SEARCH · Engineering Papers

Results for “HUBBLE EFFECT”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 397 records · Page 22

All sources NASA NTRS DOE OSTI

NASA NTRS2022

In-space Servicing, Assembly, and Manufacturing (ISAM) State of Play 2022 Edition

The future of spaceflight will yield increasingly more ambitious missions to support civil, national security, and commercial space sectors. Achieving these ambitious missions is not feasible using the traditional paradigm of launching an integrated, fully functioning system on a single launch vehicle. For example, science and human exploration missions will desire payloads that are larger than any foreseeable launch vehicle fairing, national security missions will require persistent assets that are mobile and resilient, and commercial space missions will require cost-effective ways to update to the latest technology on orbit. In-space Servicing, Assembly, and Manufacturing (ISAM) can vastly expand the performance, availability, and lifetime of space systems compared to the traditional paradigm of launching an asset with no intent to ever touch it again. ISAM capabilities foster an ecosystem that changes the space operations paradigm, creating the foundation for sustainable exploration and serving as a multiplier for other capabilities like space logistics, power generation, and reusability. Previous achievements in ISAM have enabled ambitious human and robotic space missions. NASA’s International Space Station (ISS) operations and maintenance, servicing missions of the Hubble Space Telescope (HST), and Northrop Grumman’s Mission Extension Vehicle (MEV) demonstrate the dramatic operational missions that can be achieved using ISAM capabilities. Many current and upcoming flight demonstrations are advancing areas that will enable the next generation of civil, national security, and commercial space missions. This document describes the current state of ISAM missions, capabilities, and developments. Compiling and organizing the available ISAM capabilities will help mission designers incorporate ISAM technologies into their concepts, create the starting point for technology development plans and roadmaps, and provide technologists a survey of the field they are developing. This document divides the ISAM capabilities into 11 capability areas that describe the functions or activities that would be performed in space using ISAM. This version of the ISAM State of Play is part of a continuing journey to encourage the use of ISAM capabilities in space. Compiling and organizing the current state of ISAM provides a simple resource for those working in the ISAM ecosystem to ensure that the advancements being made build upon the investments of the past. The state of play is ever changing as new capabilities are developed, and this document will be periodically updated to ensure that it is relevant to those who need it in the future.

ISAM↗

NASA NTRS1987

Solar object tracking for the Hubble Space Telescope

The Hubble Space Telescope (HST) is designed to carry five major scientific instruments to collect imagery, spectrographic, and photometric astronomical data. The Pointing Control System is to achieve pointing accuracies and line of sight jitter levels an order of magnitude less than can be achieved with ground mounted telescopes. In addition, the HST must be able to acquire and track solar system targets with apparent motion up to 0.21 arcsec/s. Such targets include planetary satellites, planetary surface features and comets. It is to perform this tracking with an accuracy under 0.03 arcsec at the maximum rate. Tracking of solar objects by the Space Telescope accounts for the effects of velocity aberration and parallax, as well as solar targeting a celestial object in a science instrument aperture. The design of the Pointing Control System solar object tracking features is discussed, with emphasis on the special timing and granulation problems inherent with a sampled-data, multirate digital control system.

Rodden, J. J.↗

DOE OSTI2022

Characters, quasinormal modes, and Schwinger pairs in dS 2 with flux

An integral representation of the 1-loop partition function for charged scalars and spinors, minimally coupled to a uniform U(1) field on S 2 , is given in terms of SO(1, 2) Harish-Chandra group characters and evaluated exactly in terms of Hurwitz ζ-functions. Analytically continuing the U(1) field, we interpret the path integrals as quasicanonical partition functions in dS 2 with an electric field. The character itself is obtained as a trace over states living at the future boundary of de Sitter and has a quasinormal mode expansion. The imaginary part of the partition function captures Schwinger pair creation in the static patch at finite temperature. The thermal enhancement is most noticeable for scalar masses below Hubble and leads to non-monotonicity of the current as a function of the field. This parameter range, when dimensionally reducing from a charged or rotating Nariai spacetime, is excluded by Swampland-inspired bounds. Around the AdS 2 black hole, in contrast to dS 2 , there is a threshold to pair creation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

First Star Formation in the Presence of Primordial Magnetic Fields

It has been recently claimed that primordial magnetic fields could relieve the cosmological Hubble tension. Fields of sufficient strength to relieve this tension would result in a magnetic field whose Alfvén velocity, va, is comparable to the speed of sound, cs, at the start of structure formation. We consider the impact of such fields on the formation of the first cosmological objects, minihalos (<10 6 M ⊙ ), forming stars with zoom-in cosmological simulations tracking a single such minihalo. We seed each simulation with present-day field strengths of 2 × 10 –12 –2 × 10 –10 G corresponding to initial ratios of Alfvén velocity to the speed of sound of va/cs ≈ 0.03–3. We find that when va/cs=1, the effects are modest. However, when va ~ cs, the starting time of the gravitational collapse is delayed and the duration extended as much as by Δz = 2.5 in redshift. When va > cs, the collapse is completely suppressed and the minihalos continue to grow and are unlikely to collapse until reaching the atomic cooling limit. Employing current observational limits on primordial magnetic fields we conclude that inflationaryproduced primordial magnetic fields could have a significant impact on first star formation.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS1997

An investigation into the milliarcsecond attitude control errors of Hubble Space Telescope

An analysis of the fine pointing errors of the Hubble Space Telescope (HST), in the range from 1 to 15 milliarcsecs, is reported on. The emphasis is on the study of the performance characteristics of the pointing control system, fine guidance sensors and the optical telescope assembly, which produce relative attitude and astrometric measurement errors. Since the first servicing mission in December 1993, the HST relative short term position stability is of the order of 3 milliarcsecs RMS when averaged over 1 min intervals. At this level of accuracy, longer term systematic attitude errors in this range can have a noticeable impact on the telescope's observations. The various error sources are described, including: internal temperature effects; spacecraft structure temperature effects; calibration procedures, and computational inaccuracies.

Bradley, A. J.↗

NASA NTRS2003

Lifetime Predictions of a Titanium Silicate Glass with Machined Flaws

A dynamic fatigue study was performed on a Titanium Silicate glass to assess its susceptibility to delayed failure and to compare the results with those of a previous study. Fracture mechanics techniques were used to analyze the results for the purpose of making lifetime predictions. The material strength and lifetime was seen to increase due to the removal of residual stress through grinding and polishing. Influence on time-to-failure is addressed for the case with and without residual stress present. Titanium silicate glass otherwise known as ultra-low expansion (ULE)* glass is a candidate for use in applications requiring low thermal expansion characteristics such as telescope mirrors. The Hubble Space Telescope s primary mirror was manufactured from ULE glass. ULE contains 7.5% titanium dioxide which in combination with silica results in a homogenous glass with a linear expansion coefficient near zero. delayed failure . This previous study was based on a 230/270 grit surface. The grinding and polishing process reduces the surface flaw size and subsurface damage, and relieves residual stress by removing the material with successively smaller grinding media. This results in an increase in strength of the optic during the grinding and polishing sequence. Thus, a second study was undertaken using samples with a surface finish typically achieved for mirror elements, to observe the effects of surface finishing on the time-to-failure predictions. An allowable stress can be calculated for this material based upon modulus of rupture data; however, this does not take into account the problem of delayed failure, most likely due to stress corrosion, which can significantly shorten lifetime. Fortunately, a theory based on fracture mechanics has been developed enabling lifetime predictions to be made for brittle materials susceptible to delayed failure. Knowledge of the factors governing the rate of subcritical flaw growth in a given environment enables the development of relations between lifetime, applied stress and failure probability for the material under study. Dynamic fatigue is one method of obtaining the necessary information to develop these relationships. In this study, the dynamic fatigue method was used to construct a time-to-failure diagram for polished ULE glass.

Tucker, Dennis S.↗

NASA NTRS1991

Initial performance improvements due to design modifications for the Pointing Control System on the Hubble Space Telescope

Shortly after Hubble Space Telescope was deployed on orbit it became apparent that the Pointing Control System was experiencing unexpectedly large disturbances during certain portions of the orbit. While these disturbances were most pronounced during transitions of the Earth's shadow, significant disruptions to the pointing occurred at other times in the orbit. Careful analysis of the flight data has lead to the conclusion that the disturbances are caused by a combination of rapid thermal deformations of the Solar Arrays together with striction-friction mechanisms within the array that randomly release stored thermal/mechanical energy. This paper describes the baseline pointing control system design and the flight data that characterized the effects of the extraneous disturbances. The paper goes on to describe the procedure for modifying the onboard controller to attenuate the disturbances to levels consistent with the science operations. Flight data demonstrating the improved performance are shown and are tabulated to compare performance prior to and after phase I of the redesign.

Nurre, G. S.↗

NASA NTRS2000

Black Holes Shed Light on Galaxy Formation

This videotape is comprised of several segments of animations on black holes and galaxy formation, and several segments of an interview with Dr. John Kormendy. The animation segments are: (1) a super massive black hole, (2) Centarus A active black hole found in a collision, (3) galaxy NGC-4261 (active black hole and jet model), (4) galaxy M-32 (orbits of stars are effected by the gravity of the black hole), (5) galaxy M-37 (motion of stars increases as mass of black hole increases), (6) Birth of active galactic nuclei, (7) the collision of two galaxy leads to merger of the black holes, (8) Centarus A and simulation of the collision of 2 galaxies. There are also several segments of an interview with John Kormendy. In these segments he discusses the two most important aspects of his recent black hole work: (1) the correlations between galaxies speed and the mass of the black holes, and (2) the existence of black holes and galactic formation. He also discusses the importance of the Hubble Space Telescope and the Space Telescope Imaging Spectrograph to the study of black holes. He also shows the methodology of processing images from the spectrograph in his office.

Source record↗

NASA NTRS1997

Thermally-Induced Structural Disturbances of Rigid Panel Solar Arrays

The performance of a significant number of spacecraft has been impacted negatively by attitude disturbances resulting from thermally-induced motions of flexible structures. Recent examples of spacecraft affected by these disturbances include the Hubble Space Telescope (HST) and the Upper Atmosphere Research Satellite (UARS). Thermally-induced structural disturbances occur as the result of rapid changes in thermal loading typically initiated as a satellite exits or enters the Earth's shadow. Temperature differences in flexible appendages give rise to structural deformations, which in turn result in disturbance torques reacting back on the spacecraft. Structures which have proven susceptible to these disturbances include deployable booms and solar arrays. This paper investigates disturbances resulting from thermally-induced deformations of rigid panel solar arrays. An analytical model for the thermal-structural response of the solar array and the corresponding disturbance torque are presented. The effect of these disturbances on the attitude dynamics of a simple spacecraft is then investigated using a coupled system of governing equations which includes the effects of thermally-induced deformations. Numerical results demonstrate the effect of varying solar array geometry on the dynamic response of the system.

Johnston, John D.↗

NASA NTRS2021

FUMES. II. Ly α Reconstructions of Young, Active M Dwarfs

The H I Ly α (1215.67 Å) emission line dominates the far-UV spectra of M dwarf stars, but strong absorption from neutral hydrogen in the interstellar medium makes observing Ly α challenging even for the closest stars. As part of the Far-Ultraviolet M-dwarf Evolution Survey, the Hubble Space Telescope has observed 10 early-to-mid M dwarfs with ages ranging from ∼24 Myr to several Gyr in order to evaluate how the incident UV radiation evolves through the lifetime of exoplanetary systems. We reconstruct the intrinsic Ly α profiles from STIS G140L and E140M spectra, and achieve reconstructed fluxes with 1σ uncertainties ranging from 5% to a factor of two for the low-resolution spectra (G140L) and 3%–20% for the high-resolution spectra (E140M). We observe broad, 500–1000 km s −1 wings of the Ly α line profile, and analyze how the line width depends on stellar properties. We find that stellar effective temperature and surface gravity are the dominant factors influencing the line width with little impact from the star's magnetic activity level, and that the surface flux density of the Ly α wings may be used to estimate the chromospheric electron density. The Ly α reconstructions on the G140L spectra are the first attempted on λ/Δλ ∼ 1000 data. We find that the reconstruction precision is not correlated with the signal-to-noise ratio of the observation—rather, it depends on the intrinsic broadness of the stellar Ly α line. Young, low-gravity stars have the broadest lines and therefore provide more information at low spectral resolution to the fit to break degeneracies among model parameters.

Allison Youngblood↗

NASA NTRS1993

Impact of shorter wavelengths on optical quality for laws

This study explores parametrically as a function of wavelength the degrading effects of several common optical aberrations (defocus, astigmatism, wavefronttilts, etc.), using the heterodyne mixing efficiency factor as the merit function. A 60 cm diameter aperture beam expander with an expansion ratio of 15:1 and a primary mirror focal ratio of f/2 was designed for the study. An HDOS copyrighted analysis program determined the value of merit function for various optical misalignments. With sensitivities provided by the analysis, preliminary error budget and tolerance allocations were made for potential optical wavefront errors and boresight errors during laser shot transit time. These were compared with the baseline 1.5 m CO2 laws and the optical fabrication state of the art (SOA) as characterized by the Hubble Space Telescope. Reducing wavelength and changing optical design resulted in optical quality tolerances within the SOA both at 2 and 1 micrometer. However, advanced sensing and control devices would be necessary to be tightened by a factory of 1.8 for a 2 micrometer system and by 3.6 for a 1 micrometer system relative to the baseline CO2 LAWS. Available SOA components could be used for operation at 2 micrometers but operation at 1 micrometer does not appear feasible.

Wissinger, Alan B.↗

DOE OSTI2022

Galaxy morphologies revealed with Subaru HSC and super-resolution techniques. I. Major merger fractions of L UV ∼ 3–15 L*UV dropout galaxies at z ∼ 4–7

Abstract We perform a super-resolution analysis of the Subaru Hyper Suprime-Cam (HSC) images to estimate the major merger fractions of z ∼ 4–7 dropout galaxies at the bright end of galaxy UV luminosity functions (LFs). Our super-resolution technique improves the spatial resolution of the ground-based HSC images, from ∼1″ to $\lesssim \!\!{0{^{\prime \prime }_{.}}1}$, which is comparable to that of the Hubble Space Telescope, allowing us to identify z ∼ 4–7 bright major mergers at a high completeness value of $\gtrsim \!\!90\%$. We apply the super-resolution technique to 6412, 16, 94, and 13 very bright dropout galaxies at z ∼ 4, 5, 6, and 7, respectively, in a UV luminosity range of LUV ∼ 3–$15\, L_{\rm UV}^*$ corresponding to −24 ≲ MUV ≲ −22. The major merger fractions are estimated to be $f_{\rm merger}\sim 10\%$–$20\%$ at z ∼ 4 and $\sim 50\%$–$70\%$ at z ∼ 5–7, which shows no fmerger difference compared to those of a control faint galaxy sample. Based on the fmerger estimates, we verify contributions of source blending effects and major mergers to the bright-end of double power-law (DPL) shape of z ∼ 4–7 galaxy UV LFs. While these two effects partly explain the DPL shape at LUV ∼ 3–$10\, L_{\rm UV}^*$, the DPL shape cannot be explained at the very bright end of $L_{\rm UV}\gtrsim 10\, L_{\rm UV}^*$, even after the AGN contribution is subtracted. The results support scenarios in which other additional mechanisms such as insignificant mass quenching and low dust obscuration contribute to the DPL shape of galaxy UV LFs.

Shibuya, Takatoshi↗

NASA NTRS1993

Impact of shorter wavelengths on optical quality for laws

This study explores parametrically as a function of wavelength the degrading effects of several common optical aberrations (defocus, astigmatism, wavefront tilts, etc.), using the heterodyne mixing efficiency factor as the merit function. A 60 cm diameter aperture beam expander with an expansion ratio of 15:1 and a primary mirror focal ratio of f/2 was designed for the study. An HDOS copyrighted analysis program determined the value of merit function for various optical misalignments. With sensitivities provided by the analysis, preliminary error budget and tolerance allocations were made for potential optical wavefront errors and boresight errors during laser shot transit time. These were compared with the baseline l.5 m CO2 LAWS and the optical fabrication state of the art (SOA) as characterized by the Hubble Space Telescope. Reducing wavelength and changing optical design resulted in optical quality tolerances within the SOA both at 2 and 1 micrometers. However, advanced sensing and control devices would be necessary to maintain on-orbit alignment. Optical tolerance for maintaining boresight stability would have to be tightened by a factor of 1.8 for a 2 micrometers system and by 3.6 for a 1 micrometers system relative to the baseline CO2 LAWS. Available SOA components could be used for operation at 2 micrometers but operation at 1 micrometers does not appear feasible.

Wissinger, Alan B.↗

DOE OSTI2020

A Gas Giant Planet in the OGLE-2006-BLG-284L Stellar Binary System

We present the analysis of microlensing event OGLE-2006-BLG-284, which has a lens system that consists of two stars and a gas giant planet with a mass ratio of q {sub p} = (1.26 ± 0.19) × 10{sup −3} to the primary. The mass ratio of the two stars is q {sub s} = 0.289 ± 0.011, and their projected separation is s {sub s} = 2.1 ± 0.7 au, while the projected separation of the planet from the primary is s {sub p} = 2.2 ± 0.8 au. For this lens system to have stable orbits, the three-dimensional separation of either the primary and secondary stars or the planet and primary star must be much larger than the projected separations. Since we do not know which is the case, the system could include either a circumbinary or a circumstellar planet. Because there is no measurement of the microlensing parallax effect or lens system brightness, we can only make a rough Bayesian estimate of the lens system masses and brightness. We find host star and planet masses of M{sub L1}=0.35{sub −0.20}{sup +0.30} M{sub ⊙}, M{sub L2}=0.10{sub −0.06}{sup +0.09} M{sub ⊙}, and m{sub p}=144{sub −82}{sup +126} M{sub ⊕}, and the K-band magnitude of the combined brightness of the host stars is K{sub L}=19.7{sub −1.0}{sup +0.7}. The separation between the lens and source system will be ∼90 mas in mid-2020, so it should be possible to detect the host system with follow-up adaptive optics or Hubble Space Telescope observations.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS1996

A human factors analysis of EVA time requirements

Human Factors Engineering (HFE), also known as Ergonomics, is a discipline whose goal is to engineer a safer, more efficient interface between humans and machines. HFE makes use of a wide range of tools and techniques to fulfill this goal. One of these tools is known as motion and time study, a technique used to develop time standards for given tasks. A human factors motion and time study was initiated with the goal of developing a database of EVA task times and a method of utilizing the database to predict how long an ExtraVehicular Activity (EVA) should take. Initial development relied on the EVA activities performed during the STS-61 mission (Hubble repair). The first step of the analysis was to become familiar with EVAs and with the previous studies and documents produced on EVAs. After reviewing these documents, an initial set of task primitives and task time modifiers was developed. Videotaped footage of STS-61 EVAs were analyzed using these primitives and task time modifiers. Data for two entire EVA missions and portions of several others, each with two EVA astronauts, was collected for analysis. Feedback from the analysis of the data will be used to further refine the primitives and task time modifiers used. Analysis of variance techniques for categorical data will be used to determine which factors may, individually or by interactions, effect the primitive times and how much of an effect they have.

Pate, D. W.↗

NASA NTRS2010

The HYTHIRM Project: Flight Thermography of the Space Shuttle During the Hypersonic Re-entry

This report describes a NASA Langley led endeavor sponsored by the NASA Engineering Safety Center, the Space Shuttle Program Office and the NASA Aeronautics Research Mission Directorate to demonstrate a quantitative thermal imaging capability. A background and an overview of several multidisciplinary efforts that culminated in the acquisition of high resolution calibrated infrared imagery of the Space Shuttle during hypervelocity atmospheric entry is presented. The successful collection of thermal data has demonstrated the feasibility of obtaining remote high-resolution infrared imagery during hypersonic flight for the accurate measurement of surface temperature. To maximize science and engineering return, the acquisition of quantitative thermal imagery and capability demonstration was targeted towards three recent Shuttle flights - two of which involved flight experiments flown on Discovery. In coordination with these two Shuttle flight experiments, a US Navy NP-3D aircraft was flown between 26-41 nautical miles below Discovery and remotely monitored surface temperature of the Orbiter at Mach 8.4 (STS-119) and Mach 14.7 (STS-128) using a long-range infrared optical package referred to as Cast Glance. This same Navy aircraft successfully monitored the Orbiter Atlantis traveling at approximately Mach 14.3 during its return from the successful Hubble repair mission (STS-125). The purpose of this paper is to describe the systematic approach used by the Hypersonic Thermodynamic Infrared Measurements team to develop and implement a set of mission planning tools designed to establish confidence in the ability of an imaging platform to reliably acquire, track and return global quantitative surface temperatures of the Shuttle during entry. The mission planning tools included a pre-flight capability to predict the infrared signature of the Shuttle. Such tools permitted optimization of the hardware configuration to increase signal-to-noise and to maximize the available dynamic range while mitigating the potential for saturation. Post flight, analysis tools were used to assess atmospheric effects and to convert the 2-D intensity images to 3-D temperature maps of the windward surface. Comparison of the spatially resolved global thermal measurements to surface thermocouples and CFD prediction is made. Successful demonstration of a quantitative, spatially resolved, global temperature measurement on the Shuttle suggests future applications towards hypersonic flight test programs within NASA, DoD and DARPA along with flight test opportunities supporting NASA's project Constellation.

Horvath, Thomas J.↗

DOE OSTI2022

Cosmological implications of the full shape of anisotropic clustering measurements in BOSS and eBOSS

We present the analysis of the full shape of anisotropic clustering measurement from the extended Baryon Oscillation Spectroscopic Survey (eBOSS) quasar sample together with the combined galaxy sample from the Baryon Oscillation Spectroscopic Survey (BOSS), re-analysed using an updated recipe for the non-linear matter power spectrum and the non-local bias parameters. We obtain constraints for flat Lambda cold dark matter cosmologies, focusing on the cosmological parameters that are independent of the Hubble parameter h. Our recovered value for the Root Mean Square (RMS) linear perturbation theory variance as measured on the scale of 12 Mpc is σ 12 = 0.805 ± 0.049, while using the traditional reference scale of 8 h –1 Mpc gives σ 8 = 0.815 ± 0.044. We quantify the agreement between our measurements and the latest cosmic microwave background data from Planck using the suspiciousness metric, and find them to be consistent within 0.64 ± 0.03σ. Combining our clustering constraints with the 3 × 2pt data sample from the Dark Energy Survey Year 1 release slightly degrades this agreement to the level of 1.54 ± 0.08σ, while still showing an overall consistency with Planck. We furthermore study the effect of imposing a Planck – like prior on the parameters that define the shape of the linear matter power spectrum, and find significantly tighter constraints on the parameters that control the evolution of density fluctuations. In particular, the combination of low-redshift data sets prefers a value of the physical dark energy density ω DE = 0.335 ± 0.011, which is 1.7σ higher than the one preferred by Planck.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS1999

The Sunyaev-Zel'dovich Effect in Abell 370

We present interferometric measurements of the Sunyaev-Zel'dovich (SZ) effect towards the galaxy cluster Abell 370. These measurements, which directly probe the pressure of the cluster's gas, show the gas is strongly aspherical, on agreement with the morphology revealed by x-ray and gravitational lensing observations. We calculate the cluster's gas mass fraction by comparing the gas mass derived from the SZ measurements to the lensing-derived gravitational mass near the critical lensing radius. We also calculate the gas mass fraction from the SZ data by deriving the total mass under the assumption that the gas is in hydrostatic equilibrium (HSE). We test the assumptions in the HSE method by comparing the total cluster mass implied by the two methods. The Hubble constant derived for this cluster, when the known systematic uncertainties are included, has a very wide range of values and therefore does not provide additional constraints on the validity of the assumptions. We examine carefully the possible systematic errors in the gas fraction measurement. The gas fraction is a lower limit to the cluster's baryon fraction and so we compare the gas mass fraction, calibrated by numerical simulations to approximately the virial radius, to measurements of the global mass fraction of baryonic matter, OMEGA(sub B)/OMEGA(sub matter). Our lower limit to the cluster baryon fraction is f(sub B) = (0.043 +/- 0.014)/h (sub 100). From this, we derive an upper limit to the universal matter density, OMEGA(sub matter) <= 0.72/h(sub 100), and a likely value of OMEGA(sub matter) <= (0.44(sup 0.15, sub -0.12)/h(sub 100).

Grego, Laura↗