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Attitude stability of spinning rigid symmetric satellite in elliptic orbit examined for motion about equilibrium position with spin axis normal to orbit plane
The 3P to 1D electron-impact excitation cross section within the ground configuration of both neutral carbon and silicon is calculated in the distorted-wave approximation of the two-state Hartree-Fock coupled equations. An essential element of the present treatment is that orthogonality to core orbitals is not assumed in deriving equations for the scattering orbitals. A local adiabatic polarization potential is also added to the distorted-wave equations. Both elements are necessary in getting good agreement with close-coupling results for carbon to low impacting energies. The agreement is sufficiently good that predictions for silicon should be accurate to within a factor of 2.
Rendezvous, docking, and other Space Station proximity operations will be routine in nature in years to come. However, the specific parameters describing each maneuver, such as initial range and position, will vary from mission to mission so a means for depicting and interacting with graphic representations of proposed mission plans is necessary. Orbital operations are inherently non-intuitive due to non-linearities in the equations of motion of orbiting vehicles. Consequently, relative motion between two spacecraft cannot always be easily visualized. For these reasons, real time interactive visual aids and planning tools will be helpful, if not necessary, for future missions both in pre-flight training and on-orbit. Two such displays, Navie and eivaN, are currently available for examination and human factors testing. Since the docking tasks were fundamentally different with each device and because Navie imposed more constraints on the users than eivaN did, the orbital mechanics effects had a more pronounced effect on the Navie results.
This software implements penetration limit equations for common micrometeoroid and orbital debris (MMOD) shield configurations, windows, and thermal protection systems. Allowable MMOD risk is formulated in terms of the probability of penetration (PNP) of the spacecraft pressure hull. For calculating the risk, spacecraft geometry models, mission profiles, debris environment models, and penetration limit equations for installed shielding configurations are required. Risk assessment software such as NASA's BUMPERII is used to calculate mission PNP; however, they are unsuitable for use in shield design and preliminary analysis studies. The software defines a single equation for the design and performance evaluation of common MMOD shielding configurations, windows, and thermal protection systems, along with a description of their validity range and guidelines for their application. Recommendations are based on preliminary reviews of fundamental assumptions, and accuracy in predicting experimental impact test results. The software is programmed in Visual Basic for Applications for installation as a simple add-in for Microsoft Excel. The user is directed to a graphical user interface (GUI) that requires user inputs and provides solutions directly in Microsoft Excel workbooks.
Equations of motion computerized simulation for attitude stabilization of orbiting telescope coupled to crew compartment
Historically, orbital masses have been used as automatic balancers in rotating machines. However, in these applications, the masses are free to move and rotate with the rotor from zero to operating speeds. For gas turbine applications it is desirable for the orbital masses to be fixed and unmoving, until their release from a sudden unbalance at the operating speed, such as occurs from a blade-out event. The objective of this work is to develop the dynamical equations of motion for orbital masses on a rotating shaft. In subsequent work these equations will be incorporated into a rotor structural dynamics computer code and the feasibility of attenuating rotor unbalance response with orbital masses will be investigated.
System of state transition partial derivatives for which tracking information normal matrix for lunar orbiter is nearly diagonalized
Formulations of the equations of motion for two bodies orbiting a central body are compared. All equations compared will be valid for both close approaches and large separations. This will allow a more careful study of the regions in which the individual equations are most applicable.
Due to range safety considerations, the Sea-viewing Wide Field-of-view Sensor (SeaWiFS) ocean color instrument may be required to be launched into a near-noon descending node, as opposed to the ascending node used by the predecessor sensor, the Coastal Zone Color Scanner (CZCS). The relative importance of ascending versus descending near-noon orbits was assessed here to determine if descending node will meet the scientific requirements of SeaWiFS. Analyses focused on ground coverage, local times of coverage, solar and viewing geometries (zenith and azimuth angles), and sun glint. Differences were found in the areas covered by individual orbits, but were not important when taken over a 16 day repeat time. Local time of coverage was also different: for ascending node orbits the Northern Hemisphere was observed in the morning and the Southern Hemisphere in the afternoon, while for descending node orbits the Northern Hemisphere was observed in the afternoon and the Southern in the morning. There were substantial differences in solar azimuth and spacecraft azimuth angles both at equinox and at the Northern Hemisphere summer solstice. Negligible differences in solar and spacecraft zenith angles, relative azimuth angles, and sun glint were obtained at the equinox. However, large differences were found in solar zenith angles, relative azimuths, and sun glint for the solstice. These differences appeared to compensate across the scan, however, an increase in sun glint in descending node over that in ascending node on the western part of the scan was compensated by a decrease on the eastern part of the scan. Thus, no advantage or disadvantage could be conferred upon either ascending node or descending node for noon orbits. Analyses were also performed for ascending and descending node orbits that deviated from a noon equator crossing time. For ascending node, afternoon orbits produced the lowest mean solar zenith angles in the Northern Hemisphere, and morning orbits produced the lowest angles for the Southern Hemisphere. For descending node, morning orbits produced the lowest mean solar zenith angles for the Northern Hemisphere; afternoon orbits produced the lowest angles for the Southern Hemisphere.
The general relativistic correction to the position of a satellite is found by retaining Newtonian physics for an observer on the satellite and introducing a potential. The potential is expanded in terms of the Keplerian elements of the orbit and substituted in Lagrange's equations. Integration of the equations shows that a typical earth satellite with small orbital eccentricity is displaced by about 17 cm. from its unperturbed position after a single orbit, while the periodic displacement over the orbit reaches a maximum of about 3 cm. The moon is displaced by about the same amounts. Application of the equations to Mercury gives a total displacement of about 58 km. after one orbit and a maximum periodic displacement of about 12 km.
The effects of using an approximate state transition matrix in orbit estimation are investigated. The approximate state transition matrix results when higher order geopotential terms in the equations of motion are ignored in the formation of the variational equations. Two methods of orbit estimation are considered: the differential correction procedure (DC) and the extended Kalman filter (EKF). The system used for the study is the Research & Development version of the Goddard Trajectory Determination System. The effects of the approximation are analyzed on a number of orbits. These orbits of various inclinations and semimajor axes. Other parameters studied include geopotential models and DC arc length.
During hot firing ground testing of the Space Shuttle's Main Engine, vibrations of the liquid oxygen pump occur at frequencies which cannot be explained by the linear Jeffcott model of the rotor. The model becomes nonlinear after accounting for deadband, side forces, and rubbing. Two phenomena present in the numerical solutions of the differential equations are unexpected periodic orbits of the rotor and tracking of the nonlinear frequency. A multiple scale asymptotic expansion of the differential equations is used to give an analytic explanation of these characteristics.
During hot firing ground testing of the Space shuttle's Main Engine, vibrations of the liquid oxygen pump occur at frequencies which cannot be explained by the linear Jeffcott model of the rotor. The model becomes nonlinear after accounting for deadband, side forces, and rubbing. Two phenomena present in the numerical solutions of the differential equations are unexpected periodic orbits of the rotor and tracking of the nonlinear frequency. A multiple scale asymptotic expansion of the differential equations is used to give an analytic explanation of these characteristics.
Direct force control, where the angle of attack and sideslip angle are modulated, has been proposed as an alternative to bank angle control for aero-assist maneuvers. This paper reimplements the current state-of-the-art aerocapture guidance for bank angle control, Fully Numeric Predictor-corrector Aerocapture Guidance (FNPAG), for direct force control. The optimal control theory underlying the structure of FNPAG is shown to not be applicable to the direct force control approach. Several solution structures for the longitudinal channel are compared by simulating dispersed three-degree-of-freedom trajectories for a reference mission consisting of a low lift-to-drag vehicle and a highly elliptical, 1-sol target orbit around Mars. The equations of motion for the lateral channel are derived, and a controller is designed to target a specified orbital plane. Finally, a Monte Carlo is used to demonstrate the performance of the new guidance.
The concept of ascending vertically from the equator on earth to the point in geosynchronous orbit directly above was investigated. The gravity losses were found to be so great that vertical ascent is not practical with only chemical-rocket propulsion. With laser propulsion, propellant requirements with vertical ascent are reduced and might allow the use of single-stage vehicles from earth to geosynchronous orbit. Combined or composite chemical and laser propulsion is shown to be useful. A gravity ladder suspended from geosynchronous orbit part of the distance to earth is shown to reduce the vehicle propulsion requirements.
The use of two Class 2/fixed mesh/fixed order/multistep integration packages of the PECE type for the numerical integration of the second order, nonlinear, ordinary differential equation of the satellite orbit problem. These two methods are referred to as the general and the second sum formulations. The derivation of the basic equations which characterize each formulation and the role of the basic equations in the PECE algorithm are discussed. Possible starting procedures are examined which may be used to supply the initial set of values required by the fixed mesh/multistep integrators. The results of the general and second sum integrators are compared to the results of various fixed step and variable step integrators.
Atmospheric drag causes the greatest uncertainty in the spacecraft flight dynamics equation for spacecraft in Low Earth Orbit (LEO). The continuously varying atmospheric density levels require increased spacecraft tracking to accurately predict spacecraft location. In addition, periodic propulsive maneuvers must be designed and performed to counteract the effects of drag on the spacecraft orbit. If atmospheric drag effects can be continuously and autonomously counteracted through the use of a drag-free control system, they will essentially be eliminated from the spacecraft flight dynamics equation. The main perturbations on the spacecraft will then be those due to the Earth s gravitational field, which are easily predicted. Although theoretically beneficial from a flight dynamics perspective, the costs associated with drag-free control must be determined and weighed against those benefits before the feasibility of drag-free control of spacecraft in LEO can be determined. Through the use of a MATLAEV Satellite Tool Kit simulation, this paper attempts to quantify one such cost associated with drag-free control: the amount of fuel needed for continuous drag compensation as measured by cumulative orbital velocity changes, or AV. This AV cost can then be compared to the fuel required for more traditional, periodic orbit raising maneuvers of every two to four weeks. The simulation considers various sized spacecraft, as measured by the spacecraft ballistic coefficient, in circular orbits of various altitudes and inclinations. The time between orbit raising maneuvers is allowed to decrease until it approaches near continuous. In this manner, the trend in AV cost can be seen as drag compensation moves from periodic to near continuous.
A real-time guidance scheme is presented for the problem of maximizing the payload into orbit subject to the equations of motion of a rocket over a nonrotating spherical earth. The flight is constrained to a path in the equatorial plane while reaching an orbital altitude at orbital injection speeds. The dynamics of the problem can be separated into primary and perturbation effects by a small parameter, epsilon, which is the ratio of the atmospheric scale height to the radius of the earth. The Hamilton-Jacobi-Bellman or dynamic programming equation is expanded in an asymptotic series where the zeroth-order term (epsilon = 0) can be obtained in closed form. The neglected perturbation terms are included in the higher-order terms of the expansion, which are determined from the solution of first-order linear partial differential equations requiring only integrations which are quadratures. The quadratures can be performed rapidly with emerging computer capability, so that real-time approximate optimization can be used to construct the launch guidance law. The application of this technique to flight in three-dimensions is made apparent from the solution presented.