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Improved line parameters at 296 K for the Chi 2Pi-Chi 2Pi (1-0) bands of (35)ClO and (37)ClO have been calculated with J up to 43.5. The integrated intensity for the 2048 lines in the main and satellite bands has been normalized to 9.68-sq cm/atm at 296K.
Applying the standard weighted mean formula, [Sigma (sub i)n(sub i)ssigma(sub i, sup -2)], to determine the weighted mean of data, n(sub i), drawn from a Poisson distribution, will, on average, underestimate the true mean by approx. 1 for all true mean values larger than approx.3 when the common assumption is made that the error of the i th observation is sigma(sub i) = max square root of n(sub i), 1).This small, but statistically significant offset, explains the long-known observation that chi-square minimization techniques which use the modified Neyman'chi(sub 2) statistic, chi(sup 2, sub N) equivalent Sigma(sub i)((n(sub i) - y(sub i)(exp 2)) / max(n(sub i), 1), to compare Poisson - distributed data with model values, y(sub i), will typically predict a total number of counts that underestimates the true total by about 1 count per bin. Based on my finding that weighted mean of data drawn from a Poisson distribution can be determined using the formula [Sigma(sub i)[n(sub i) + min(n(sub i), 1)](n(sub i) + 1)(exp -1)] / [Sigma(sub i)(n(sub i) + 1)(exp -1))], I propose that a new chi(sub 2) statistic, chi(sup 2, sub gamma) equivalent, should always be used to analyze Poisson- distributed data in preference to the modified Neyman's chi(exp 2) statistic. I demonstrated the power and usefulness of,chi(sub gamma, sup 2) minimization by using two statistical fitting techniques and five chi(exp 2) statistics to analyze simulated X-ray power - low 15 - channel spectra with large and small counts per bin. I show that chi(sub gamma, sup 2) minimization with the Levenberg - Marquardt or Powell's method can produce excellent results (mean slope errors approx. less than 3%) with spectra having as few as 25 total counts.
The primary objective of this program was to obtain FUSE observations of the interstellar H2 absorption toward six early-type stars in the core of the open star cluster Chi Persei. High resolution optical observations of the interstellar Na I absorption toward these stars and others in the core of Chi Per have revealed a rich variety of small-scale diffuse ISM structure in both the distant Perseus and more local Orion spiral arms. At the 1 arc minute angular scales typically probed by the separations of these stars, this structure corresponds to respective physical length scales of 0.6 and 0.15 pc in the Perseus and Orion arm gas. The principal scientific goal of the FUSE observations was to determine if this small-scale Na I structure toward the core of Chi Per was reflected in the abundance and/or excitation of interstellar H2. In September 2001, we obtained FUSE observations of the Chi Per stars BD +56 563, BD +56 571, BD +56 573, BD +56 574, BD +56 575, and BD +56 578 for this program. The data reveal that the Perseus arm gas exhibits significant small-scale variations in the strength of its molecular hydrogen absorption while the Orion arm H2 absorption is relatively uniform. We presented these results at the January 2003 American Astronomical Society meeting in Seattle, WA (points, Meyer, Lauroesch, Nguyen, and Friedman 2002, Bulletin of the American Astronomical Society, 34,1229). Since Na I is not a dominant ion in H I clouds, the variations detected in the Perseus arm Na I line profiles could be due to spatial differences in either the physical structure or the physical conditions in the gas. Although many of the H2 absorption profiles are too saturated or too weak to be definitive in this regard, it is clear that small-scale variations are present in H2 gas with excitation as high as the J=4 rotational level. In contrast, lower spatial resolution H I 21 cm studies of the Perseus arm gas across the face of the h and Chi Per double cluster have shown smoother, continuous variations on the larger scale. In order to investigate if the global velocity structure of H2 toward h and Chi Per more closely follows the chaotic structure seen in interstellar Na I absorption or the smoother, continuous H I structure, we have expanded our FUSE study with a Cycle 4 program (D902, PI: Points) to survey the H2 absorption toward a number of other stars across the face of the double cluster. We have obtained FUSE spectra of 14 additional h and Chi Per stars through this program and are now combining all of the data into a comprehensive study that will be submitted for publication next year.
The validity of applying chi-square based confidence intervals to far-field acoustic flyover spectral estimates was investigated. Simulated data, using a Kendall series and experimental acoustic data from the NASA/McDonnell Douglas 500E acoustics test, were analyzed. Statistical significance tests to determine the equality of distributions of the simulated and experimental data relative to theoretical chi-square distributions were performed. Bias and uncertainty errors associated with the spectral estimates were easily identified from the data sets. A model relating the uncertainty and bias errors to the estimates resulted, which aided in determining the appropriateness of the chi-square distribution based confidence intervals. Such confidence intervals were appropriate for nontonally associated frequencies of the experimental data but were inappropriate for tonally associated estimate distributions. The appropriateness at the tonally associated frequencies was indicated by the presence of bias error and noncomformity of the distributions to the theoretical chi-square distribution. A technique for determining appropriate confidence intervals at the tonally associated frequencies was suggested.
Using data from Allegheny Observatory's Thaw/MAP astrometric system, absolute parallaxes are presented for Chi Cygni, 51 Andromedae, the newly discovered RS CVn variable OP Andromedae, and selected stars in these fields. Using existing angular diameter measures and the new parallaxes, linear diameters for Chi Cygni and 51 And are given. Chi Cygni has a perturbation in declination having a period of 0.75 yr and an amplitude of +/- 5 mas. Owing to the extreme variability of Chi Cygni, no further characterization of the system is possible at this time. Other results of spectral interest include the detection of a perturbation in the motion of BD +47 deg 466. This system was found to have a parallax of 14.4 +/- 1.2 mas.
The NASA Artemis program will return humans to the moon. This time, with the help of commercial and international partners, the program’s objective is a permanent moon base. The moon base infrastructure, including an orbiting moon station and moon surface assets, will be developed for astronauts to stay for the long haul to learn to live and work on another planet in preparation for an eventual Humans-to-Mars mission. As the roundtrip communication delays increase in deep space exploration, more onboard systems autonomy and functionality will be needed to maintain and control the vehicle or habitat. These mission constraints will change the current Earth-based spacecraft ground control support approach that will demand more safe, efficient, and effective Computer-Human Interface (CHI) control. For Artemis, CHI is defined as the elements that the crew interfaces with-audio, video, lighting, and crew controls. Understanding how CHI will need to evolve to support deep space missions will be critical for the Artemis program-especially crew controls which is the focus of this paper. How does NASA ensure crew controls are reliable to control complex systems and prevent a catastrophic event due to human error-especially when the astronauts could be physiologically and/or psychologically impaired? NASA’s approach to mitigating catastrophic hazards in human spaceflight system development such as crew controls is through a holistic system engineering and Human System Integration methodology that embraces NASA’s Human-Rating Requirements-ensuring human performance characteristics to control/safely recover the crew from hazardous situations within the human interface design are considered. This paper discusses, at a high level, CHI for the Artemis program. Next, a discussion of what it means to human-rate a space system crew controls and how trust in the human-computer interface begins with the NASA human rating requirements. Finally, a discussion on how systems engineering, and the human system integration process ensures that crew control implementation incorporates the NASA human-rating requirements.
The NASA Artemis program will return humans to the Moon. This time, with the help of commercial and international partners, the program's objective is a permanent moon base. The moon base infrastructure, including an orbiting moon station and moon surface assets, will be developed for astronauts to stay for the long haul to learn to live and work on another planet in preparation for an eventual Humans-to-Mars mission. As the roundtrip communication delays increase in deep space exploration, the crew will need more onboard systems autonomy and functionality to maintain and control the vehicle or habitat. These mission constraints will change the current Earth-based spacecraft to ground control support approach that will demand more safe, efficient, and effective Computer-Human Interface (CHI) control. For Artemis, CHI is defined as the elements that the crew interfaces with: audio, video, lighting, and crew controls subsystems. Understanding how CHI will need to evolve to support deep space missions will be critical for the Artemis program--especially crew controls, which is the focus of this paper. How does NASA ensure crew controls are reliable enough to control complex systems and prevent a catastrophic event due to human error--especially when the astronauts could be physiologically and/or psychologically impaired? NASA's approach to mitigating catastrophic hazards in human spaceflight system development such as crew controls, is through a holistic system engineering and Human System Integration methodology that focuses on incorporating NASA's Human-Rating Requirements-that ensures human performance characteristics to control/safely recover the crew from hazardous situations within the human interface design are considered. This paper discusses, at a high level, CHI for the Artemis program. Next, a discussion of what it means to human-rate a space system crew controls and how trust in the human-computer interface begins with the NASA human rating requirements. Finally, a discussion on how systems engineering and the human system integration process ensures that crew control implementation incorporates the NASA human-rating requirements.
The NASA Artemis program will return humans to the Moon. This time, with the help of commercial and international partners, the program's objective is a permanent moon base. The moon base infrastructure, including an orbiting moon station and moon surface assets, will be developed for astronauts to stay for the long haul to learn to live and work on another planet in preparation for an eventual Humans-to-Mars mission. As the roundtrip communication delays increase in deep space exploration, the crew will need more onboard systems autonomy and functionality to maintain and control the vehicle or habitat. These mission constraints will change the current Earth-based spacecraft to ground control support approach that will demand more safe, efficient, and effective Computer-Human Interface (CHI) control. For Artemis, CHI is defined as the elements that the crew interfaces with: audio, video, lighting, and crew controls subsystems. Understanding how CHI will need to evolve to support deep space missions will be critical for the Artemis program--especially crew controls, which is the focus of this paper. How does NASA ensure crew controls are reliable enough to control complex systems and prevent a catastrophic event due to human error--especially when the astronauts could be physiologically and/or psychologically impaired? NASA's approach to mitigating catastrophic hazards in human spaceflight system development such as crew controls, is through a holistic system engineering and Human System Integration methodology that focuses on incorporating NASA's Human-Rating Requirements-that ensures human performance characteristics to control/safely recover the crew from hazardous situations within the human interface design are considered. This paper discusses, at a high level, CHI for the Artemis program. Next, a discussion of what it means to human-rate a space system crew controls and how trust in the human-computer interface begins with the NASA human rating requirements. Finally, a discussion on how systems engineering and the human system integration process ensures that crew control implementation incorporates the NASA human-rating requirements.
Assuming that chi Oph is an extreme Be star, some consequences are investigated for the interpretation that the IR excesses in such stars are produced by H(-) free-bound emission. The column density of H(-) in the shell surrounding chi Oph is estimated from the observed IR excess, and Copernicus UV spectrophotometric data are used to search for a predicted absorption feature at 1129.54 A due to H(-) and to derive an upper limit to the H(-) column density. No feature resembling the predicted H(-) line is seen in the spectrum of chi Oph, and a marked discrepancy is noted between the estimated column density and the derived upper limit. Possible causes of these discrepancies are discussed, including incorrect interpretation of the IR excess in extreme Be stars, incorrect theoretical calculations describing the predicted H(-) UV absorption line, and the possibility that the line of sight through the shell does not intersect the regions where the IR excess originates.
This paper examines the use of the Chi-square statistic as a means of evaluating filter performance. The goal of the process is to characterize the filter performance in the metric of covariance realism. The Chi-squared statistic is the value calculated to determine the realism of a covariance based on the prediction accuracy and the covariance values at a given point in time. Once calculated, it is the distribution of this statistic that provides insight on the accuracy of the covariance. The process of tuning an Extended Kalman Filter (EKF) for Aqua and Aura support is described, including examination of the measurement errors of available observation types, and methods of dealing with potentially volatile atmospheric drag modeling. Predictive accuracy and the distribution of the Chi-squared statistic, calculated from EKF solutions, are assessed.
The Goddard Space Flight Center (GSFC) Flight Dynamics Facility (FDF) performs orbit determination (OD) for the Aqua and Aura satellites. Both satellites are located in low Earth orbit (LEO), and are part of what is considered the A-Train satellite constellation. Both spacecraft are currently in the science phase of their respective missions. The FDF has recently been tasked with delivering definitive covariance for each satellite.The main source of orbit determination used for these missions is the Orbit Determination Toolkit developed by Analytical Graphics Inc. (AGI). This software uses an Extended Kalman Filter (EKF) to estimate the states of both spacecraft. The filter incorporates force modelling, ground station and space network measurements to determine spacecraft states. It also generates a covariance at each measurement. This covariance can be useful for evaluating the overall performance of the tracking data measurements and the filter itself. An accurate covariance is also useful for covariance propagation which is utilized in collision avoidance operations. It is also valuable when attempting to determine if the current orbital solution will meet mission requirements in the future.This paper examines the use of the Chi-square statistic as a means of evaluating filter performance. The Chi-square statistic is calculated to determine the realism of a covariance based on the prediction accuracy and the covariance values at a given point in time. Once calculated, it is the distribution of this statistic that provides insight on the accuracy of the covariance.For the EKF to correctly calculate the covariance, error models associated with tracking data measurements must be accurately tuned. Over estimating or under estimating these error values can have detrimental effects on the overall filter performance. The filter incorporates ground station measurements, which can be tuned based on the accuracy of the individual ground stations. It also includes measurements from the NASA space network (SN), which can be affected by the assumed accuracy of the TDRS satellite state at the time of the measurement.The force modelling in the EKF is also an important factor that affects the propagation accuracy and covariance sizing. The dominant force in the LEO orbit regime is the drag force caused by atmospheric drag. Accurate accounting of the drag force is especially important for the accuracy of the propagated state. The implementation of a box and wing model to improve drag estimation accuracy, and its overall effect on the covariance state is explored.The process of tuning the EKF for Aqua and Aura support is described, including examination of the measurement errors of available observation types (Doppler and range), and methods of dealing with potentially volatile atmospheric drag modeling. Predictive accuracy and the distribution of the Chi-square statistic, calculated based of the ODTK EKF solutions, are assessed versus accepted norms for the orbit regime.
This report contains a detailed theoretical description of an all-purpose, interactive curve-fitting routine that is based on P. R. Bevington's description of the quadratic expansion of the Chi-Square statistic. The method is implemented in the associated interactive, graphics-based computer program. Taylor's expansion of Chi-Square is first introduced, and justifications for retaining only the first term are presented. From the expansion, a set of n simultaneous linear equations is derived, then solved by matrix algebra. A brief description of the code is presented along with a limited number of changes that are required to customize the program of a particular task. To evaluate the performance of the method and the goodness of nonlinear curve fitting, two typical engineering problems are examined and the graphical and tabular output of each is discussed. A complete listing of the entire package is included as an appendix.
Results are presented from a computer simulation comparing two statistical fitting techniques on data samples with large and small counts per bin; the results are then related specifically to X-ray astronomy. The Marquardt and Powell minimization techniques are compared by using both to minimize the chi-squared statistic. In addition, Cash's C statistic is applied, with Powell's method, and it is shown that the C statistic produces better fits in the low-count regime than chi-squared.
The Goddard High-Resolution Spectrograph on the HST has been used to obtain high S/N observations of the sharp-lined, Hg- and Pt-rich B-type star, Chi Lupi, with a resolving power of 87,000. The observations reveal a level of spectroscopic detail never before observed at ultraviolet wavelengths for any star other than the sun. Concentrating on the region around the resonance line of Hg II at 1942 A, the profile and central position of this line confirm beyond doubt that the Hg isotope anomaly in Chi Lupi is real and extreme, with Hg being heavily concentrated in the form of Hg-204. The problems in atomic physics which impair the accurate analysis of spectra of this quality are emphasized.
The Material Processing in the Space Program of NASA-MSFC was active in developing numerous optical techniques for the characterization of fluids in the vicinity of various materials during crystallization and/or solidification. Two-color holographic interferometry demonstrates that temperature and concentration separation in transparent (T-CHI) model systems is possible. The experiments were performed for particular (succinonitrile) systems. Several solutions are possible in Microgravity Sciences and Applications (MSA) experiments on future Shuttle missions. The theory of the T-CHI concept is evaluated. Although particular cases are used for explanations, the concepts developed will be universal. A breadboard system design is also presented for ultimate fabrication and testing of theoretical findings. New developments in holography involving optical fibers and diode lasers are also incorporated.
Trigonometric parallaxes for stars in the regions of the binary stars Delta Equulei (HR 8123) and Chi(sup l) Orionis (HR 2047) are derived from data collected with the Multichannel Astrometric Photometer (MAP) and the Thaw Refractor of the University of Pittsburgh's Allegheny Observatory. The weighted mean parallax of all trigonometric studies of delta Equ is now +5.42 +/- 0.93 mas, corresponding to absolute magnitudes of 3.87 +/- 0.04 and 3.95 +/- 0.04 mag, respectively, for the primary and secondary. Using the Popper and Dworetsky orbit we find a photocentric semimajor axis of 2.9 +/- 0.8 mas and individual masses of 1.21 +/- 0.090 and 1.19 +/- 0.088 solar masses, respectively, for the primary and secondary components. The weighted mean trigonometric parallax of all studies of the binary star Chi(sup l) Ori is +111.0 +/- 0.92 mas, implying an absolute visual magnitude for the dominant GO V primary of 4.63 +/- 0.018 mag. The photocentric semimajor axis, derived from a fraction of the orbit, is 96.9 +/- 5.4 mas.
Echelle mode spectra obtained with the Goddard High Resolution Spectrograph (GHRS) onboard the Hubble Space Telescope (HST) have been used to determine the abundances of the heavy elements Pt, Au, and Hg in the chemically peculiar HgMn-type stars kappa Cancri and chi Lupi. The abundances were determined by fitting observed line profiles with synthetically generated spectra and are found to be enhanced relative to solar system values by between three and five orders of magnitude in both stars. The Hg isotope mixture in kappa Cancri is found to resemble the terrestrial mixture while that of chi Lupi is dominated by the heaviest isotope. As determined from multiple ionization states, the abundances place constraints upon theories attempting to explain the large superficial abundances of heavy elements.
The purpose of this study was to measure the physical conditions of gas along sight lines toward 6 stars in the core Chi Persei open cluster. These sight lines traverse gas in both the Orion and Perseus spiral arms of the Galaxy, at distances of 500 and 2000 pc, respectively. The stars have angular separations ranging from 45 to 280 arcsec; 60 arcsec corresponds to linear distances of 0.15 and 0.6 pc in the two arms. Thus, abundance variations in these observations would constitute evidence for small-scale variations in the properties of the interstellar medium. Ground-based Na I observations at high resolution (approx. 15 km/sec) toward 172 stars (including the 6 in this study) in the double open cluster h and Chi Persei have revealed complex spatial variation. These variations are especially evident in the gas at velocities of -40 and -55 km/sec, corresponding to the Perseus spiral arm. 21 cm observations of HI emission using the Low Resolution DRAO Survey, with a 12-arcmin beam, also show variations. Averaging the Na I apparent optical depth profiles of neighboring sight lines in order to mimic such a beam size reduces the variation, as compared to the individual Na I measurements, but still show variations larger than seen in the 21 cm profiles. Na I is not the dominant ionization state of Na in the interstellar medium. Thus, it is possible that the variations seen really trace physical structures in the interstellar medium, or they may simply result from variations in the radiation field seen by the gas, or be due to some other environmental circumstance. To distinguish among these possibilities in the present study we obtained FUSE spectra toward the 6 targets in order to measure the molecular hydrogen absorption profiles along these sight lines. The higher J states of H2 are populated by the ambient W radiation field, and thus can provide insight into the environment affecting the gas. If both the high and low J states reveal absorption line profiles with variations similar to that observed in Na I, this would indicate that the variations are due to real structures in the interstellar medium. On the other hand, if the only the high J profiles mimicked the Na I profiles, then the variations may be attributable to environmental effects. We found that the H2 profiles showed considerable variation over the 6 sight lines, and that the profiles, despite having somewhat lower velocity resolution, resemble the Na I profiles. Thus, it appears that the gas really does exhibit variations in physical structures along these sight lines. Useful follow-up work would be to obtain higher signal-to-noise FUSE observations of H2, since the present data are of only moderate quality, and to obtain data on additional targets in this double cluster, in order to map out in more detail the extent and magnitude of the small-scale variations.