Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “LEAST SQUARE FIT”

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.

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

At least 199 records · Page 11

Possible measurements of J sub 2 and the sun's angular momentum with the solar probe

The metric tensor is given for describing the dynamical effects of the sun on a solar probe and the gravitational redshift of a probe-based clock in a covariance analysis for the detectability of the solar quadrupole moment and the solar angular momentum. Unknown parameters were determined by least squares fit to the probe tracking data. A polar orbit was assumed with perihelion at 5 solar radii and with an earth-sun-probe angle of 135 deg at perihelion. Tracking was assumed to be Doppler only, with a basic uncertainity of .1 mm/sec in the radial velocity. A drag-free system which could reduce nongravitational forces below the level of 2 times 10 to the minus 12th power was found necessary to preserve this same level of accuracy. Both one way and two way Doppler were supposed in order to determine the gravitational redshift as well as the pure spacecraft dynamics.

Nordtvedt, K.↗

On the relative locations of the bow shocks of the terrestrial planets

The observed bow shock encounters at Mercury, Venus and Mars are least square fit using the same technique so that their sizes and shapes can be intercompared. The shock front of Mercury most resembles the terrestrial shock in shape, and the shock stand off distance is consistent with the observed moment. The shapes of the Venus and Mars shock fronts more resemble each other than the earth's and the stand off distances are consistent with direct interaction of the solar wind with the ionosphere on the dayside. The Venus shock is closer to the planet than the Mars shock suggesting more absorption of the solar wind at Venus.

Russell, C. T.↗

Heliocentric distance dependence of the interplanetary magnetic field

Numerous spacecraft measurements bearing on the heliocentric distance dependencies of both large- and small-scale properties of the interplanetary magnetic field (IMF) are assembled and compared. These data tend to indicate that the average of the radial field component varies as the inverse square of distance. However, the azimuthal component is rather strongly a function of time, being influenced by both the time-dependent solar wind speed and the evolution of the source field at the sun. Thus, unless the solar wind speed dependence is taken into account, individual sets of measurements by a single spacecraft give an azimuthal component gradient which is steeper than the inverse distance dependence predicted from the Parker spiral model. A least squares fit to the composite (five spacecraft) solar rotation average data set gives a result close to the inverse distance dependence. Preliminary Helios results suggest general consistency with the spiral model.

Behannon, K. W.↗

Martian cratering V - Toward an empirical Martian chronology, and its implications

This paper estimates ages of Martian features by dividing least-square-fitted crater densities by an estimated Martian crater production rate. This method is more rigorous than methods based purely on assumptions about correspondence of lunar and Martian cratering rates. Results are interpreted as supporting the conclusion of Burns et al (in press) that Mars shifted climatic states due to a change in obliguity caused by buildup of massive volcanics. Prior to a few gy. ago, conditions favored erosion, deposition, and fluvial channel formation. Recent volcanics postdate this era, and the surfaces of the major shields are fairly well constrained in age to a few hundred my, in agreement with Masursky et al.

Hartmann, W. K.↗

Apparent depth/apparent diameter relation for lunar craters

Photogrammetric measurements from Apollo metric-quality pictures ensure high accuracy of apparent depth (R sub a) and apparent diameter (D sub a) data for fresh lunar craters. R sub a is a direct function of D sub a and the R sub a/D sub a distribution inflects sharply at an apparent diameter of about 15 km. Each of the two resulting subgroups of craters requires two separate least-squares fits. For simple lunar craters (less than 15 km across), the ratio of R sub a to D sub a is about 0.2; the ratio for complex (larger) craters ranges from 0.1 to 0.01. Apparent depth does not exceed 3400 m, regardless of crater size, possibly as a result of isostasy, substrate layering, or curvature of the moon. R sub a/D sub a differences for mare versus terra craters are either absent or are equivocal. The ratio of apparent diameter to rim-crest diameter (D sub a/D sub r) averages 0.83 for smaller craters and 0.86 for larger craters, indicating another simple-to-complex contrast in crater morphology on the moon, and confirms a prediction by R. B. Baldwin for simple craters. Close similarity of D sub a/D sub r for terrestrial experimental craters and simple lunar craters is especially consistent with impact origin for the moon's craters.

Pike, R. J.↗

Energies of formation for ejecta blankets of giant impacts

Ejection energy-diameter scaling relations for impact craters are studied by assuming the energy is equal to a constant times the diameter raised to a (different) constant power. These scaling relations are derived from least-squares fits to calculated ejection energies over a range of crater diameters and vary according to ejection angle, ejecta blanket distribution, planetary radius, and the depth-diameter ratio. Extremely broad changes in ejection angle and ejecta blanket distribution result in relatively small changes in the total energy. The way in which the exponent in the scaling relation is dependent on the planetary radius of curvature as well as on the exponent of the power-law depth-diameter scaling relation is described. Two ejection energy-diameter scaling relations, one for simple craters with depth-diameter ratios of approximately 0.2 and the other for large complex craters, are presented. The scaling relations explicitly include target density, surface gravity, and planetary radius.

Croft, S. K.↗

The radii of Uranian rings alpha, beta, gamma, delta, epsilon, eta, 4, 5, and 6 from their occultations of SAO 158687

All available timing data for the occultations of SAO 158687 on March 10, 1977, by the cited rings of Uranus are analyzed. Least-squares fits to the data are performed using a model which postulates that rings alpha, beta, gamma, and delta are circular and coplanar. A solution obtained under the assumption that the ring plane coincides with the plane of the satellite orbits is adopted which yields radii of 44,844 km for ring alpha, 45,799 km for ring beta, 47,746 km for ring gamma, and 48,423 km for ring delta. The uncertainties in these values are discussed along with the apparent shapes and inclinations of these main rings. The mean radii estimated for the other rings are: 47,323 km for ring eta, 42,663 km for ring 4, 42,360 km for ring 5, and 41,980 km for ring 6.

Elliot, J. L.↗

The radial dependences of the interplanetary magnetic field between 1 and 5 AU Pioneer 10

Pioneer 10 vector helium magnetometer data acquired in 1972-1973 during Bartels solar rotations 1896-1918 are used to investigate the radial dependences of the distant interplanetary magnetic field (IMF) between 1 and 5 AU. Least-square fits were determined for the radial dependences of the averages of the magnitudes of IMF components and total field and plane projections, and radial fits were prepared for the standard deviations of these variables over the solar rotation, one day, and three-hour intervals. The variation of the weighted averages of the radial component of the field with respect to the heliocentric distance, the variation of the tangential component of the field, and the characteristics of a subset corresponding to a relatively low average solar wind velocity are reported.

Rosenberg, R. L.↗

The magnetic field of Mercury

Data from Mariner 10 observations of Mercury indicate that there exists an intrinsic magnetic field of the planet, sufficiently strong at present to deflect the solar wind flow around the planet and to form a detached bow shock wave in the super Alfvenic solar wind. Four methods used to analyze the magnetic field data and derive quantitative values for the description of the planetary field include (1) comparison of bow shock and magnetopause relative positions at Mercury to those at Earth; (2) direct spherical harmonic analysis of the data; (3) modeling of the magnetosphere by an image dipole and infinite 2-D current sheet in addition to the planetary field; and (4) scaling of a mathematical model for the terrestrial magnetosphere. The results obtained yield dipole moments ranging from 2.4 to 5.1x10 to the 22d power, with the lower values associated cw cm with certain models using partial quadrupole and octupole terms to improve the least squares fitting of models to observations.

Ness, N. F.↗

Tables of thermospheric temperature, density and composition derived from satellite and ground based measurements. Volume 1: Ap=4

The tables contain the neutral temperature, neutral densities for N2, O2, O, Ar, He and H, mean molecular weight, and total mass density as predicted by the Mass Spectrometer and Incoherent Scatter empirical thermosphere model for selected altitudes, latitudes, local times, days and other geophysical conditions. The model is based on a least squares fit to density data from mass spectrometers on five satellites and temperature data from four incoherent scatter stations, providing coverage for most of solar sunspot cycle 20. Included in the model data base are longitudinally average N3, He, and O densities from the OGO-6 mass spectrometer longitudinally average N2, He, O and Ar densities from the AEROS-A (NATE) mass spectrometer the N2, He, O, and Ar densities from the San Marco 3 mass spectrometer the N2 densities from the AE-B mass spectrometer and the N2, He, O, and Ar densities from the AE-C (OSS, NACE, NATE) mass spectrometers. The O2 and H densities are inferred using ion mass spectrometer data from AE-C (BIMS). Neutral exospheric temperature data are included from Arecibo, St. Santin, Millstone Hill and Jicamarca.

Hedin, A. E.↗

Tables of thermospheric temperature, density and composition derived from satellite and ground based measurements. Volume 3: Ap=100

The neutral temperature, neutral densities for N2, O2, O, Ar, He and H, mean molecular weight, and total mass density as predicted by the Mass Spectrometer and Incoherent Scatter empirical thermosphere model are presented in tabular form. The predictions are based on selected altitudes, latitudes, local times, days and other geophysical conditions. The model is dependent on a least squares fit to density data from mass spectrometers on five satellites and temperature data from four incoherent scatter stations, providing coverage for most of solar sunspot cycle 20.

Hedin, A. E.↗

Variations in the upper stratosphere's ozone profile

The ozone concentration profile was measured on five balloon flights using an instrument which employs the strong absorption in ultraviolet to measure ozone in situ. Altitudes up to 44 km were obtained. All the flights were made during the daytime except for one that was launched at 3 AM local time to obtain a nighttime profile and to observe sunrise effects. Although the measurements were obtained at different times of day and during different seasons, ozone concentrations in the upper stratosphere varied by only a few percent. Quadratic, least squares fits to the data between 34 km and 40 km for the four daytime flights, yield a mean concentration at 37 km of 1.02 x 10 to the 12th power molecules/cu cm with a 2 percent standard deviation. Measurements made through sunrise show a small increase in ozone at 37 km commencing shortly after the beginning of astronomical twilight. The concentration at 37 km returned to predawn levels about 2 1/2 hours later.

Robbins, D. E.↗

The 10 February 1977 lunar occultation of Uranus. Radius, limb darkening, and polar brightening at 6900 A

Contact timings, corrected for lunar limb effects, indicate an equatorial radius of 25700 + or - 500 km for the visible disk for Uranus. A modified Minnaert function is used to model limb darkening and polar brightening. Least squares fits to the observed light curve indicate that Uranus is slightly limb darkened in the passband of the observations (450 A FWHM centered near 6900 A) and that polar brightening is present.

Radick, R. R.↗

Total ozone determination by spectroradiometry in the middle ultraviolet

A method has been developed to determine total ozone from multispectral measurements of the direct solar irradiance. The total ozone is determined by a least squares fit to the spectrum between 290 nm and 380 nm. The aerosol extinction is accounted for by expanding it in a power series in wavelength; use of the linear term proved adequate. A mobile laboratory incorporating a sky scanner has been developed and used to obtain data to verify the method. Sun tracking, wavelength setting of the double monochromator, and data acquisition are under control of a minicomputer. Results obtained at Wallops Island, Virginia, and Palestine, Texas, agree well with simultaneous Dobson and Canterbury spectrometer and balloon ECC ozonesonde values. The wavelength calibration of the monochromator and the values for the normalized ozone absorption are the most important factors in an accurate determination of total ozone.

Garrison, L. M.↗

Photographic stellar photometry with the PDS microdensitometer

A technique for photographic stellar photometry with the PDS microdensitometer is described. It employs a least-squares fit to a model density profile to derive an instrumental magnitude index, an image-abnormality index, and the local value of the background density for each image. The instrumental magnitude index is calibrated in terms of true magnitude by the same methods as for iris photometry. A preliminary test of the method using plates of the open cluster NGC 188 indicates that a precision comparable to or slightly better than that of conventional iris photometry or other methods of PDS reduction may easily be attained. Possibilities for the future elaboration of the technique are mentioned.

Stetson, P. B.↗

Integrating matrices for arbitrarily spaced grid points

Integrating matrices are derived for arbitrarily spaced grid points using either interpolating or least squares fit orthogonal polynomials. Several features of the equally spaced grid case are also discussed.

Lakin, W. D.↗

Submillimeter, millimeter, and microwave spectral line catalogue

A computer accessible catalogue of submillimeter, millimeter, and microwave spectral lines in the frequency range between O and 3000 GHz (such as; wavelengths longer than 100 m) is discussed. The catalogue was used as a planning guide and as an aid in the identification and analysis of observed spectral lines. The information listed for each spectral line includes the frequency and its estimated error, the intensity, lower state energy, and quantum number assignment. The catalogue was constructed by using theoretical least squares fits of published spectral lines to accepted molecular models. The associated predictions and their estimated errors are based upon the resultant fitted parameters and their covariances.

Poynter, R. L.↗

The magnetic field of Mercury

The paper examines the magnetic field observations and their analyses relating to the determination of the Mercury magnetic field. Methods of analyzing data included: (1) comparison of bow shock and magnetopause relative positions at Mercury to the earth, (2) direct spherical harmonic analysis, (3) magnetosphere modeling by an image dipole, and (4) scaling of a mathematical model for the terrestrial magnetosphere. Dipole moments were determined using partial quadrupole and octupole terms to improve the least-square fit of models to observations; analyses by method (2) yield a convergent series of dipole moments values considered to best represent the intrinsic planetary field. Finally, it is suggested that the origin of the magnetic field of Mercury cannot be uniquely determined, but the sources of convective energy may be radiogenic decay and heat release, gravitational settling, and differentiation of processional torques.

Ness, N. F.↗