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NASA NTRS1989

Rotation of Halley's comet

Numerical simulations supported by analytical calculations are used to model the suspected condition of Comet Halley's nucleus, which has been suggested to not be in a state of principal-axis rotation. It is found easy to numerically generate lightcurves from modulated jets of material which exhibit both of the observed periodicities of 2.2 and 7.4 days, after choosing initial conditions for a representative nucleus such that the shorter period is the rotation period, and the longer period is that of precession of the spin vector in the body frame-of-reference. The improbability of exciting a spin precession about the axis of minimum moment-of-inertia, the relative instability of this state to the jet-induced torques, and the smaller probability of observing significant seasonal changes in the lightcurve in this state, all favor the model in which Halley's nucleus precesses about the axis of maximum moment-of-inertia.

Peale, S. J.↗
NASA NTRSDate not supplied

Corrugated Rollable Tubular Booms

A promising candidate for a new class of deployable composite boom is the COrrugated ROllable TUbular Boom (COROTUB), which is to be employed on future large space structures by the National Aeronautics and Space Administration (NASA). This is due to its two corrugated thin-shells forming a closed-section,which yields high bending and torsion stiffness, allowing for high dimensional stability. The corrugation geometry that dictates the boom cross-section shape is completely defined by closed-form analytical equations given a set of key input parameters available to the designer. Parametric studies changing two geometric variables are used to evaluate which parameters most influence the cross-section’s area moment of inertia and torsional constant. The number of corrugations, flattened height of the boom, and concave and convex corrugation radii are varied to study the complete boom design space. Deeper corrugations increase the local buckling loads (crimpling) of the thin-shell boom but reduce the area moment of inertia and therefore the global Euler buckling load of the compressive member,and thus a fine balance is sought. Finite element analyses of pure bending and compression load cases for 1.22 m boom specimens were carried out to study this design trade-off in detail. Based on previous work, several thin-ply composite laminates have been selected for the different shells that form the cross-section. Feasible boom designs with a maximized stiffness and load-carrying capacity will be manufactured to study their rollability and for experimental characterization. Structural characterization tests and additional numerical analyses will provide guidelines towards future corrugated boom designs and adequate boundary conditions to maximize the boom bending strength.

Deployable Booms↗
NASA NTRSDate not supplied

Rollable Corrugated Tubular Booms

A promising candidate for a new class of deployable composite boom is the COrrugated ROllable TUbular Boom (COROTUB), which is to be employed on future large space structures by the National Aeronautics and Space Administration (NASA). The COROTUB’s two corrugated thin shells form a closed section, which yields high bending and torsional stiffness, allowing for high dimensional stability. The corrugation geometry that dictates the boom cross-section shape was completely defined by closed-form analytical equations given a set of key design parameters. Parametric studies of two geometric variables were used to evaluate which parameters most influence the cross-section’s area moment of inertia and torsional constant. The number of corrugations, flattened height of the boom, and concave and convex corrugation radii were varied to study the complete boom design space. Deeper corrugations increased the local buckling (crimpling) loads of the thin-shell boom but reduced the area moment of inertia and therefore the global buckling load of the beam-column member, and thus a fine balance was sought. Finite element analyses of pure bending and compression load cases for short, 1.22-m-long fully-deployed booms ofeither the same size (flattened height) or similar inertia properties, were first carried out to efficiently study this design trade-off in detail.A second computational study evaluated the boom transition shape and the structural response of a 6-m-long partially-deployed boom, where the effects of partially bracing the root of the boom were also assessed. It was found that bracing length could greatly affect the strength and stiffness of this boom.Bracing type (as in the discrete number of clamps at the root) had no effect on stiffness, but particularly impacted strength for loading cases and boundary conditions that promoted the onset of local web buckling at the root. The corrugated designs were also found to improve, by as much as 20%, the boom bending and axial strength and boom transition length from flat to deployed when compared to a state-of-the-art boom alternative of the same size, for short bracing distances, such as those that would be required by small satellite applications. In addition, they showed a comparable structural response for longer bracing supports.

Booms↗
NASA NTRS2004

Techniques for deriving tissue structure from multiple projection dual-energy x-ray absorptiometry

Techniques for deriving bone properties from images generated by a dual-energy x-ray absorptiometry apparatus include receiving first image data having pixels indicating bone mineral density projected at a first angle of a plurality of projection angles. Second image data and third image data are also received. The second image data indicates bone mineral density projected at a different second angle. The third image data indicates bone mineral density projected at a third angle. The third angle is different from the first angle and the second angle. Principal moments of inertia for a bone in the subject are computed based on the first image data, the second image data and the third image data. The techniques allow high-precision, high-resolution dual-energy x-ray attenuation images to be used for computing principal moments of inertia and strength moduli of individual bones, plus risk of injury and changes in risk of injury to a patient.

Charles, Jr., Harry K.↗
NASA NTRS2011

Two-Arm Flexible Thermal Strap

Airborne and space infrared cameras require highly flexible direct cooling of mechanically-sensitive focal planes. A thermal electric cooler is often used together with a thermal strap as a means to transport the thermal energy removed from the infrared detector. While effective, traditional thermal straps are only truly flexible in one direction. In this scenario, a cooling solution must be highly conductive, lightweight, able to operate within a vacuum, and highly flexible in all axes to accommodate adjustment of the focal plane while transmitting minimal force. A two-armed thermal strap using three end pieces and a twisted section offers enhanced elastic movement, significantly beyond the motion permitted by existing thermal straps. This design innovation allows for large elastic displacements in two planes and moderate elasticity in the third plane. By contrast, a more conventional strap of the same conductance offers less flexibility and asymmetrical elasticity. The two-arm configuration reduces the bending moment of inertia for a given conductance by creating the same cross-sectional area for thermal conduction, but with only half the thickness. This reduction in the thickness has a significant effect on the flexibility since there is a cubic relationship between the thickness and the rigidity or bending moment of inertia. The novelty of the technology lies in the mechanical design and manufacturing of the thermal strap. The enhanced flexibility will facilitate cooling of mechanically sensitive components (example: optical focal planes). This development is a significant contribution to the thermal cooling of optics. It is known to be especially important in the thermal control of optical focal planes due to their highly sensitive alignment requirements and mechanical sensitivity; however, many other applications exist including the cooling of gimbal-mounted components.

Urquiza, Eugenio↗
NASA NTRS1994

Contributions to the Earth's obliquity rate, precession, and nutation

The precession and nutation of the Earth's equator arise from solar, lunar, and planetary torques on the oblate Earth. The mean lunar orbit plane is nearly coincident with the ecliptic plane. A small tilt out of the ecliptic is caused by planetary perturbations and the Earth's gravitational harmonic J(sub2). These planetary perturbations on the lunar orbit result in torques on the oblate Earth which contribute to precession, obliquity rate, and nutation while the J(sub 2) perturbations contribute to precession and nutation. Small additional contributions to the secular rates arise from tidal effects and planetary torques on the Earth's bulge. The total correction to the obliquity rate is -0.024sec/century, it is an observable motion in space (the much larger conventional obliquity rate is wholly from the motion of the ecliptic, not the equator), and it is not present in the IAU-adopted expressions for the orientation of the Earth's equator. The J(sub2) effects have generally been allowed for in past nutation theories and some procession theories. For the planetary effect, the contributions to the 18.6 yr nutation are -0.03 mas (milliarcseconds) for the in-phase Delta phi plus out-of-phase contributions of 0.14 mas in Delta phi and -0.03 mas in Delta epsilon. The latter terms demonstrate that out-of-phase contributions can arise by means other than dissipation. The sum of the contributions to the precession rate is considered and the inferred value of the moment of inertia combination (C-A)/C, which is used to scale the coefficients in the nutation series, is evaluated. Using an updated value for the precession rate, the rigid body (C-A)/C = 0.003 273 763 4 which, in combination with a satellite-derived J(sub2), gives a normalized polar moment of inertia C/MR(exp2) = 0.330 700 7. The planetary contributions to the precession and obliquity rates are not constant for long times causing accelerations in both quantities. Acceleration in precession also arises from tides and changing J(sub2). Contributions from the improved theory, masses, ecliptic motion, and measured values of the precession rate and obliquity are combined to give expressions (polynomials in time) for precession, obliquity, and Greenwich Mean Sidereal Time.

Williams, James G.↗
NASA NTRS1994

Contributions to the Earth's Obliquity Rate, Precession, and Nutation

The precession and nutation of the Earth's equator arise from solar, lunar, and planetary torques on the oblate Earth. The mean lunar orbit plane is nearly coincident with the ecliptic plane. A small tilt out of the ecliptic is caused by planetary perturbations and the Earth's gravitational harmonic J(sub 2). These planetary perturbations on the lunar orbit result in torques on the oblate Earth which contribute to precession, obliquity rate, and nutation while the J(sub 2) perturbations contribute to precession and nutation. Small additional contributions to the secular rates arise from tidal effects and planetary torques on the Earth's bulge. The total correction to the obliquity rate is -0.024 sec/century, it is an observable motion in space (the much larger conventional obliquity rate is wholly from the motion of the ecliptic, not the equator), and it is not present in the IAU-adopted expressions for the orientation of the Earth's equator. The effects have generally been allowed for in past nutation theories and some precession theories. For the planetary effect, the contributions to the 18.6 yr nutation are -0.03 mas (milliarcseconds) for the in-phase Delta(psi) plus out-of-phase contributions of 0.14 mas in Delta(psi) and -0.03 mas in Delta(sub epsilon). The latter terms demonstrate that out-of-phase contributions can arise by means other than dissipation. The sum of the contributions to the precession rate is considered and the inferred value of the moment of inertia combination (C-A)/C, which is used to scale the coefficients in the nutation series, is evaluated. Using an updated value for the precession rate, the rigid body (C-A)/C =0.003 273 763 4 which, in combination with a satellite-derived J(sub 2), gives a normalized polar moment of inertia C/MR(exp 2) = 0.330 700 7. The planetary contributions to the precession and obliquity rates are not constant for long times causing accelerations in both quantities. Acceleration in precession also arises from tides and changing J(sub 2) Contributions from the improved theory, masses, ecliptic motion, and measured values of the precession rate and obliquity are combined to give expressions (polynomials in time) for precession, obliquity, and Greenwich Mean Sidereal Time.

Williams, James G.↗
NASA NTRS2010

A New Method for Interfacing Unsuited Subjects to Overhead Suspension Partial Gravity Simulators

The purpose of performing unsuited testing as part of a reduced gravity extravehicular (EVA) suited human performance research program is to define baseline performance. These results are then coupled with suited test results to evaluate how the suit system affects human performance at reduced gravity. The primary drawback to this approach is that previous studies used notably different systems to interface suited and unsuited subjects to overhead-suspension, partial-gravity simulators. A spreader bar (SB) assembly previously used for unsuited tests allowed limited pitch and roll of the subject, whereas the gimbal for suited tests allowed more pitch and roll, although the mass distribution led to large moments of inertia in the yaw axis. It is hypothesized that use of the same methods for offload of both unsuited and suited subjects is needed to make meaningful comparisons. A new gimbal (GIM) was designed with the idea that it could function with both suited and unsuited subjects. GIM was designed to minimize mass and moments of inertia and to be adjustable to co-locate the 3 axes of rotation with the subject s center of gravity. OBJECTIVE: To evaluate human performance differences between SB and GIM. METHODS: Ten unsuited subjects were off-loaded to 1/6-g using both interfaces. Subjects completed tasks including overground and treadmill ambulation, picking up objects, shoveling, postural stability, range of motion testing, and recovery from the kneeling and prone positions. Metabolic, biomechanical, and/or subjective data were collected based on task. RESULTS: Initial analyses suggest that subjects completed all tasks with lower levels of compensation and a more terrestrial approach to movement when suspended via GIM. With SB, subjects were not able to fall or get into a prone position and had increased difficulty both retrieving objects off the floor and with overground ambulation, especially at gait initiation, because they were unable to bend their torso. GIM shows promise as a new method.

Norcross, Jason R.↗
NASA NTRS2011

A New Method for Interfacing Unsuited Subjects to Overhead Suspension Partial Gravity Simulators

The purpose of performing unsuited testing as part of a reduced gravity extravehicular (EVA) suited human performance research program is to define baseline performance. These results are then coupled with suited test results to evaluate how the suit system affects human performance at reduced gravity. The primary drawback to this approach is that previous studies used notably different systems to interface suited and unsuited subjects to overhead-suspension, partial-gravity simulators. A spreader bar (SB) assembly previously used for unsuited tests allowed limited pitch and roll of the subject, whereas the gimbal for suited tests allowed more pitch and roll, although the mass distribution led to large moments of inertia in the yaw axis. It is hypothesized that use of the same methods for offload of both unsuited and suited subjects is needed to make meaningful comparisons. A new gimbal (GIM) was designed with the idea that it could function with both suited and unsuited subjects. GIM was designed to minimize mass and moments of inertia and to be adjustable to co-locate the 3 axes of rotation with the subject s center of gravity. OBJECTIVE: To evaluate human performance differences between SB and GIM. METHODS: Ten unsuited subjects were offloaded to 1/6-g using both interfaces. Subjects completed tasks including overground and treadmill ambulation, picking up objects, shoveling, postural stability, range of motion testing, and recovery from the kneeling and prone positions. Metabolic, biomechanical, and/or subjective data were collected based on task. RESULTS: Initial analyses suggest that subjects completed all tasks with lower levels of compensation and a more terrestrial approach to movement when suspended via GIM. With SB, subjects were not able to fall or get into a prone position and had increased difficulty both retrieving objects off the floor and with overground ambulation, especially at gait initiation, because they were unable to bend their torso. GIM shows promise as a new method.

Norcross, Jason↗
NASA NTRS2000

A Determination of the Precession and Rotation-Rate of Mars from Tracking and Altimetry Data

The doppler tracking of the MGS spacecraft and the laser altimetry acquired by the MOLA instrument on MGS have been used to measure the rotation of Mars. By observing the repeating pattern of gravity anomalies and the topography the direction of the rotation axis in both inertial space and body fixed coordinates, and the rate of rotation of the planet on its axis have been derived. The tracking of MGS in orbit about Mars by stations on Earth permit the orbit of MGS to be obtained in an inertial coordinate system enabling the periodic perturbation of the MGS orbit by Mars' gravity field to be used as a sensor to detect the vector rotation of Mars under the orbit of MGS. The altimetry data acquired by MOLA on MGS permit the topography to help define the orbit of MGS about Mars in a body fixed coordinate system thus enabling the pole of rotation of the planet to be determined in a coordinate system defined by the altimetry. Together they enable the precession of the rotation axis to be observed from which the moment of inertia can be derived, changes in length of day to be measured, and a method to check for possible Mars polar motion. Tracking data on the Mariner 9, Viking 1 and 2, from the 1970's have been analyzed with MGS data obtained in the mapping orbit in 1999 to provide a new estimate of the moment of inertia.

Smith, David E.↗
NASA NTRS1973

Some effects of elasticity on lunar rotation

A general Hamiltonian for a rotating moon in the field of the earth is expanded in terms of parameters orienting the spin angular momentum relative to the principal axes of the moon and relative to coordinate axes fixed in the orbital plane. The effects of elastic distortion are included as modifications of the moment of inertia tensor, where the magnitude of the distortion is parameterized by the Love number k2. The amplitudes of the principal periodic terms in the longitude of a point on the moon due to variations of the tide caused by the earth are discussed. A detailed derivation of the free wobble of the lunar spin axis about the axis of maximum moment of inertia is given. If the moon's rigidity is close to that of the earth there is no effect of elasticity on the rotation which can be measured with the laser ranging and, therefore, no elastic properties of the moon can be determined from variations in the rotation.

Peale, S. J.↗
NASA NTRS2021

The Determination of the Rotational State and Interior Structure of Venus with VERITAS

Understanding the processes that led Venus to its current state and will drive its future evolution is a major objective of the next generation of orbiters. In this work we analyze the retrieval of the spin vector, the tidal response and the moment of inertia of Venus with VERITAS, a NASA Discovery-class mission. By simulating a systematic joint analysis of Doppler tracking data and tie points provided by the onboard synthetic aperture radar we show that VERITAS will provide accuracies (3σ) in the estimates of the tidal Love number k_2 to 4.6×10^(-4), its tidal phase lag to 0.05°, and the moment of inertia factor to 9.8×10^(-4) (0.3% of the expected value). Applying these results to recent models of the Venus interior, we show that VERITAS will provide much improved constraints on the interior structure of the planet.

G Cascioli↗
NASA NTRS2001

Three Dimensional Cross-Sectional Properties From Bone Densitometry

Bone densitometry has previously been used to obtain cross-sectional properties of bone in a single scan plane. Using three non-coplanar scans, we have extended the method to obtain the principal area Moments of inertia and orientations of the principal axes at each cross-section along the length of the scan. Various 5 aluminum phantoms were used to examine scanner characteristics to develop the highest accuracy possible for in vitro non-invasive analysis of mass distribution. Factors considered included X-ray photon energy, initial scan orientation, the included angle of the 3 scans, and Imin/Imax ratios. Principal moments of inertia were accurate to within 3.1% and principal angles were within 1 deg. of the expected value for phantoms scanned with included angles of 60 deg. and 90 deg. at the higher X-ray photon energy. Low standard deviations in error also 10 indicate high precision of calculated measurements with these included angles. Accuracy and precision decreased slightly when the included angle was reduced to 30 deg. The method was then successfully applied to a pair of excised cadaveric tibiae. The accuracy and insensitivity of the algorithms to cross-sectional shape and changing isotropy (Imin/Imax) values when various included angles are used make this technique viable for future in vivo studies.

Cleek, Tammy M.↗
NASA NTRS1978

Superdense neutron matter

A relativistic theory of high-density matter is presented which takes into account the short-range interaction due to the exchange of spin-2 mesons. An equation of state is derived and used to compute neutron-star properties. The prediction of the theory for the values of maximum mass and moment of inertia for a stable neutron star are 1.75 solar masses and 1.68 by 10 to the 45th power g-sq cm, in very good agreement with the presently known observational bounds. The corresponding radius is found to be 10.7 km. It is found that the inclusion of the spin-2 interaction reduces the disagreement between the relativistic and nonrelativistic theories in their predictions of masses and moments of inertia.

Canuto, V.↗
NASA NTRS1976

Relation of a contracting earth to the apparent accelerations of the sun and moon

It has been concluded that the theoretical ratio of the apparent secular accelerations of the moon and the sun implied by tidal theory is far higher than the ratio of observed values. This paper shows that the discrepancy can be entirely removed within the range of uncertainty of the various quantities involved if terms making allowance for a secularly decreasing terrestrial moment of inertia are included in the dynamical equations for the apparent secular accelerations. Such a decrease has already been predicted on the basis of the phase-change hypothesis for the nature of earth's core. The development of this hypothesis is reviewed, the modified dynamical equations are derived, and values of tidal couples implied by existing observational data are examined. The numerically determined rate of decrease of earth's moment of inertia is found to be in close agreement with that predicted by the phase-change hypothesis. The results indicate that a diminishing gravitational constant is unlikely, that the moon would have been in close proximity to earth only 1 billion years ago, and that earth's rotation period at that time would have been about 5 hr.

Lyttleton, R. A.↗
NASA NTRS2002

Cross-sectional structural parameters from densitometry

Bone densitometry has previously been used to obtain cross-sectional properties of bone from a single X-ray projection across the bone width. Using three unique projections, we have extended the method to obtain the principal area moments of inertia and orientations of the principal axes at each scan cross-section along the length of the scan. Various aluminum phantoms were used to examine scanner characteristics to develop the highest accuracy possible for in vitro non-invasive analysis of cross-sectional properties. Factors considered included X-ray photon energy, initial scan orientation, the angle spanned by the three scans (included angle), and I(min)/I(max) ratios. Principal moments of inertia were accurate to within +/-3.1% and principal angles were within +/-1 degrees of the expected value for phantoms scanned with included angles of 60 degrees and 90 degrees at the higher X-ray photon energy (140 kVp). Low standard deviations in the error (0.68-1.84%) also indicate high precision of calculated measurements with these included angles. Accuracy and precision decreased slightly when the included angle was reduced to 30 degrees. The method was then successfully applied to a pair of excised cadaveric tibiae. The accuracy and insensitivity of the algorithms to cross-sectional shape and changing isotropy (I(min)/I(max)) values when various included angles are used make this technique viable for future in vivo studies.

NASA Center ARC↗
NASA NTRS2014

GRAIL Refinements to Lunar Seismic Structure

Joint interpretation of disparate geophysical datasets helps reduce drawbacks that can result from analyzing them individually. The Apollo seismic network was situated on the lunar nearside surface in a roughly equilateral triangle having sides approximately 1000 km long, with stations 12/14 nearly co-located at one corner. Due to this limited geographical extent, near-surface ray coverage from moonquakes is low, but increases with depth. In comparison, gravity surveys and their resulting gravity anomaly maps have traditionally offered optimal resolution at crustal depths. Gravimetric maps and seismic data sets are therefore well suited to joint inversion, since the complementary information reduces inherent model ambiguity. Previous joint inversions of the Apollo seismic data (seismic phase arrival times) and Clementine- or Lunar Prospector-derived gravity data (mass and moment of inertia) attempted to recover the subsurface structure of the Moon by focusing on hypothetical lunar compositions that explored the density/velocity relationship. These efforts typically searched for the best fitting thermodynamically calculated velocity/density model, and allowed variables like core size, velocity, and/or composition to vary freely. Seismic velocity profiles derived from the Apollo seismic data through travel time inversion vary both in the depth of the crust and mantle layers, and the seismic velocities and densities assigned to those layers. The lunar mass and moment of inertia likewise only constrain gross variations in the density profile beyond that of a uniform density sphere. As a result, composition and structure models previously obtained by jointly inverting these data retain the original uncertainties inherent in the input data sets. We perform a joint inversion of Apollo seismic delay times and gravity data collected by the GRAIL lunar gravity mission, in order to recover seismic velocity and density as a function of latitude, longitude, and depth within the Moon. We relate density (p) to seismic velocity (v) using a depth-dependent linear relationship. The corresponding coefficient (B) can reflect a variety of material properties, including temperature and composition. The inversion seeks to recover the set of p, v, and B perturbations that minimize (in a least-squares sense) the difference between the observed and calculated data.

Weber, Renee C.↗