Comment on 'Magnetic field properties of Jupiter's tail at distances from 80 t0 7500 Jovian radii' by M. L. Goldstein, R. P. Lepping, and E. C. Sittler, Jr
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Hill, T. W.↗
SEARCH · Engineering Papers
Results for “radii”
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Distant (200-238 earth radii) magnetotail lobe characteristics during quiet solar wind conditions
Simultaneous ISEE-3 magnetic field and IMP-8 magnetic field and plasma data have been used to investigate the distant tail lobe average properties under quiet solar wind conditions. Under solar wind pressures of not greater than 5 x 10 to the -10th dynes/sq cm, an average tail lobe strength of 7.1 + or - 1.2 nT, and an average plasma beta of 0.3, are found. Results suggest that under quiet solar wind conditions the distant tail lobes are relatively free from plasma and are usually dominated by the magnetic field pressure.
Tsurutani, Bruce T.↗
On the concept of varying influence radii for a successive corrections objective analysis
This paper discusses objective analysis techniques known as 'methods of successive corrections' which were introduced by Cressman (1959) and developed for the analysis of mesoscale weather systems by Barnes (1964 and 1973). Theoretical filter response characteristics of the Barnes method are compared for filter parameters set to retrieve the short wavelengths and then build in the long wavelengths. The accuracy of the method is judged by the ability of the filters to restore desired wavelengths and remove undesired wavelengths. It was found that no single selection of filter parameters for the two-pass Barnes method gives the best analysis for all wavelengths. A three-pass hybrid method is shown to reduce this problem.
Achtemeier, Gary L.↗
Mass distributions in elliptical galaxies at large radii
Recently, X-ray observations have shown that elliptical galaxies generally contain large quantities of hot gas. Central dominant cluster ellipticals have even more gas, which they have accreted from the surrounding clusters. The mass distributions in these galaxies can be derived from the condition of hydrostatic equilibrium. M87, the best studied central dominant galaxy, has a massive, dark halo with a total mass of about 4 x 10 to the 12th solar masses within a radius of 300 kpc. The total mass-to-light ratio within this radius is at least 150 solar mass/solar luminosity. The X-ray observations of normal ellipticals also strongly suggest that they have heavy halos, although the distribution of the mass is much less certain than in M87.
Sarazin, Craig L.↗
Effective radii of annuli in surface photometry
When surface photometry is done in concentric annuli, there is a tendency toward distortion of the true profile because of the finite widths of the annuli. This distortion can be avoided by choosing an effective radius for the annulus such that the actual surface brightness at that radius is equal to the average surface brightness over the annulus. This effective radius depends on the shape of the radial profile, but its calculation can be performed in an iterative way. Formulas for the effective radius are given for some typical profile shapes.
King, Ivan R.↗
On the Concept of Varying Influence Radii for a Successive Corrections Objective Analysis
There has been a long standing concept by those who use successive corrections objective analysis that the way to obtain the most accurate objective analysis is first, to analyze for the long wavelengths and then to build in the details of the shorter wavelengths by successively decreasing the influence of the more distant observations upon the interpolated values. Using the Barnes method, the filter characteristics were compared for families of response curves that pass through a common point at a reference wavelength. It was found that the filter cutoff is a maximum if the filter parameters that determine the influence of observations are unchanged for both the initial and corrections passes. This information was used to define and test the following hypothesis. If accuracy is defined by how well the method retains desired wavelengths and removes undesired wavelengths, then the Barnes method gives the most accurate analyses if the filter parameter on the initial and corrections passes are the same. This hypothesis does not follow the usual conceptual approach to successive corrections analysis.
Achtemeier, Gary L.↗
Radii effect on the translation spring constant of force transducer beams
Multi-component strain-gage force transducer design requires the designer to determine the spring constant of the numerous beams or flexures incorporated in the transducer. The classical beam deflection formulae that are used in calculating these spring constants typically assume that the beam has a uniform moment of inertia along the entire beam length. In practice all beams have a radius at the end where the beam interfaces with the shoulder of the transducer, and on short beams in particular this increases the beam spring constant considerably. A Basic computer program utilizing numerical integration is presented to determine this effect.
Scott, C. E.↗
Mid- and high-latitude total ozone observations from over three earth radii measured from Dynamics Explorer I
Column ozone measurements obtained from a Spin-scan Ozone Imager (SOI) aboard the Dynamics Explorer I (DE-I) satellite are discussed. The orbital geometry has many features similar to the Molniya satellite orbits. The ozone imagery obtained from DE-I are unique in being synoptic views of a region of continental scale for a period of a few hours. A brief description of the instrument, data, and orbit is followed by a discussion of some applications of DE-I data and the potential usefulness of an ozone imager aboard a satellite in a Molniya-type orbit.
Reynolds, Nathaniel D.↗
A study of the effects of radii of gyration and altitude on aileron effectiveness at high speed
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AIRPLANES, PURSUIT↗
11 micrometer emissivities and droplet radii for marine stratocumulus
The results of a new multispectral infrared retrieval scheme for obtaining fractional cloud cover and 11 micrometer emissivity with those of the spatial coherence method which obtains fractional cloud cover assuming that the clouds are opaque at infrared wavelengths. Both methods are applied to 4-km NOAA advanced very high resolution radiometer global area coverage data for 250-km-scale regions containing single-layered marine stratocumulus off the coast of South America. The average 11 micrometer emissivity for low level clouds is found to be between 0.70 and 0.85. The low emissivity is evidently due to the thinning of clouds at their edges. Semitransparent cloud edges evidently make up a substantial portion of the area covered by such clouds. This result indicates that cloud cover obtained using the spatial coherence method is underestimated by 0.1 to 0.2, as has been claimed in a previous study. The fractional cloud cover for the ensemble of 250-km-scale regions studied here increased slightly from 0.60 for daytime observations to 0.63 for nighttime observations. The 11 micrometer emissivity also increased slightly, but about half of the increase was related to the increase in cloud cover and a decrease in the relative area covered by cloud edge material. Presumably, the other half was due to an increase in cloud liquid water. Cloud height showed no significant change. The average effective droplet radius increased from 9.3 micrometers for daytime observations to 10.2 micrometers at night.
Luo, Gang↗
Method of Conjugate Radii for Solving Linear and Nonlinear Systems
This paper describes a method to solve a system of N linear equations in N steps. A quadratic form is developed involving the sum of the squares of the residuals of the equations. Equating the quadratic form to a constant yields a surface which is an ellipsoid. For different constants, a family of similar ellipsoids can be generated. Starting at an arbitrary point an orthogonal basis is constructed and the center of the family of similar ellipsoids is found in this basis by a sequence of projections. The coordinates of the center in this basis are the solution of linear system of equations. A quadratic form in N variables requires N projections. That is, the current method is an exact method. It is shown that the sequence of projections is equivalent to a special case of the Gram-Schmidt orthogonalization process. The current method enjoys an advantage not shared by the classic Method of Conjugate Gradients. The current method can be extended to nonlinear systems without modification. For nonlinear equations the Method of Conjugate Gradients has to be augmented with a line-search procedure. Results for linear and nonlinear problems are presented.
Nachtsheim, Philip R.↗
Accreting Millisecond Pulsars: Neutron Star Masses and Radii
High amplitude X-ray brightness oscillations during thermonuclear X-ray bursts were discovered with the Rossi X-ray Timing Explorer (RXTE) in early 1996. Spectral and timing evidence strongly supports the conclusion that these oscillations are caused by rotational modulation of the burst emission and that they reveal the spin frequency of neutron stars in low mass X-ray binaries. The recent discovery of X-ray burst oscillations from two accreting millisecond pulsars has confirmed this basic picture and provided a new route to measuring neutron star properties and constraining the dense matter equation of state. I will briefly summarize the current observational understanding of accreting millisecond pulsars, and describe recent attempts to determine the mass and radius of the neutron star in XTE J1814-338.
Strohmayer, Tod↗
RADII and Effective Temperatures for G,K and M Giants and Supergiants
Interferometrically determined angular diameters obtained at the Palomar Testbed Interferometer (PTI) for 80 giant and supergiant stars are presented in this paper.
Temperatures Palomar Testbed Interferometer (PTI) ↗
Quantum Effects in Cosmochemistry: Complexation Energy and Van Der Waals Radii
The subject of quantum effects in cosmochemistry was recently addressed with the goal of understanding how they contribute to Q-phase noble gas abundances found in meteorites. It was the pursuit of the Q-phase carrier of noble gases and their anomalous abundances that ultimately led to the identification, isolation, and discovery of presolar grains. In spite of its importance, Q-phase investigations have led a number of authors to reach conclusions that do not seem to be supported by quantum chemistry. In view of the subject's fundamental significance, additional study is called for. Two quantum properties of Q-phase candidates known as endohedral carbon-cage clathrates such as fullerenes will be addressed here. These are complexation energy and instability induced by Pauli blocking (exclusion principle).
Mittlefehldt, D. W.↗
A Simple, Velocity Dependent, Collision Probability Algorithm for Small Combined Hard Body Radii Close Approach Events
Over the last few years progress has been made in the velocity dependent collision probability problem. Recent progress in this problem has been approached via integration of the probability flux into the surface of the combined hard body object. The algorithm presented uses the surface flux approach and is designed to compute the collision probability rate between two objects given their time dependent states and state error covariance matrices. With regards to the computation of the collision probability (Pc) rate, two major differences exist between the development of this algorithm and the usual Pc algorithm. First, the shape of the at-risk volume is assumed to be a cube rather than a sphere. The size of the cube is chosen so that it circumscribes the usual hard body sphere chosen for the spherical Pc problem. This will result in half the length of a side of the cube being equal to the hard body radius (HBR) of the sphere. Second, it is assumed that the HBR of the cube is much smaller than the smallest combined position uncertainty (σ(sub min) > 5*HBR) at each time point of evaluation. This is necessary as the actual collision probability calculation is based on a first order, small variable expansion in the position components of the Gaussian probability density function. This leads to the collision probability rate being to second order in the combined HBR. The collision probability rate is in a concise, closed form containing exponential and error functions.
Frisbee, Joe↗
Recommended Methods for Setting Mission Conjunction Analysis Hard Body Radii
For real-time conjunction assessment (CA) operations, computation of the Probability of Collision (P(sub c)) typically depends on the state vector, its covariance, and the combined hard body radius (HBR) of both the primary and secondary space-craft. However, most algorithmic approaches that compute the P(sub c) use generic conservatively valued HBRs that may tend to go beyond the physical limitations of both spacecraft, enough to drastically change the results of a conjunction assessment mitigation decision. On the other hand, if the attitude of the spacecraft is known and available, then a refined HBR can be obtained that could result in an improved and accurate numerically-computed P(sub c) value. The goal of this analysis is to demonstrate the various calculated P(sub c) values obtained based on a number of different HBR calculation techniques, oriented in the encounter or conjunction plane at the time of closest approach (TCA). Since in most conjunctions the secondary object is a debris object and thus orders of magnitude smaller than the primary, the greatest operational benefit is wrought by developing a better size estimate and representation for the primary object. We present an analysis that includes the attitude information of the primary object in the HBR calculation and assesses the resulting P(sub c) values for conjunction assessment decision making.
Mashiku, Alinda K.↗
Recommended Methods for Setting Mission Conjunction Analysis Hard Body Radii
For real-time conjunction assessment (CA) operations, computation of the Probability of Collision (P(sub c)) typically depends on the state vector, its covariance, and the combined hard body radius (HBR) of both the primary and secondary space-craft. However, most algorithmic approaches that compute the P(sub c) use generic conservatively valued HBRs that may tend to go beyond the physical limitations of both spacecraft, enough to drastically change the results of a conjunction assessment mitigation decision. On the other hand, if the attitude of the spacecraft is known and available, then a refined HBR can be obtained that could result in an improved and accurate numerically-computed P(sub c) value. The goal of this analysis is to demonstrate the various calculated P(sub c) values obtained based on a number of different HBR calculation techniques, oriented in the encounter or conjunction plane at the time of closest approach (TCA). Since in most conjunctions the secondary object is a debris object and thus orders of magnitude smaller than the primary, the greatest operational benefit is wrought by developing a better size estimate and representation for the primary object. We present an analysis that includes the attitude information of the primary object in the HBR calculation and assesses the resulting P(sub c) values for conjunction assessment decision making.
Mashiku, Alinda K.↗
Refining the Transit Timing and Photometric Analysis of TRAPPIST-1: Masses, Radii, Densities, Dynamics, and Ephemerides
We have collected transit times for the TRAPPIST-1 system with the Spitzer Space Telescope over four years. We add to these ground-based, HST, and K2 transit-time measurements, and revisit an N-body dynamical analysis of the seven-planet system using our complete set of times from which we refine the mass ratios of the planets to the star. We next carry out a photodynamical analysis of the Spitzer light curves to derive the density of the host starand the planet densities. We find that all seven planets’ densities may be described with a single rocky mass–radius relation which is depleted in iron relative to Earth, with Fe 21 wt% versus 32 wt% for Earth, and otherwise Earth-like in composition. Alternatively, the planets may have an Earth-like composition but enhanced in light elements,such as a surface water layer or a core-free structure with oxidized iron in the mantle. We measure planet masses toa precision of 3%–5%, equivalent to a radial-velocity(RV)precision of 2.5 cm s−1, or two orders of magnitude more precise than current RV capabilities. We find the eccentricities of the planets are very small, the orbits are extremely coplanar, and the system is stable on 10 Myr timescales. We find evidence of infrequent timing outliers, which we cannot explain with an eighth planet; we instead account for the outliers using a robust likelihood function. We forecast JWST timing observations and speculate on possible implications of the planet densities forthe formation, migration, and evolution of the planet system.
Eric Agol↗