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All sourcesNASA NTRSDOE OSTI
NASA NTRS2012

Gravity Field and Internal Structure of Mercury from MESSENGER

Radio tracking of the MESSENGER spacecraft has provided a model of Mercury's gravity field. In the northern hemisphere, several large gravity anomalies, including candidate mass concentrations (mascons), exceed 100 milli-Galileos (mgal). Mercury's northern hemisphere crust is thicker at low latitudes and thinner in the polar region and shows evidence for thinning beneath some impact basins. The low-degree gravity field, combined with planetary spin parameters, yields the moment of inertia C/M(R(exp 2) = 0.353 +/- 0.017, where M and R are Mercury's mass and radius, and a ratio of the moment of inertia of Mercury's solid outer shell to that of the planet of C(sub m)/C = 0.452 +/- 0.035. A model for Mercury s radial density distribution consistent with these results includes a solid silicate crust and mantle overlying a solid iron-sulfide layer and an iron-rich liquid outer core and perhaps a solid inner core.

Smith, David E.↗
NASA NTRS2013

What Should the FeO Content of a Terrestrial Planet Be?

Basalts from the Earth, the Moon, Mars, and Vesta are strongly depleted in elements that prefer to reside in the metallic state (siderophile elements). Therefore, it is believed that all these bodies have metallic cores. We do not yet have siderophile element analyses of venusian or mercurian basalts, but we assume that Venus, too, as a terrestrial planet, has a metallic core. For the Earth, Moon, Mercury, and Mars, the moments-of-inertia of these bodies are consistent with metallic cores of various sizes. Because Venus rotates so slowly, it may be difficult to determine the moment-of-inertia of Venus in order to confirm this assumption. However, despite many possible complexities, it seems likely that most of the major and minor terrestrial planets have experienced some sort of metal/silicate equilibration, and we will use this as a boundary condition. One immediate contrast between the Earth and Moon is the difference in FeO content between lunar and terrestrial basalts. Both bodies presumably formed near 1 AU and formed from the same feeding zone of planetesimals, judging by their oxygen isotopes [13]. If, for example, the Moon formed from the Earth by a giant impact, then this event must have occurred before high-pressure equilibria had the opportunity to deplete the Earth s mantle in FeO. Alternatively, the bulk silicate Moon may be dominated by material from the impactor. Regardless, it would be useful to know the pressures where FeO incorporation into a metallic core is not of interest. If the Giant Impact hypothesis is correct, this should set an upper limit for the size of the proto-Earth at the time of the impact.

Jones, John H.↗
NASA NTRS2006

Free Body Dynamics of a Spinning Cylinder With Planar Restraint (a.k.a. Barrel of Fun)

The dynamic motion of a cylinder on a floor or hard surface is both entertaining and instructive. With maintenance torques, motion can be sustained and controlled as illustrated in a video clip that can be viewed in the PDF file of this document. The analysis of such a cylinder with and without end caps is burned on rotation about its center of mass and restrained by a plane normal to the axis passing through its center of mass at an angle alpha. For small values of alpha, the governing equations are simplified, and for symmetric bodies, stability requires rotation greater than [2 square root of(JWL*)]/J(sub X), where J is the transverse mass moment of inertia, W is the weight of the cylinder, L* is the cylinder length from the base to the center of mass, and JX is the mass moment of inertia about the longitudinal axis OX of the barrel. Comparisons to data are made and some applications are discussed.

Moraru, Laurentiu↗
NASA NTRS2012

Gravity, Topography, and Magnetic Field of Mercury from Messenger

On 18 March 2011, the MErcury Surface, Space ENvironment, GEochemistry, and Ranging (MESSENGER) spacecraft was inserted into a 12-hour, near-polar orbit around Mercury, with an initial periapsis altitude of 200 km, initial periapse latitude of 60 deg N, and apoapsis at approximately 15,200 km altitude in the southern hemisphere. This orbit has permitted the mapping of regional gravitational structure in the northern hemisphere, and laser altimetry from the MESSENGER spacecraft has yielded a geodetically controlled elevation model for the same hemisphere. The shape of a planet combined with gravity provides fundamental information regarding its internal structure and geologic and thermal evolution. Elevations in the northern hemisphere exhibit a unimodal distribution with a dynamic range of 9.63 km, less than that of the Moon (19.9 km), but consistent with Mercury's higher surface gravitational acceleration. After one Earth-year in orbit, refined models of gravity and topography have revealed several large positive gravity anomalies that coincide with major impact basins. These candidate mascons have anomalies that exceed 100 mGal and indicate substantial crustal thinning and superisostatic uplift of underlying mantle. An additional uncompensated 1000-km-diameter gravity and topographic high at 68 deg N, 33 deg E lies within Mercury's northern volcanic plains. Mercury's northern hemisphere crust is generally thicker at low latitudes than in the polar region. The low-degree gravity field, combined with planetary spin parameters, yields the moment of inertia C/MR2 = 0.353 +/- 0.017, where M=3.30 x 10(exp 23) kg and R=2440 km are Mercury's mass and radius, and a ratio of the moment of inertia of Mercury's solid outer shell to that of the planet of Cm/C = 0.452 +/- 0.035. One proposed model for Mercury's radial density distribution consistent with these results includes silicate crust and mantle layers overlying a dense solid (possibly Fe-S) layer, a liquid Fe-rich outer core of radius 2030 +/- 37 km, and an assumed solid inner core. Magnetic field measurements indicate a northward offset of Mercury's axial magnetic dipole from the geographic equator by 479 +/-3 km and provide evidence for a regional-scale magnetic field approximately collocated with the northern volcanic plains of possible crustal origin. These results from MESSENGER indicate a complex and asymmetric evolution of internal structure and dynamics in this end-member inner planet.

Neumann, Gregory A.↗
NASA NTRS1999

A View of the Lunar Interior Through Lunar Laser Range Analysis

Laser ranges between observatories on the Earth and retroreflectors on the Moon started in 1969 and continue to the present. Recent range accuracies are 2 cm while earliest ranges are an C, order of magnitude less certain. Four retroreflectors are ranged: three located at the Apollo 11, 14, and 15 sites and one on the Lunakhod 2 rover. Accurate analysis of the range data determines a number of lunar science parameters. The lunar interior variables include a fluid core parameter. The Lunar Laser Ranging effort is reviewed elsewhere. Many parameters are detected through their influence on rotation. Also detected are solid-body tides and accurate selenocentric reflector locations. Determined through the rotation are moment-of-inertia differences, gravitational harmonics, potential Love number, and dissipation effects due to tides and molten core. The rotation of the Moon is not at its minimum energy state; some recently active process has caused free librations. The moment differences contributed to the recent improvement of the Moon's moment of inertia from the Lunar Prospector gravity field. The Love numbers provide bulk elastic properties. Future possibilities for measurement include oblateness of the core-mantle boundary and core moment. A study of dissipation signatures in the rotation determines tidal Q vs. frequency and concludes that the Moon has a molten core. At 1 month the tidal Q is 37 and at 1 yr it is 60. The core radius is < or = 352 km for Fe and < or = 374 km for the Fe-FeS eutectic. The core detection exceeds 3x its uncertainty. The spin of the core is not aligned with the spin of the mantle and torque arises from the velocity difference at the boundary. Yoder's turbulent boundary layer theory is used to compute the radii. The present heat generation from tides and core interaction is minor compared to radiogenic heating. The heating for ancient times is more interesting. Peale and Cassen investigated lunar tidal heating while the lunar orbit expanded due to tides on Earth. Their calculations predate the measurement of Q and should be multiplied by 3.45 to match the lunar-laser-determined Love number and monthly Q. Tidal-heating computations depend on how fast the lunar orbit evolved and whether the tidal dissipation is localized. Neither is known, but plausible assumptions lead to early central region temperature increases of several hundred degrees. Most of the energy is deposited early in the Moon's history. The turbulent boundary layer theory allows a prediction of energy dissipated at the core-mantle boundary during orbit evolution. Under the assumption that the properties of the early core are the same as at present, the energy dissipated by core-mantle interaction is about the same as for tidal dissipation, but it is deposited in a smaller volume. This source of energy is capable of promoting convection in an early fluid core and driving a dynamo. This is a transient phase with a duration depending on the rate of orbit evolution. Plausible assumptions lead to a duration of a few hundred million years. Thus, the remnant magnetization of many lunar rocks is compatible with a brief global magnetic field powered by dynamical energy dissipation. Analysis of the lunar laser ranges is providing information on lunar geophysics. Future data will improve accuracies of present solution parameters, and several more interior effects should be detectable.

Williams, J. G.↗
NASA NTRS1995

Hindlimb suspension diminishes femoral cross-sectional growth in the rat

Growth, functional adaptation, and torsional strength were examined in the femora of 39-day-old male Sprague-Dawley rats subjected to hindlimb suspension for 0, 1, 2, 3, or 4 weeks and were compared with measurements for age-matched control animals. Our goal was to understand the effect of reduced loading on the normal age-related changes in femoral properties during growth. The control animals exhibited growth-related increases in all geometric and torsional properties of the femur. The mean body mass and femoral length of the hindlimb-suspended rats were similar to those of the controls throughout the experiment. Over 4 weeks, the femoral cross-sectional and torsional measurements from the hindlimb-suspended rats demonstrated increases in comparison with the basal values (+33% cross-sectional area, +64% polar moment of inertia, +67% ultimate torque, and +181% torsional rigidity), but the age-matched controls showed significantly greater growth-related increases (+71% cross-sectional area, +136% polar moment of inertia, +127% ultimate torque, and +367% torsional rigidity). The differences in femoral structural strength between the hindlimb-suspended animals and the age-matched controls were attributable to differences in altered cross-sectional geometry.

NASA Discipline Musculoskeletal↗
NASA NTRS1972

Results of intravehicular manned cargo-transfer studies in simulated weightlessness

A parametric investigation was conducted in a water immersion simulator to determine the effect of package mass, moment of inertia, and size on the ability of man to transfer cargo in simulated weightlessness. Results from this study indicate that packages with masses of at least 744 kg and moments of inertia of at least 386 kg-m2 can be manually handled and transferred satisfactorily under intravehicular conditions using either one- or two-rail motion aids. Data leading to the conclusions and discussions of test procedures and equipment are presented.

Spady, A. A., Jr.↗
NASA NTRS2010

INSPIRE Final Presentation

The objective of this research effort is to determine the most appropriate, cost efficient, and effective method to utilize for finding moments of inertia for the Uninhabited Aerial Vehicle (UAV) Dryden Remotely Operated Integrated Drone (DROID). A moment is a measure of the body's tendency to turn about its center of gravity (CG) and inertia is the resistance of a body to changes in its momentum. Therefore, the moment of inertia (MOI) is a body's resistance to change in rotation about its CG. The inertial characteristics of an UAV have direct consequences on aerodynamics, propulsion, structures, and control. Therefore, it is imperative to determine the precise inertial characteristics of the DROID.

Haro, Helida C.↗
DOE OSTI2023

Nuclear rotation at the fission limit in Rf 254

A ground-state rotational band in the fissile nucleus Rf254 was observed for the first time. Levels up to spin 14 and excitation energy of 1.56 MeV were observed. The Rf254 nuclei were produced using the Pb206(Ti50,2n) fusion-evaporation reaction. It is the weakest reaction channel ever studied using in-beam γ-ray spectroscopic methods. The reaction products were separated from the beam in the Argonne gas-filled analyzer (AGFA). The Rf254 nuclei were implanted into a double-sided Si strip detector at the AGFA focal plane and tagged with subsequent ground-state spontaneous fission decays using temporal and spatial correlations. Prompt γ rays in coincidence with the Rf254 recoils were detected in the Gammasphere array of Ge detectors. In order to identify the ground-state rotational band in Rf254, a method for identifying rotational bands in low statistics γ-ray spectra was developed. The deduced Rf254 kinematic moment of inertia is smaller compared to neighboring even-even nuclei. This is most likely associated with a slightly lower quadrupole deformation and stronger pairing correlations in Rf254. The behavior of the moment of inertia as a function of rotational frequency is similar to that of the lighter N=150 isotones Fm250 and No252.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS2001

Microgravity Emissions Laboratory Developed

The Microgravity Emissions Laboratory (MEL) was developed for the support, simulation, and verification of the International Space Station microgravity environment. The MEL utilizes an inertial measurement system using acceleration emissions generated by various operating components of the space station. These emissions, if too large, could hinder the science performed on the space station by disturbing the microgravity environment. Typical test components are disk drives, pumps, motors, solenoids, fans, and cameras. These components will produce inertial forces, which disturb the microgravity on-orbit station environment. These components, usually housed within a station rack, must meet acceleration limits imposed at the rack interface for minimizing the onboard station-operating environment. The NASA Glenn Research Center developed this one-of-a-kind laboratory for testing components and, eventually, rack-level configurations. The MEL approach is to measure the component's generated inertial forces. This force is a product of the full diagonal mass matrix including the test setup (the center of gravity, mass moment of inertia, and weight) and the resolved diagonal rigid-body acceleration determined from measurements using the 10 apparatus accelerometers. The mass matrix can be test derived. The bifilar torsional pendulum method is used to measure the moment of inertia for the test component.

Goodnight, Thomas W.↗
NASA NTRS1942

The Porpoising Characteristics of a Planing Surface Representing the Forebody of a Flying-Boat Hull

Porpoising characteristics were observed on V-body fitted with tail surfaces for different combinations of load, speed, moment of inertia, location of pivot, elevator setting, and tail area. A critical trim was found which was unaltered by elevator setting or tail area. Critical trim was lowered by moving pivot either forward or down or increasing radius or gyration. Increase in mass and moment of inertia increased amplitude of oscillations. Complete results are tabulated and shown graphically.

HULL BOTTOMS, VEE↗
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.↗