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NASA NTRS1993

Accurate computation and continuation of homoclinic and heteroclinic orbits for singular perturbation problems

In earlier papers, Doedel and the authors have developed a numerical method and derived error estimates for the computation of branches of heteroclinic orbits for a system of autonomous ordinary differential equations in R(exp n). The idea of the method is to reduce a boundary value problem on the real line to a boundary value problem on a finite interval by using a local (linear or higher order) approximation of the stable and unstable manifolds. A practical limitation for the computation of homoclinic and heteroclinic orbits has been the difficulty in obtaining starting orbits. Typically these were obtained from a closed form solution or via a homotopy from a known solution. Here we consider extensions of our algorithm which allow us to obtain starting orbits on the continuation branch in a more systematic way as well as make the continuation algorithm more flexible. In applications, we use the continuation software package AUTO in combination with some initial value software. The examples considered include computation of homoclinic orbits in a singular perturbation problem and in a turbulent fluid boundary layer in the wall region problem.

Vaughan, William W.↗

NASA NTRS1993

Space Station Freedom assembly and operation at a 51.6 degree inclination orbit

This study examines the implications of assembling and operating Space Station Freedom at a 51.6 degree inclination orbit utilizing an enhanced lift Space Shuttle. Freedom assembly is currently baselined at a 220 nautical mile high, 28.5 degree inclination orbit. Some of the reasons for increasing the orbital inclination are (1) increased ground coverage for Earth observations, (2) greater accessibility from Russian and other international launch sites, and (3) increased number of Assured Crew Return Vehicle (ACRV) landing sites. Previous studies have looked at assembling Freedom at a higher inclination using both medium and heavy lift expendable launch vehicles (such as Shuttle-C and Energia). The study assumes that the shuttle is used exclusively for delivering the station to orbit and that it can gain additional payload capability from design changes such as a lighter external tank that somewhat offsets the performance decrease that occurs when the shuttle is launched to a 51.6 degree inclination orbit.

Troutman, Patrick A.↗

NASA NTRS1992

The design and evolution of the beta two-stage-to-orbit horizontal takeoff and landing launch system

The Beta launch system was originally conceived in 1986 as a horizontal takeoff and landing, fully reusable, two-stage-to-orbit, manned launch vehicle to replace the Shuttle. It was to be capable of delivering a 50,000 lb. payload to low polar orbit. The booster propulsion system consisted of JP fueled turbojets and LH fueled ramjets mounted in pods in an over/under arrangement, and a single LOX/LH fueled SSME rocket. The second stage orbiter, which staged at Mach 8, was powered by an SSME rocket. A major goal was to develop a vehicle design consistent with near term technology. The vehicle design was completed with a GLOW of approximately 2,000,000 lbs. All design goals were met. Since then, interest has shifted to the 10,000 lbs. to low polar orbit payload class. The original Beta was down-sized to meet this payload class. The GLOW of the down-sized vehicle was approximately 1,000,000 lbs. The booster was converted to exclusively air-breathing operation. Because the booster depends on conventional air-breathing propulsion only, the staging Mach number was reduced to 5.5. The orbiter remains an SSME rocket-powered stage.

Burkardt, Leo A.↗

NASA NTRS1991

Systems engineering studies of on-orbit assembly operation

While the practice of construction has a long history, the underlying theory of construction is relatively young. Very little has been documented as to techniques of logistic support, construction planning, construction scheduling, construction testing, and inspection. The lack of 'systems approaches' to construction processes is certainly one of the most serious roadblocks to the construction of space structures. System engineering research efforts at CSC are aimed at developing concepts and tools which contribute to a systems theory of space construction. The research is also aimed at providing means for trade-offs of design parameters for other research areas in CSC. Systems engineering activity at CSC has divided space construction into the areas of orbital assembly, lunar base construction, interplanetary transport vehicle construction, and Mars base construction. A brief summary of recent results is given. Several models for 'launch-on-time' were developed. Launch-on-time is a critical concept to the assembly of such Earth-orbiting structures as the Space Station Freedom, and to planetary orbiters such as the Mars transfer vehicle. CSC has developed a launch vehicle selection model which uses linear programming to find optimal combinations of launch vehicles of various sizes (Atlas, Titan, Shuttles, HLLV's) to support SEI missions. Recently, the Center developed a cost trade-off model for studying on orbit assembly logistics. With this model it was determined that the most effective size of the HLLV would be in the range of 120 to 200 metric tons to LEO, which is consistent with the choices of General Stafford's Synthesis Group Report. A second-generation Dynamic Construction Activities Model ('DYCAM') process model has been under development, based on our past results in interruptability and our initial DYCAM model. This second-generation model is built on the paradigm of knowledge-based expert systems. It is aimed at providing answers to two questions: (1) what are some necessary or sufficient conditions for judging conceptual designs of spacecraft?, and (2) can a methodology be formulated such that these conditions may be used to provide computer-aided tools for evaluating conceptual designs and planning for space assembly sequences? Early simulation results indicate that the DYCAM model has a clear ability to emulate and simulate human orbital construction processes.

Morgenthaler, George W.↗

NASA NTRS1991

Mars approach navigation using Doppler and range measurements to surface beacons and orbiting spacecraft

Approximate analytical models are developed and used to construct an error covariance analysis for investigating the range of orbit determination accuracies which might be achieved for typical Mars approach trajectories. The sensitivity or orbit determination accuracy to beacon/orbiter position errors and to small spacecraft force modeling errors is also investigated. The results indicate that the orbit determination performance obtained from both Doppler and range data is a strong function of the inclination of the approach trajectory to the Martian equator, for surface beacons, and for orbiters, the inclination relative to the orbital plane. Large variations in performance were also observed for different approach velocity magnitudes; Doppler data in particular were found to perform poorly in determining the downtrack (along the direction of flight) component of spacecraft position. In addition, it was found that small spacecraft acceleration modeling errors can induce large errors in the Doppler-derived downtrack position estimate.

Thurman, Sam W.↗

NASA NTRS1993

TSS-1 - Orbiter current and voltage experiments

Although the deployment distance of the TSS-1 tethered satellite was only about 1 percent of nominal, experiments to study the current collection and vehicle charging effects at low voltages were performed. We present measurements of Orbiter charging resulting from electron beam emission from the Orbiter, currents in the TSS system with and without electron beam emissions, and the effects of Orbiter thrusters on charging and currents. Generally, charging induced by beam emission was limited to a few volts, though during times with low ambient plasma density the Orbiter was charged up to 80 V. Thrusters are seen to enhance Orbiter charging during beam emission, and reduce ion current collection at other times.

Thompson, D. C.↗

NASA NTRS1993

Orbital dynamics of PSR1257+12 and its two planetary companions

I present a review of the orbital dynamics of the three body problem of PSR1257+12 and its two putative planetary companions. The orbital dynamics provides two 'reality checks' on the planetary interpretation of the pulse arrival time residuals observed by Wolszczan and Frail (1992). First, by examining the dynamical stability of the system for the deduced orbital periods, one can place upper limits on the companion masses of about two times the mass of Jupiter. Since the lower limits of the companion masses deduced from the observations are well below this upper limit, the planetary interpretation passes this first 'reality check'. Second, the 3:2 near-commensurability of the orbital periods effects periodic variations of the Keplerian orbital parameters. The amplitude of these variations provides a direct measure of the masses of the companions relative to the mass of the pulsar. The signature of these variations in pulse time-of-arrival data is not straightforward, but, if the planetary interpretation is correct, it should become detectable as an additional quasi-periodic phase residual over a period of a few years.

Malhotra, Renu↗

NASA NTRS1993

Particle orbits in model current sheet with a nonzero B(y) component

The problem of charged particle motions in magnetotaillike model current sheets is revisited with the inclusion of a nonzero dawn-dusk magnetic field component. Three cases are examined considering both trapped and escaped orbits. The results show that a nonzero B(y) component disturbs the particle orbits by destroying orbit symmetry in the phase space about the z = 0 plane. It also changes the bounce frequency of particle orbits. The presence of B(y) thus modifies the Speiser orbits, particularly near the ejection phase. The process of ejected particle such as ejection direction, ejection velocity, and pitch angles are shown to depend on the sign of the charge.

Zhu, Zhongwei↗

NASA NTRS1993

Stationary occultations from low Earth orbit

The process of stationary lunar occultations is considered for observers in LEO. The orbit of the Hubble Space Telescope (HST) is used as a prototype. The noncoplanarity of the HST and lunar orbits disrupts many of the expected stationary events, and orbital drag complicates the prediction problem. In a typical year, the apparent speed of the lunar limb seen by the HST is slower than a typical ground-based event only about 0.7 percent of the time. The orbit prediction can be wrong by as much as 20 deg in 53 days, with most of the error lying in the plane of the orbit.

Percival, Jeffrey W.↗

NASA NTRS1992

The form of spin orbitals for open-shell restricted Hartree-Fock reference functions

A new set of spin orbitals is proposed for single-reference correlation procedures based on an open-shell restricted Hartree-Fock (RHF) reference function. The spatial parts of the new spin orbitals are from an open-shell RHF calculation. These spin orbitals form a complete, orthonormal set. The RHF single determinant based on these spin orbitals is an S sub 2 eigenfunction, but a linear combination of S sub z eigenfunctions. The advantage of these spin orbitals is that equations for perturbation theory or coupled-cluster theory are symmetric in the spin indices and hence the number of independent parameters to be determined is dramatically reduced.

Jayatilaka, Dylan↗

NASA NTRS1993

Navier-Stokes simulations of the Shuttle Orbiter aerodynamic characteristics with emphasis on pitch trim and bodyflap

An analysis of the longitudinal aerodynamics of the Shuttle Orbiter in the hypersonic flight regime is made through the use of computational fluid dynamics (CFD). Particular attention is given to establishing the cause of the 'pitching moment anomaly' which occurred on the Orbiter's first flight and to computing the aerodynamics of a complete Orbiter configuration at flight conditions. Data from ground based facilities as well as Orbiter flight data are used to validate the computed results. Analysis shows that the 'pitching moment anomaly' is a real gas chemistry effect which cannot be simulated in ground-based facilities. Computed flight aerodynamics for the Orbiter are within 5 percent of the measured flight values and trim bodyflap deflections are predicted to within 10 percent.

Weilmuenster, K. J.↗

NASA NTRS1992

Atmospheric gravitational influence on geodetic satellite orbits - Starlette analysis

The atmosphere is constantly in motion. The changing gravitational force due to the air mass movement will slightly perturb the orbit of a satellite. As the instrument accuracy for geodetic satellites improves, failure to model this perturbation can result in significant systematic errors in the orbit determination. The latter, in turn, will degrade the Earth's gravity solutions. A direct modeling technique to analyze the atmospheric gravitational influence on geodetic satellite is developed. We use the global surface pressure data from the ECMWF Initial Analysis Database to compute the gravitational force due to atmospheric perturbation exerted on given satellite as a function of time during selected orbital arcs. Satellite Laser Ranging (SLR) tracking data for selected Starlette (altitude 900 km) orbital arcs are used to test the computed force model. Although only a slight reduction in the rms residuals is observed when the atmospheric gravitational perturbation is included in the force model for data reduction of the SLR data, significant improvement is obtained in the predictability of the satellite orbit. Comprehensive studies involving more definitive test criteria and more refined models are still needed.

Chao, B. F.↗

NASA NTRS1993

On-orbit servicing for USAF space missions: A phased development approach

On-orbit servicing has been studied for years by the U.S. Air Force Space Systems Division--which recently cosponsored the Space Assembly, Maintenance, and Servicing Study with NASA and SDIO; but an Air force servicing program has yet to emerge. The Air Force has a limited set of servicing requirements, and the practices of 'pipelining' (incremental improvements to a space vehicle series) and orbital sparing provide many similar benefits. It is postulated that an Air Force Program will be initiated in response to a new critical mission requirement that calls for a spacecraft with the operational character of a Servicer, which will evolve into a servicing program. Such a requirement may be emerging. The Air Force organizations charged with on-orbit test safety for the Department of Defense are concerned with the hazard from uncontrolled reentry of low Earth orbit test spacecraft, which are increasing in number. Analysis and observations of actual reentries show that debris reaches the Earth's surface. A phased development of a system to remove these spacecraft from orbit can evolve into a servicing program.

Shanney, Bill↗

NASA NTRS1993

Orbital simulations of satellite escape/capture and the origin of satellites such as Triton

We investigate satellite escape/capture in the context of the restricted, circular three body problem as applied to the Sun, Neptune, and Triton. We have computed a large number of coplanar prograde and retrograde orbital simulations over a range of initial distances and velocities. The satellite starts at superior conjunction within approximately 2 Hill radii of Neptune and has a velocity orthogonal to the Sun-planet line. Orbits with these initial conditions can be reflected with respect to time, so an escape is simply the reverse of a capture. We numerically integrate the equations of motion to compute the satellite's position until it escapes, collides with Neptune, or after 100 planetary years fails to escape, when computations cease. The initial distance x and velocity v in the restricted problem uniquely define the Jacobi constant C, a conserved energy-like quantity. Plots of the simulation outcomes in the prograde and retrograde C, x phase spaces reveal distinct zones in which temporary satellites approach the planet closely enough that permanent capture can be effected by gas drag with a protoplanetary nebula or by collision with a pre-existing satellite. Single and double close-flybys constitute the most common possible capture orbits. Long term multiple flyby orbits occur near the stability limits between bound and unbound orbits, and are more common among retrograde captures.

Benner, Lance A. M.↗

NASA NTRS1993

On the accuracy of ERS-1 orbit predictions

Since the launch of ERS-1, the D-PAF (German Processing and Archiving Facility) provides regularly orbit predictions for the worldwide SLR (Satellite Laser Ranging) tracking network. The weekly distributed orbital elements are so called tuned IRV's and tuned SAO-elements. The tuning procedure, designed to improve the accuracy of the recovery of the orbit at the stations, is discussed based on numerical results. This shows that tuning of elements is essential for ERS-1 with the currently applied tracking procedures. The orbital elements are updated by daily distributed time bias functions. The generation of the time bias function is explained. Problems and numerical results are presented. The time bias function increases the prediction accuracy considerably. Finally, the quality assessment of ERS-1 orbit predictions is described. The accuracy is compiled for about 250 days since launch. The average accuracy lies in the range of 50-100 ms and has considerably improved.

Koenig, Rolf↗

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 NTRS1993

SeaTrack: Ground station orbit prediction and planning software for sea-viewing satellites

An orbit prediction software package (Sea Track) was designed to assist High Resolution Picture Transmission (HRPT) stations in the acquisition of direct broadcast data from sea-viewing spacecraft. Such spacecraft will be common in the near future, with the launch of the Sea viewing Wide Field-of-view Sensor (SeaWiFS) in 1994, along with the continued Advanced Very High Resolution Radiometer (AVHRR) series on NOAA platforms. The Brouwer-Lyddane model was chosen for orbit prediction because it meets the needs of HRPT tracking accuracies, provided orbital elements can be obtained frequently (up to within 1 week). Sea Track requires elements from the U.S. Space Command (NORAD Two-Line Elements) for the satellite's initial position. Updated Two-Line Elements are routinely available from many electronic sources (some are listed in the Appendix). Sea Track is a menu-driven program that allows users to alter input and output formats. The propagation period is entered by a start date and end date with times in either Greenwich Mean Time (GMT) or local time. Antenna pointing information is provided in tabular form and includes azimuth/elevation pointing angles, sub-satellite longitude/latitude, acquisition of signal (AOS), loss of signal (LOS), pass orbit number, and other pertinent pointing information. One version of Sea Track (non-graphical) allows operation under DOS (for IBM-compatible personal computers) and UNIX (for Sun and Silicon Graphics workstations). A second, graphical, version displays orbit tracks, and azimuth-elevation for IBM-compatible PC's, but requires a VGA card and Microsoft FORTRAN.

Lambert, Kenneth S.↗

NASA NTRS1994

Charge efficiency of Ni/H2 cells during transfer orbit of Telstar 4 satellites

The TELSTAR 4 communication satellites being manufactured by Martin Marietta Astro Space (Astro Space) for AT&T are three axis stabilized spacecraft scheduled to be launched on expendable vehicles such as the Atlas or Ariane rockets. Typically, these spacecraft consist of a box that holds the electronics and supports the antenna reflectors and the solar array wings. The wings and reflectors are folded against the sides of the box during launch and the spacecraft is spun for attitude control in that phase; they are then deployed after achieving the final orbit. The launch phase and transfer orbits required to achieve the final geosynchronous orbit typically take 4 to 5 days during which time the power required for command, telemetry, attitude control, heaters, etc., is provided by two 50 AH nickel hydrogen batteries augmented by the exposed outboard solar panels. In the past, this situation has presented no problem since there was a considerable excess of power available from the array. In the case of large high powered spacecraft such as TELSTAR 4, however, the design power levels in transfer orbit approach the time-averaged power available from the exposed surface area of the solar arrays, resulting in a very tight power margin. To compound the difficulty, the array output of the spinning spacecraft in transfer orbit is shaped like a full wave rectified sine function and provides very low charging rates to the batteries during portions of the rotation. In view of the typically low charging efficiency of alkaline nickel batteries at low rates, it was decided to measure the efficiency during a simulation of the TELSTAR 4 conditions at the expected power levels and temperatures on three nickel hydrogen cells of similar design. The unique feature of nickel hydrogen cells that makes the continuous measurement of efficiency possible is that hydrogen is one of the active materials and thus, cell pressure is a direct measure of the state of charge or available capacity. The pressure is measured with a calibrated strain gage mounted on the outside of the pressurized cell.

Fang, W. C.↗