simulations provide sensitivity in velocity requirements and delivery accuracies to error sources affecting the navigation process. The orbit determination capability at the final pre-Venus maneuver is shown to be the dominant contributor to the velocity requirements for the primary mission. Similarly, the orbit determination capability at the final pre-Mercury maneuver is shown to be the dominant contributor to the delivery accuracy at Mercury.
An explicit, analytic guidance technique is developed for the hyperbolic approach phases of interplanetary and lunar spacecraft trajectories. The guidance technique is based upon a first-order analytic solution for the perturbed planet-centered (or moon-centered) trajectory. This trajectory is represented as the sum of two components: (1) the unperturbed osculating hyperbola at pericenter, and (2) first-order position and velocity perturbations due to gravitational effects of the sun and other planets. A closed-form analytic approximation for these perturbations valid for the entire approach trajectory is derived, thereby eliminating the need for numerical integration of the equations of motion. By means of this analytic trajectory model, the approach guidance problem is reduced to an equivalent two-body problem. The guidance objectives are specified in terms of actual, attainable conditions at pericenter, and the required corrective velocity is determined explicitly for both fixed and variable times of arrival.
A nonlinear theory which considered the convective accelerations of blood and the nonlinear elastic behavior and taper angle of the vascular wall was used to study the nature of blood flow in the descending thoracic aorta of living dogs under a wide range of pressures and flows. Velocity profiles, wall friction, and discharge waves were predicted from locally measured input data about the pressure-gradient wave and arterial distention. The results indicated that a major part of the mean pressure gradient was balanced by convective accelerations; the theory, which took this factor into account, predicted the correct velocity distributions and flow waves.
A new NASA interplanetary flight project, called Jupiter Orbiter Probe (JOP), has been recently approved by Congress. JOP involves a dual mission intended to explore the planet Jupiter and its environment with an atmospheric probe and a planetary orbiter spacecraft. The probe and orbiter vehicles are to be launched in tandem as a single spacecraft during the time from December 1981 to January 1982. The spacecraft will arrive at Jupiter at the earliest on November 14, 1984. Navigating the JOP spacecraft will be a critical task for the JOP mission. Attention is given to aspects of probe and orbiter delivery, Jupiter orbit insertion and perijove raise, the Satellite Tour, navigation development and the navigation system, the probe delivery, example orbits, velocity perturbation and correction, orbit determination characteristics, orbit determination and control profile, and the correction velocity requirements.
A mass driver is an electrical device used to accelerate payloads of any material to a high velocity. Small vehicles (called buckets) containing superconducting coils carry the payloads. These buckets are accelerated by pulsed magnetic fields, timed by information on their position, and are guided by induced magnetic fields set up in a surrounding guideway. Upon reaching the correct velocity, the buckets release their payloads, then they are slowed for recirculation to be reused. A rationale is presented that leads to a relatively simple and near-optimum design, as well as basic programs for calculating acceleration. The transverse oscillation frequencies are found to be invariant to guideway transverse dimensions.
This paper describes an algorithm for the high accuracy computation of some statistical quantities of the magnitude of a random trajectory correction maneuver (TCM). The trajectory correction velocity increment Delta V is assumed to be a three-component random vector with each component being a normally distributed random scalar having a possibly nonzero mean. Knowledge of the statitiscal properties of the magnitude of a random TCM is important in the planning and execution of maneuver strategies for deep-space missions such as Galileo. The current algorithm involves the numerical integration of a set of differential equations. This approach allows the computation of density functions for specific Delta V magnitude distributions to high accuracy without first having to generate large numbers of random samples. Possible applications of the algorithm to maneuver planning, planetary quarantine evaluation, and guidance success probability calculations are described.
Errors in laser velocimeter measurements associated with the lag of seeding particles in subsonic and transonic flows were investigated experimentally and theoretically. In a low-speed flow, errors exceeding 5 percent were measured for particle diameters greater than 5 microns. In transonic flows, errors up to 60 percent were measured for particles with 2-3-micron diameters and up to 30 percent for 1-2-micron particles. A three-dimensional method was developed to determine the magnitude of errors due to the lag in seeding particle response based on a simplified particle force balance model and an empirical coefficient of drag model for spherical bodies. A one-dimensional version of this model was shown to be successful in correcting velocity measurements in both the subsonic and transonic flow regions.
An exploratory analysis of vehicle guidance during the approach to a target planet is presented. The objective of the guidance maneuver is to guide the vehicle to a specific perigee distance with a high degree of accuracy and minimum corrective velocity expenditure. The guidance maneuver is simulated by considering the random sampling of real measurements with significant error and reducing this information to prescribe appropriate corrective action. The instrumentation system assumed includes optical and/or infrared devices to indicate range and a reference angle in the trajectory plane. Statistical results are obtained by Monte-Carlo techniques and are shown as the expectation of guidance accuracy and velocity-increment requirements. Results are nondimensional and applicable to any planet within limits of two-body assumptions. The problem of determining how many corrections to make and when to make them is a consequence of the conflicting requirement of accurate trajectory determination and propulsion. Optimum values were found for a vehicle approaching a planet along a parabolic trajectory with an initial perigee distance of 5 radii and a target perigee of 1.02 radii. In this example measurement errors were less than i minute of arc. Results indicate that four corrections applied in the vicinity of 50, 16, 15, and 1.5 radii, respectively, yield minimum velocity-increment requirements. Thrust devices capable of producing a large variation of velocity-increment size are required. For a vehicle approaching the earth, miss distances within 32 miles are obtained with 90-percent probability. Total velocity increments used in guidance are less than 3300 feet per second with 90-percent probability. It is noted that the above representative results are valid only for the particular guidance scheme hypothesized in this analysis. A parametric study is presented which indicates the effects of measurement error size, initial perigee, and initial energy on the guidance requirements. Measurement error size significantly affects both guidance accuracy and velocity-increment expenditure. The initial trajectory, as given by its perigee and energy, affects the velocity-increment expenditure but not final guidance accuracy.
Three existing and two new excitation magnitude scaling options for active separation control at Reynolds numbers below one Million. The physical background for the scaling options was discussed and their relevance was evaluated using two different sets of experimental data. For F+ approx. 1, 2D excitation: a) The traditional VR and C(mu) - do not scale the data. b) Only the Re*C(mu) is valid. This conclusion is also limited for positive lift increment.. For F+ > 10, 3D excitation, the Re corrected C(mu), the St corrected velocity ratio and the vorticity flux coefficient, all scale the amplitudes equally well. Therefore, the Reynolds weighted C(mu) is the preferred choice, relevant to both excitation modes. Incidence also considered, using Ue from local Cp.
The assembly of galaxies can be described by the distribution of their star formation as a function of cosmic time. Thanks to the WFC3 grism on the Hubble Space Telescope (HST) it is now possible to measure this beyond the local Universe. Here we present the spatial distribution of H emission for a sample of 54 strongly star-forming galaxies at z 1 in the 3D-HST Treasury survey. By stacking the H emission, we find that star formation occurred in approximately exponential distributions at z approximately 1, with a median Sersic index of n = 1.0 +/- 0.2. The stacks are elongated with median axis ratios of b/a = 0.58 +/- 0.09 in H consistent with (possibly thick) disks at random orientation angles. Keck spectra obtained for a subset of eight of the galaxies show clear evidence for rotation, with inclination corrected velocities of 90.330 km s(exp 1-). The most straightforward interpretation of our results is that star formation in strongly star-forming galaxies at z approximately 1 generally occurred in disks. The disks appear to be scaled-up versions of nearby spiral galaxies: they have EW(H alpha) at approximately 100 A out to the solar orbit and they have star formation surface densities above the threshold for driving galactic scale winds.
The assembly of galaxies can be described by the distribution of their star formation as a function of cosmic time.Thanks to the WFC3 grism on the Hubble Space Telescope (HST) it is now possible to measure this beyond thelocal Universe. Here we present the spatial distribution of H emission for a sample of 54 strongly star-forming-galaxies at z~1 in the 3D-HST Treasury survey. By stacking the Halpha emission, we find that star formation occurredin approximately exponential distributions at z~1, with a median Sersic index of n=1.0 plus or minus 0.2. The stacks areelongated with median axis ratios of b/a 0.58 plus or minus 0.09 in Halpha consistent with (possibly thick) disks at randomorientation angles. Keck spectra obtained for a subset of eight of the galaxies show clear evidence for rotation, withinclination corrected velocities of 90-330 km per second. The most straightforward interpretation of our results is that starformation in strongly star-forming galaxies at z~1 generally occurred in disks. The disks appear to be scaled-upversions of nearby spiral galaxies: they have EW(Halpha)~100 Angstroms out to the solar orbit and they have star formation surface densities above the threshold for driving galactic scale winds.
Context. Ultra-fast outflows (UFOs) have become an established feature in analyses of the X-ray spectra of active galactic nuclei (AGN). According to the standard picture, they are launched at accretion disc scales with relativistic velocities, up to 0.3-0.4 times the speed of light. Their high kinetic power is enough to induce an efficient feedback on a galactic scale, possibly contributing to the co-evolution between the central supermassive black hole (SMBH) and the host galaxy. It is, therefore, of paramount importance to gain a full understanding of UFO physics and, in particular, of the forces driving their acceleration and the relation to the accretion flow from which they originate. Aims. In this paper, we investigate the impact of special relativity effects on the radiative pressure exerted onto the outflow. The radiation received by the wind decreases for increasing outflow velocity, v, implying that the standard Eddington limit argument has to be corrected according to v. Due to the limited ability of the radiation to counteract the black hole gravitational attraction, we expect to find lower typical velocities with respect to the non-relativistic scenario. Methods. We integrated the relativistic-corrected outflow equation of motion for a realistic set of starting conditions. We concentrated on a range of ionisations, column densities, and launching radii consistent with those typically estimated for UFOs. We explore a one-dimensional, spherical geometry and a three-dimensional setting with a rotating, thin accretion disc. Results. We find that the inclusion of special relativity effects leads to sizeable differences in the wind dynamics and that v is reduced up to 50% with respect to the non-relativistic treatment. We compare our results with a sample of UFOs from the literature and we find that the relativistic-corrected velocities are systematically lower than the reported ones, indicating the need for an additional mechanism, such as magnetic driving, to explain the highest velocity components. Finally, we note that these conclusions, derived for AGN winds, are generally applicable.
One of the challenges of analyzing convective cell properties is quick evolution of the individual convective cells. While the operational radar data provide great a data set to analyze the evolution of radar observables of convective precipitation clouds statistically, previous studies also suggested that, because of the quick evolution of cell life cycle, conventional radar volume scan strategies taking ~5-7 minutes might not capture the detailed evolution. The TRACER campaign deployed CSAPR2, which performed frequent update of RHI and sector PPI scans to track convective cells every < 2 minutes guided by a new cell-tracking framework, Multisensor Agile Adaptive Sampling (MAAS; Kollias et al. 2020). This allows for capturing fast-evolving radar observables. The submitted data files are CSAPR2 data in CfRadial format collected during the TRACER field campaign from June to September 2020. The data files include processed radar variables including: noise-masked reflectivity and differential reflectivity corrected for rain attenuation and systematic biases, noise-masked dealiased radial velocity, specific differential phase, locations of target cells (latitude, longitude, radar range), and radar-echo classification.