Lunar surface mass distribution from dynamical point-mass solution
Lunar surface mass distribution, using dynamic point mass solution
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Lunar surface mass distribution, using dynamic point mass solution
Radiation Shielding Evaluation Toolset (RADSET) is a computer program that rapidly calculates the spatial distribution of mass of an arbitrary structure for use in ray-tracing analysis of the radiation-shielding properties of the structure. RADSET was written to be used in conjunction with unmodified commercial computer-aided design (CAD) software that provides access to data on the structure and generates selected three-dimensional-appearing views of the structure. RADSET obtains raw geometric, material, and mass data on the structure from the CAD software. From these data, RADSET calculates the distribution(s) of the masses of specific materials about any user-specified point(s). The results of these mass-distribution calculations are imported back into the CAD computing environment, wherein the radiation-shielding calculations are performed.
A smooth three-dimensional mass distribution is approximated by a model with multiple thin screens, with surface mass density varying smoothly on each screen. It is found that 16 screens are sufficient for a good approximation of the three-dimensional distribution of matter. It is also found that in this multiscreen model the distribution of amplifications of single images is dominated by the convergence due to matter within the beam. The shear caused by matter outside the beam has no significant effect. This finding considerably simplifies the modeling of lensing by a smooth three-dimensional mass distribution by effectively reducing the problem to one dimension, as it is sufficient to know the mass distribution along a straight light ray.
Meteorite mass distributions provide important insight into real and apparent differences between Antarctic and non-Antarctic meteorites. Antarctic meteorites are typically smaller than non-Antarctic meteorites and represent a different portion of the mass distribution of infalling meteorites. This results from the different methods employed to acquire the collections and from the much smaller effective collecting area for Antarctic meteorites. Comparisons of the proportions and mass distributions of H and L chondrites for different ice fields suggest that previously reported high H to L ratio among Antarctic meteorites compared to witnessed falls results from an unrecognized H5 shower fall that covered the Allan Hills Main and Near Western ice fields in the relatively recent past. The probable presence of unrecognized shower falls among the Antarctic meteorites means that population statistics, even corrected for presently recognized pairing, cannot be used to support the suggestion by Dennison et al. (1986) of a temporal variation in the mixture of meteorites arriving on earth.
An array of multiple foils varying from 1.5 to 3.0 microns exposed on Long Duration Exposure Facility's (LEDF's) geocentrically stabilized exposure platform provides perforation distributions which relate to particulate flux mass distributions and impact velocity in LDEF's orbital reference frame. The application of physical modeling enables a preliminary separation into orbital and interplanetary components, both of which have differing velocities and hence penetration effectiveness. Thin foil hypervelocity calibration data and parametric penetration formulae developed to relate target hole diameter to projectile dimensions are critically examined and a new formula offered for the ballistic limit situation. Incorporating projectile density, target density, and target strength and dimensional scaling from submicron particulates to centimeter scale data, it contrast very significantly with previous formulae in the interpretation of space impact data. Perforation flux distributions for the leading, trailing, and space pointing faces and associated mass distributions for the two populations are presented.
Static spherically symmetric charged mass distribution exact solutions derived for electrons in scalar tensor theory of gravity by Hamilton-Jacobi method
Fitting mass distribution to gravitational potential, for simulating lunar potential
Mass distribution for lunar potential model
IUE data and a distance measuring method that considered central stars in optically thick nebulae were used to examine mass distributions of planetary nebulae. Other data such as spectral type, spatial and kinematic characteristics, etc., were studied to derive relationships between population type and mass distribution. A central star mass range of at least 0.55 solar mass was obtained. Stars with masses of at least 0.64 solar mass, concentrated in the galactic disk, originated from 1.5 solar mass stars. Low mass nuclei originated in old disk or halo populations and evolved from 1.0 solar mass objects. A mass-loss parameter value of 1/3 was calculated for red giants, implying that white dwarfs evolve from stars of under 5 solar masses. Mass distributions around planetary nuclei were concluded to follow patterns associated with the individual mass.
Approximate solution for large asteroid distribution with masses near limiting largest mass of population
Probable mass distribution of solar system based on present characteristics
The mass and velocity distributions in the outskirts (0.5-3.0/h Mpc) of simulated clusters of galaxies are examined for a suite of cosmogonic models (two Omega(sub 0) = 1 and two Omega(sub 0) = 0.2 models) utilizing large-scale particle-mesh (PM) simulations. Through a series of model computations, designed to isolate the different effects, we find that both Omega(sub 0) and P(sub k) (lambda less than or = 16/h Mpc) are important to the mass distributions in clusters of galaxies. There is a correlation between power, P(sub k), and density profiles of massive clusters; more power tends to point to the direction of a stronger correlation between alpha and M(r less than 1.5/h Mpc); i.e., massive clusters being relatively extended and small mass clusters being relatively concentrated. A lower Omega(sub 0) universe tends to produce relatively concentrated massive clusters and relatively extended small mass clusters compared to their counterparts in a higher Omega(sub 0) model with the same power. Models with little (initial) small-scale power, such as the hot dark matter (HDM) model, produce more extended mass distributions than the isothermal distribution for most of the mass clusters. But the cold dark matter (CDM) models show mass distributions of most of the clusters more concentrated than the isothermal distribution. X-ray and gravitational lensing observations are beginning providing useful information on the mass distribution in and around clusters; some interesting constraints on Omega(sub 0) and/or the (initial) power of the density fluctuations on scales lambda less than or = 16/h Mpc (where linear extrapolation is invalid) can be obtained when larger observational data sets, such as the Sloan Digital Sky Survey, become available.
Meteor shower mass distribution from radar echo counts
The cumulative mass distribution of the comet Halley dust efflux in the close encounter period -300 to +300 sec was analyzed. Analysis of the cumulative mass distribution index (alpha) shows considerable short time scale variation. There is clear evidence from the flux rates of passage through at least one major dust enhancement (dust jet) just after closest approach and this is associated with a steepening of the alpha. Comparison with measurements from other sources, and with preencounter predictions, is also made.
Giotto measured the in situ Halley dust grain mass distribution with 2 instruments, Particle Impact Analyzer and Dust Impact Detection System (DIDSY), as well as the total intercepted mass from the deceleration of the spacecraft (Giotto Radio-Science Experiment, GRE). Ground based observations made shortly before encounter have fluxes much higher than would be predicted from Giotto data. It is concluded that Giotto DIDSY and GRE data represent observations of dust originating from a narrow track along the nucleus. They are consistent with ground based data, if assumptions are made about the level of activity along this track. The actual size distribution that should be used for modeling of the whole coma should not include the large mass excess actually observed by Giotto. Extrapolation of the small grain data should be used, since for these grains the velocity dispersion is low and temporal changes at the nucleus would not affect the shape of the mass distribution.
The possibility of placing constraints on the mass distribution of a cluster of galaxies by analyzing the cluster's gravitational lensing effect on the images of more distant galaxies is investigated theoretically in the limit of weak distortion. The steps in the proposed analysis are examined in detail, and it is concluded that detectable distortion can be produced by clusters with line-of-sight velocity dispersions of over 500 km/sec. Hence it should be possible to determine (1) the cluster center position (with accuracy equal to the mean separation of the background galaxies), (2) the cluster-potential quadrupole moment (to within about 20 percent of the total potential if velocity dispersion is 1000 km/sec), and (3) the power law for the outer-cluster density profile (if enough background galaxies in the surrounding region are observed).
Spectroscopic and photometric redshifts, stellar mass estimates, and rest-frame colors from the 3D-HST survey are combined with structural parameter measurements from CANDELS imaging to determine the galaxy size-mass distribution over the redshift (z) range 0 < z < 3. Separating early- and late-type galaxies on the basis of star-formation activity, we confirm that early-type galaxies are on average smaller than late-type galaxies at all redshifts, and find a significantly different rate of average size evolution at fixed galaxy mass, with fast evolution for the early-type population, effective radius is in proportion to (1 + z) (sup −1.48), and moderate evolution for the late-type population, effective radius is in proportion to (1 + z) (sup −0.75). The large sample size and dynamic range in both galaxy mass and redshift, in combination with the high fidelity of our measurements due to the extensive use of spectroscopic data, not only fortify previous results, but also enable us to probe beyond simple average galaxy size measurements. At all redshifts the slope of the size-mass relation is shallow, effective radius in proportion to mass of a black hole (sup 0.22), for late-type galaxies with stellar mass > 3 x 10 (sup 9) solar masses, and steep, effective radius in proportion to mass of a black hole (sup 0.75), for early-type galaxies with stellar mass > 2 x 10 (sup 10) solar masses. The intrinsic scatter is approximately or less than 0.2 decimal exponents for all galaxy types and redshifts. For late-type galaxies, the logarithmic size distribution is not symmetric, but skewed toward small sizes: at all redshifts and masses a tail of small late-type galaxies exists that overlaps in size with the early-type galaxy population. The number density of massive (approximately 10 (sup 11) solar masses), compact (effective radius less than 2 kiloparsecs) early-type galaxies increases from z = 3 to z = 1.5 − 2 and then strongly decreases at later cosmic times.
An important factor in modeling the orbital debris environment is the loss rate of debris due to atmospheric drag and lunisolar perturbations. An accurate knowledge of the area-to-mass ratio of debris fragments is required to calculate the effects of atmospheric drag. It is shown here that the orbital elements as a function of time can be used to invert any propagation algorithm to yield the area-to-mass ratio of an orbiting object. From these calculations and the observed radar cross-section of the object, the mass can be calculated to an accuracy of about 30 percent. It is shown that the mass is related to the effective cross-section area by a power-law relation, but for a given area the mass distribution is very broad. An expression is given for the cumulative mass distribution.