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NASA NTRS1985

Dynamic response of a flexible space beam

Dynamic response of a candidate flexible beam for a space experiment on control of flexible structures is investigated. Studies of natural frequencies reveal a beam length in which torsion and bending frequencies virtually coincide. Eccentric tip mass causes small shifts in natural frequencies but introduces coupled torsional/bending mode shapes. Transient response studies indicate significant effects on tip responses of low damping and first bending mode excitation at higher frequencies. Steady state response suggest displacement and acceleration measurements could be made up to 5 to 12 Hz for the actuator forces/torques assumed.

Card, M. F.↗

NASA NTRS1985

Vibration/Libration Interaction Dynamics During the Orbiter Based Deployment of Flexible Members

Essential features of a general formulation for studying librational dynamics of a large class of spacecraft during deployment of flexible members are reviewed. The formulation is applicable to a variety of missions ranging from deployment of antennas, booms and solar panels to manufacturing of trusses for space platforms using the space shuttle. The governing nonlinear, non-autonomous and coupled equations of motion are extremely difficult to solve even with the help of a computer, not to mention the cost involved. To get some appreciation as to the complex interactions between flexibility, deployment and attitude dynamics as well as to help pursue stability and control analysis, the equations are linearized about their nominal deflected equilibrium configuration. The procedure is applied to the Space Shuttle based deployment of boom and plate-like members. Results suggest substantial influence of the inertia parameter, flexural rigidity of the appendages, orbit eccentricity, deployment velocity, initial conditions, etc. on the system response. The results should prove useful in planning of the Orbiter based experiments aimed at assessing effectiveness of procedures for studying dynamics and control of flexible orbiting members.

Modi, V. J.↗

NASA NTRS1996

Dual-Eccentric Clevis Joint

Redesigned clevis joint incorporates dual mating eccentric cylindrical bushings to accommodate dimensional tolerances. Eliminates need for combination of oppositely threaded collar and bushing and makes overall joint hardware fit within available space.

Fairbank, Diana L.↗

NASA NTRS2000

Optimal Configurations for Rotating Spacecraft Formations

In this paper a new class of formations that maintain a constant shape as viewed from the Earth is introduced. An algorithm is developed to place n spacecraft in a constant shape formation spaced equally in time using the classical orbital elements. To first order, the dimensions of the formation are shown to be simple functions of orbit eccentricity and inclination. The performance of the formation is investigated over a Keplerian orbit using a performance measure based on a weighted average of the angular separations between spacecraft in formation. Analytic approximations are developed that yield optimum configurations for different values of n. The analytic approximations are shown to be in excellent agreement with the exact solutions.

Hughes, Steven P.↗

NASA NTRS1999

Long-Term Stability of Planets in Binary Systems

A simple question of celestial mechanics is investigated: in what regions of phase space near a binary system can planets persist for long times? The planets are taken to be test particles moving in the field of an eccentric binary system. A range of values of the binary eccentricity and mass ratio is studied, and both the case of planets orbiting close to one of the stars, and that of planets outside the binary orbiting the systems center of mass, are examined. From the results, empirical expressions are developed for both (1) the largest orbit around each of the stars and (2) the smallest orbit around the binary system as a whole, in which test particles survive the length of the integration (10A4 binary periods). The empirical expressions developed, which are roughly linear in both the mass ratio mu and the binary eccentricity e, are determined for the range 0.0=e=0.7-0.8 and 0.1=mu=0.9 in both regions and can be used to guide searches for planets in binary systems. After considering the case of a single low-mass planet in binary systems, the stability of a mutually interacting system of planets orbiting one star of a binary system is examined, though in less detail.

Holman, Matthew J.↗

NASA NTRS1981

Canonical orbital elements in terms of an arbitrary independent variable

Within the framework of the Hamiltonian mechanics in the extended phase space, a set of canonical elements of the Delaunay type is developed in terms of an arbitary independent angular variable. Application to the four classical anomalies - eccentric, true, elliptic, and mean - is presented. Particular attention is given to the generalized time equation and its conjugate energy equation.

Bond, V. R.↗

NASA NTRS1984

The rotation of Hyperion

For almost the entire range of dimensions of Hyperion allowed by uncertainties in the observations, the satellite cannot librate stably about a rotation rate which is synchronous with its orbital mean motion. Rather, the large gravitational torques on the asymmetric satellite coupled with the large eccentricity forced by the orbital resonance with Titan cause Hyperion to tumble in a random manner. Large changes in orientation of body axes relative to inertial space and in the instantaneous spin rate occur on timescales of the order of the orbit period. Numerical evaluation of the exponential divergence of nearby trajectories in the phase space of the motion verifies that the tumbling is truly chaotic. This newly defined state of chaotic rotation for Hyperion is likely to be the only example of confined, continuously observable chaotic motion in the solar system.

Peale, S. J.↗

NASA NTRS1987

Three-step labyrinth seal for high-performance turbomachines

A three-step labyrinth seal with 12, 11, and 10 labyrinth teeth per step, respectively, was tested under static (nonrotating) conditions. The configuration represented the seal for a high-performance turbopump (e.g., the space shuttle main engine fuel pump). The test data included critical mass flux and pressure profiles over a wide range of fluid conditions at concentric, partially eccentric, and fully eccentric seal positions. The seal mass fluxes (leakage rates) were lower over the entire range of fluid conditions tested than those for data collected for similar straight and three-step cylindrical seals, and this conformed somewhat to expectations. However, the pressure profiles for the eccentric positions indicated little, if any, direct stiffness for this configuration in contrast to significant direct stiffness reported for the straight and three-step cylindrical seals over the range of test conditions. Seal dynamics depend on geometric configuration, inlet and exit parameters, fluid phase, and rotation. The method of corresponding states was applied to the mass flux data, which were found to have a pressure dependency for helium.

Hendricks, Robert C.↗

NASA NTRS1983

Transformations of the perturbed two-body problem to unperturbed harmonic oscillators

Singular, nonlinear, and Liapunov unstable equations are made regular and linear through transformations that change the perturbed planar problem of two bodies into unperturbed and undamped harmonic oscillators with constant coefficients, so that the stable solution may be immediately written in terms of the new variables. The use of arbitrary and special functions for the transformations allows the systematic discussion of previously introduced and novel anomalies. For the case of the unperturbed two-body problem, it is proved that if transformations are power functions of the radial variable, only the eccentric and the true anomalies (with the corresponding transformations of the radial variable) will result in harmonic oscillators. The present method significantly reduces computation requirements in autonomous space operations.

Szebehely, V.↗

NASA NTRS1985

Rotordynamic coefficients for compressible flow in tapered annular seals

Derivation of the governing equations for compressible flow in a tapered annular seal is based on Hirs' turbulent bulk-flow model. Zeroth and first-order perturbation equations are developed by an expansion in the eccentricity ratio. These equations are numerically integrated to obtain the leakage, and the direct and cross-coupled stiffness and damping coefficients. Seal parameters similar to the Space Shuttle Main Engine High Pressure Oxidizer Turbopump are used to demonstrate output from the analysis procedure. The effects of preswirl and seal taper are shown for three different length-to-diameter ratios. Generally the results indicate that prerotating the fluid significantly increases the cross-coupled stiffness but has little effect on the other coefficients, and increasing the convergent taper increases the direct stiffness while decreasing the direct damping and cross-coupled stiffness.

Nelson, C. C.↗

NASA NTRS1987

Urey Prize Lecture - Chaotic dynamics in the solar system

Attention is given to solar system cases in which chaotic solutions of Newton's equations are important, as in chaotic rotation and orbital evolution. Hyperion is noted to be tumbling chaotically; chaotic orbital evolution is suggested to be of fundamental importance to an accounting for the Kirkwood gaps in asteroid distribution and for the phase space boundary of the chaotic zone at the 3/1 mean-motion commensurability with Jupiter. In addition, chaotic trajectories in the 2/1 chaotic zone reach very high eccentricities by a route that carries them to high inclinations temporarily.

Wisdom, Jack↗

NASA NTRS2013

STIS Coronagraphic Imaging of Fomalhaut: Main Belt Structure and the Orbit of Fomalhaut b

We present new optical coronagraphic data of Fomalhaut obtained with HST/STIS in 2010 and 2012. Fomalhaut b is recovered at both epochs to high significance. The observations include the discoveries of tenuous nebulosity beyond the main dust belt detected to at least 209AU projected radius, and a approx. 50AU wide azimuthal gap in the belt northward of Fomalhaut b. The two epochs of Space Telescope Imaging Spectrograph (STIS) photometry exclude optical variability greater than 35%. A Markov chain Monte Carlo analysis demonstrates that the orbit of Fomalhaut b is highly eccentric, with e = 0.8 +/- 0.1, a = 177 +/- 68AU, and q = 32 +/- 24AU. Fomalhaut b is apsidally aligned with the belt and 90% of allowed orbits have mutual inclination <=36 deg. Fomalhaut b's orbit is belt crossing in the sky plane projection, but only 12% of possible orbits have ascending or descending nodes within a 25AU wide belt annulus. The high eccentricity invokes a dynamical history where Fomalhaut b may have experienced a significant dynamical interaction with a hypothetical planet Fomalhaut c, and the current orbital configuration may be relatively short-lived. The Tisserand parameter with respect to a hypothetical Fomalhaut planet at 30AU or 120AU lies in the range 2-3, similar to highly eccentric dwarf planets in our solar system. We argue that Fomalhaut b's minimum mass is that of a dwarf planet in order for a circumplanetary satellite system to remain bound to a sufficient radius from the planet to be consistent with the dust scattered light hypothesis. In the coplanar case, Fomalhaut b will collide with the main belt around 2032, and the subsequent emergent phenomena may help determine its physical nature.

Tisserand parameter↗

NASA NTRS2019

The mass and density of the dwarf planet (225088) 2007 OR10

The satellite of (225088) 2007 OR10 was discovered on archival Hubble Space Telescope images and along with new observations with the WFC3 camera in late 2017 we have been able to determine the orbit. The orbit's notable eccentricity, e ≈ 0.3, may be a consequence of an intrinsically eccentric orbit and slow tidal evolution, but may also be caused by the Kozai mechanism. Dynamical considerations also suggest that the moon is small, D(eff) < 100 km. Based on the newly determined system mass of 1.75 ·10^21 kg, 2007 OR10 is the fifth most massive dwarf planet after Eris, Pluto, Haumea and Makemake. The newly determined orbit has also been considered as an additional option in our radiometric analysis, provided that the moon orbits in the equatorial plane of the primary. Assuming a spherical shape for the primary this approach provides a size of 1230 ± 50 km, with a slight dependence on the satellite orbit orientation and primary rotation rate chosen, and a bulk density of 1.75 ± 0.07 g/cu.cm for the primary. A previous size estimate that assumed an equator-on configuration (1535(−225,+75) km) would provide a density of 0.92(−0.14,+0.46) g/cu.cm, unexpectedly low for a 1000 km-sized dwarf planet.

Csaba Kiss↗

NASA NTRS1992

Intramuscular pressure: A better tool than EMG to optimize exercise for long-duration space flight

A serious problem experienced by astronauts during long-duration space flight is muscle atrophy. In order to develop countermeasures for this problem, a simple method for monitoring in vivo function of specific muscles is needed. Previous studies document that both intramuscular pressure (IMP) and electromyography (EMG) provide quantitative indices of muscle contraction force during isometric exercise. However, at present there are no data available concerning the usefulness of IMP versus EMG during dynamic exercise. Methods: IMP (Myopress catheter) and surface EMG activity were measured continuously and simultaneously in the tibalis anterior (TA) and soleus (SOL) muscles of 9 normal male volunteers (28-54 years). These parameters were recorded during both concentric and eccentric exercises which consisted of plantarflexon and dorsiflexon of the ankle joint. A Lido Active Isokinetic Dynamometer concurrently recorded ankle joint torque and position. Results: Intramuscular pressure correlated linearly with contraction force for both SOL (r exp 2 = 0.037) and TA (R exp 2 = 0.716 and r exp 2 = 0.802, respectively). During eccentric exercises, SOL and TA IMP also correlated linearly with contraction force (r(exp 2) = 0.883 and r(exp 2) = 0.904 respectively), but SOL and TA EMG correlated poorly with force (r(exp 2) = 0.489 and r(exp 2) = 0.702 respectively). Conclusion: IMP measurement provides a better index of muscle contraction force than EMG during concentric and eccentric exercise. IMP reflects intrinsic mechanical properties of individual muscles, such as length tension relationships. Although invasive, IMP provides a more powerful tool and EMG for developing exercise hardware and protocols for astronauts exposed to long-duration space flight.

Hargens, A. R.↗

NASA NTRS1973

Diffraction studies applicable to 60-foot microwave research facilities

The principal features of this document are the analysis of a large dual-reflector antenna system by vector Kirchhoff theory, the evaluation of subreflector aperture-blocking, determination of the diffraction and blockage effects of a subreflector mounting structure, and an estimate of strut-blockage effects. Most of the computations are for a frequency of 15.3 GHz, and were carried out using the IBM 360/91 and 360/95 systems at Goddard Space Flight Center. The FORTRAN 4 computer program used to perform the computations is of a general and modular type so that various system parameters such as frequency, eccentricity, diameter, focal-length, etc. can be varied at will. The parameters of the 60-foot NRL Ku-band installation at Waldorf, Maryland, were entered into the program for purposes of this report. Similar calculations could be performed for the NELC installation at La Posta, California, the NASA Wallops Station facility in Virginia, and other antenna systems, by a simple change in IBM control cards. A comparison is made between secondary radiation patterns of the NRL antenna measured by DOD Satellite and those obtained by analytical/numerical methods at a frequency of 7.3 GHz.

Schmidt, R. F.↗

NASA NTRS2001

Evaluation of Relative Navigation Algorithms for Formation-Flying Satellites

Goddard Space Flight Center is currently developing advanced spacecraft systems to provide autonomous navigation and control of formation flyers. This paper discusses autonomous relative navigation performance for formations in eccentric, medium, and high-altitude Earth orbits using Global Positioning System (GPS) Standard Positioning Service (SPS) and intersatellite range measurements. The performance of several candidate relative navigation approaches is evaluated. These analyses indicate that the relative navigation accuracy is primarily a function of the frequency of acquisition and tracking of the GPS signals. A relative navigation position accuracy of 0.5 meters root-mean-square (RMS) can be achieved for formations in medium-attitude eccentric orbits that can continuously track at least one GPS signal. A relative navigation position accuracy of better than 75 meters RMS can be achieved for formations in high-altitude eccentric orbits that have sparse tracking of the GPS signals. The addition of round-trip intersatellite range measurements can significantly improve relative navigation accuracy for formations with sparse tracking of the GPS signals.

Kelbel, David↗

NASA NTRS2016

In-Space Production of Storable Propellants

Our exploration of the feasibility of in-space production of storable propellants from resourcesavailable on asteroids, and also on Mars and the Moon, has considered the process of sampleacquisition; the energy requirements for heating and volatile release; the thermodynamic behaviorof gas release from minerals and organic polymers containing hydrogen, oxygen, carbon, sulfur,and nitrogen; purification of the released water and carbon dioxide; the storage and transportation of these materials in the condensed state; synthesis of fuels including methanol and dimethyl ether(DME); and the co-production, concentration, stability, and storage of the complementary oxidizer high-test hydrogen peroxide (HTP). We call attention to the ability of the storable propellant/oxidizer combination of DME and HTP to carry out deep-space missions and to perform retrieval and relocation of any and all space-derived resources, such as retrieving asteroidal metal to high Earth orbit. This study's analyses are based on returning resources to a storage/processing/dispensing facility in a Highly Eccentric Earth Orbit (HEEO) with a perigee above geosynchronous orbit and an apogee approach or beyond the Moon's orbit.The methane/LOX option, notable for good engine performance, has not been included in this study because our scope includes only fully storable propellants.

Lewis, John S.↗

NASA NTRS2010

Triaxial Swirl Injector Element for Liquid-Fueled Engines

A triaxial injector is a single bi-propellant injection element located at the center of the injector body. The injector element consists of three nested, hydraulic swirl injectors. A small portion of the total fuel is injected through the central hydraulic injector, all of the oxidizer is injected through the middle concentric hydraulic swirl injector, and the balance of the fuel is injected through an outer concentric injection system. The configuration has been shown to provide good flame stabilization and the desired fuel-rich wall boundary condition. The injector design is well suited for preburner applications. Preburner injectors operate at extreme oxygen-to-fuel mass ratios, either very rich or very lean. The goal of a preburner is to create a uniform drive gas for the turbomachinery, while carefully controlling the temperature so as not to stress or damage turbine blades. The triaxial injector concept permits the lean propellant to be sandwiched between two layers of the rich propellant, while the hydraulic atomization characteristics of the swirl injectors promote interpropellant mixing and, ultimately, good combustion efficiency. This innovation is suited to a wide range of liquid oxidizer and liquid fuels, including hydrogen, methane, and kerosene. Prototype testing with the triaxial swirl injector demonstrated excellent injector and combustion chamber thermal compatibility and good combustion performance, both at levels far superior to a pintle injector. Initial testing with the prototype injector demonstrated over 96-percent combustion efficiency. The design showed excellent high -frequency combustion stability characteristics with oxygen and kerosene propellants. Unlike the more conventional pintle injector, there is not a large bluff body that must be cooled. The absence of a protruding center body enhances the thermal durability of the triaxial swirl injector. The hydraulic atomization characteristics of the innovation allow the design to be rapidly scaled from small in-space applications [500-5,000 lbf (2.2 22.2 kN)] to large thrust engine applications [80,000 lbf (356 kN) and beyond]. The triaxial injector is also less sensitive to eccentricities, manufacturing tolerances, and gap width of many traditional coaxial and pintle injector designs. The triaxial-injector injection orifice configuration provides for high injection stiffness. The low parts count and relatively large injector design features are amenable to low-cost production.

Muss, Jeff↗