Misplaced Pages

#285714

38-568: Petters may refer to: Arlie Petters (born 1964), Belizean-American mathematical physicist Tom Petters (born 1957), former CEO and chairman of Petters Group Worldwide, convicted for perpetrating a Ponzi scheme Petters Limited , a former manufacturer of internal combustion engines Petters Group Worldwide , a diversified company headquartered in Minnetonka, Minnesota See also [ edit ] Petter (disambiguation) Topics referred to by

76-829: A B.A./M.A. in Mathematics and Physics from Hunter College , CUNY in 1986 with a thesis on "The Mathematical Theory of General Relativity ", and began his Ph.D. at the Massachusetts Institute of Technology Department of Mathematics in the same year. After two years of doctoral studies, he became an exchange scholar in the Princeton University Department of Physics in absentia from MIT. Petters earned his Ph.D. in mathematics in 1991 under advisors Bertram Kostant (MIT) and David Spergel (Princeton University). He remained at MIT for two years as an instructor of pure mathematics (1991–1993) and then joined

114-417: A Kerr black hole . Petters's previous work (1991–2007) dealt with non-random gravitational lensing. Starting in 2008, his research program focused on developing a mathematical theory of random (stochastic) gravitational lensing. In two papers, Petters, Rider, and Teguia took first steps in creating a mathematical theory of stochastic gravitational microlensing. They characterized to several asymptotic orders

152-548: A Black History Month 2017 Honoree. Astrometric Astrometry is a branch of astronomy that involves precise measurements of the positions and movements of stars and other celestial bodies . It provides the kinematics and physical origin of the Solar System and this galaxy , the Milky Way . The history of astrometry is linked to the history of star catalogues , which gave astronomers reference points for objects in

190-560: A catalogue of 1,022 stars in his work the Almagest , giving their location, coordinates, and brightness. In the 10th century, the Iranian astronomer Abd al-Rahman al-Sufi carried out observations on the stars and described their positions, magnitudes and star color ; furthermore, he provided drawings for each constellation, which are depicted in his Book of Fixed Stars . Egyptian mathematician Ibn Yunus observed more than 10,000 entries for

228-469: A common technique for astrometry. In the 1980s, charge-coupled devices (CCDs) replaced photographic plates and reduced optical uncertainties to one milliarcsecond. This technology made astrometry less expensive, opening the field to an amateur audience. In 1989, the European Space Agency 's Hipparcos satellite took astrometry into orbit, where it could be less affected by mechanical forces of

266-573: A limit on the asymmetry of supernova explosions. Also, astrometric results are used to determine the distribution of dark matter in the galaxy. Astronomers use astrometric techniques for the tracking of near-Earth objects . Astrometry is responsible for the detection of many record-breaking Solar System objects. To find such objects astrometrically, astronomers use telescopes to survey the sky and large-area cameras to take pictures at various determined intervals. By studying these images, they can detect Solar System objects by their movements relative to

304-527: A precision of 15–35 arcsec . Ottoman scholar Taqi al-Din measured the right ascension of the stars at the Constantinople Observatory of Taqi ad-Din using the "observational clock" he invented. When telescopes became commonplace, setting circles sped measurements English astronomer James Bradley first tried to measure stellar parallaxes in 1729. The stellar movement proved too insignificant for his telescope , but he instead discovered

342-614: A probability of 1 for random lenses and thereby form important consistency checks for research on random image magnifications of sources near stable caustics. Petters has served as director of the Reginaldo Howard Memorial Scholarship program at Duke University . He has also been active in the African-American community particularly through his mentoring, recruiting, and lecturing. He has received several community service awards for his social outreach. Petters

380-477: A semi-classical wave theory of braneworld black hole lensing and used that theory along with braneworld cosmology to predict a testable signature of microscopic braneworld black holes on gamma-ray light. Additionally, in a 2007 paper, Petters and M.C. Werner found a system of equations that can be applied to test the Cosmic Censorship Hypothesis observationally using the realistic case of lensing by

418-530: A series of three mathematical physics papers published written with the astronomer Charles R. Keeton, he utilized higher-order gravitational lensing effects by compact bodies to test different theories of gravity with the general theory of relativity of Einstein among them. These papers computed beyond the standard weak-deflection limit the first- and second-order corrections to the image positions, magnifications, and time delays due to lensing in general relativity and alternative gravitational theories describable within

SECTION 10

#1732858471286

456-401: Is different from Wikidata All article disambiguation pages All disambiguation pages Arlie Petters Petters was raised by his grandparents in the rural community of Dangriga , Belize (formerly Stann Creek Town, British Honduras ). His mother immigrated to Brooklyn, New York, and married a U.S. citizen, with Arlie joining them when he was 14 years old. Petters earned

494-405: Is instrumental for keeping time , in that UTC is essentially the atomic time synchronized to Earth 's rotation by means of exact astronomical observations. Astrometry is an important step in the cosmic distance ladder because it establishes parallax distance estimates for stars in the Milky Way . Astrometry has also been used to support claims of extrasolar planet detection by measuring

532-900: Is known for his work in the mathematical theory of gravitational lensing . Over the ten-year period from 1991 to 2001, Petters systematically developed a mathematical theory of weak-deflection gravitational lensing, beginning with his 1991 MIT Ph.D. thesis on "Singularities in Gravitational Microlensing". In a series of papers, he and his collaborators resolved an array of theoretical problems in weak-deflection gravitational lensing covering image counting, fixed-point images, image magnification, image time delays, local geometry of caustics, global geometry of caustics, wavefronts, caustic surfaces, and caustic surfing. His work culminated in book, entitled Singularity Theory and Gravitational Lensing (Springer 2012) , which he co-authored with Harold Levine and Joachim Wambganns. This book, which addressed

570-581: Is the first tenured African-American professor in mathematics at Duke University. He is very involved in the Belizean community and founded the Petters Research Institute in 2005 to help train Belizean young people in STEM fields and foster STEM entrepreneurship. He has written five books, three of them science and mathematics problem-solving books for Belizean students. Some of his entrepreneurial work

608-748: The National Science Foundation (1998), and was the first winner of the Blackwell-Tapia Prize (2002). He was selected in 2006 by the National Academy of Sciences to be part of a permanent Portrait Collection of Outstanding African-Americans in Science, Engineering, and Medicine. In 2008 Petters was also included among the Human Relations Associates' list of "The Twenty-Five Greatest Scientists of African Ancestry,"going back to

646-601: The PPN formalism , and even determined lensing invariants for the PPN family of models. Their findings were applied to the Galactic black hole , binary pulsars , and gravitational microlensing scenarios to make testable predictions about lensed images and their time delays. Another paper took on the difficult issue of how to test hyperspace models like braneworld gravity that postulate an extra dimension to physical space. The paper developed

684-662: The Palomar Observatory 's Samuel Oschin telescope of 48 inches (1.2 m) and the Palomar-Quest large-area CCD camera. The ability of astronomers to track the positions and movements of such celestial bodies is crucial to the understanding of the Solar System and its interrelated past, present, and future with others in the Universe. A fundamental aspect of astrometry is error correction. Various factors introduce errors into

722-572: The aberration of light and the nutation of the Earth's axis. His cataloguing of 3222 stars was refined in 1807 by German astronomer Friedrich Bessel , the father of modern astrometry. He made the first measurement of stellar parallax: 0.3 arcsec for the binary star 61 Cygni . In 1872, British astronomer William Huggins used spectroscopy to measure the radial velocity of several prominent stars, including Sirius . Being very difficult to measure, only about 60 stellar parallaxes had been obtained by

760-563: The 15th century, the Timurid astronomer Ulugh Beg compiled the Zij-i-Sultani , in which he catalogued 1,019 stars. Like the earlier catalogs of Hipparchus and Ptolemy, Ulugh Beg's catalogue is estimated to have been precise to within approximately 20 minutes of arc . In the 16th century, Danish astronomer Tycho Brahe used improved instruments, including large mural instruments , to measure star positions more accurately than previously, with

798-579: The 23,882 double and multiple stars and 11,597 variable stars also analyzed during the Hipparcos mission. In 2013, the Gaia satellite was launched and improved the accuracy of Hipparcos . The precision was improved by a factor of 100 and enabled the mapping of a billion stars. Today, the catalogue most often used is USNO-B1.0 , an all-sky catalogue that tracks proper motions, positions, magnitudes and other characteristics for over one billion stellar objects. During

SECTION 20

#1732858471286

836-496: The Earth and optical distortions from its atmosphere. Operated from 1989 to 1993, Hipparcos measured large and small angles on the sky with much greater precision than any previous optical telescopes. During its 4-year run, the positions, parallaxes, and proper motions of 118,218 stars were determined with an unprecedented degree of accuracy. A new " Tycho catalog " drew together a database of 1,058,332 stars to within 20-30 mas (milliarcseconds). Additional catalogues were compiled for

874-644: The Sun's position for many years using a large astrolabe with a diameter of nearly 1.4 metres. His observations on eclipses were still used centuries later in Canadian–American astronomer Simon Newcomb 's investigations on the motion of the Moon, while his other observations of the motions of the planets Jupiter and Saturn inspired French scholar Laplace 's Obliquity of the Ecliptic and Inequalities of Jupiter and Saturn . In

912-490: The astrometric curves revealed a characteristic S-shape for fold crossings, parabolic and swallowtail features for cusp crossings, and a jump discontinuity for crossings over the fold arcs merging into a cusp. Petters, Levine, and Wambgamnns also developed a formula to calculate the size of the jump. During the period from 2005 to 2007, Petters collaborated with astronomers and physicists to explore gravitational lensing in directions beyond its traditional confines in astronomy. In

950-543: The background stars, which remain fixed. Once a movement per unit time is observed, astronomers compensate for the parallax caused by Earth's motion during this time and the heliocentric distance to this object is calculated. Using this distance and other photographs, more information about the object, including its orbital elements , can be obtained. Asteroid impact avoidance is among the purposes. Quaoar and Sedna are two trans-Neptunian dwarf planets discovered in this way by Michael E. Brown and others at Caltech using

988-459: The displacement the proposed planets cause in their parent star's apparent position on the sky, due to their mutual orbit around the center of mass of the system. Astrometry is more accurate in space missions that are not affected by the distorting effects of the Earth's atmosphere. NASA's planned Space Interferometry Mission ( SIM PlanetQuest ) (now cancelled) was to utilize astrometric techniques to detect terrestrial planets orbiting 200 or so of

1026-664: The eighteenth century. He received an honorary Doctor of Science from his alma mater, Hunter College , in 2008. Petters was named by the Queen of the United Kingdom in 2008 to membership in the Most Excellent Order of the British Empire. In recognition of his scientific accomplishments and service to society, Petters's birthplace— Dangriga , Belize—honored him in 2009 by naming a road Dr. Arlie Petters Street . He became in 2011

1064-447: The end of the 19th century, mostly by use of the filar micrometer . Astrographs using astronomical photographic plates sped the process in the early 20th century. Automated plate-measuring machines and more sophisticated computer technology of the 1960s allowed more efficient compilation of star catalogues . Started in the late 19th century, the project Carte du Ciel to improve star mapping could not be finished but made photography

1102-597: The faculty at Princeton University in the Department of Mathematics. He was an assistant professor at Princeton for five years (1993–1998) before moving to Duke University. Many media outlets have profiled Arlie Petters and his scholarship, including The New York Times , NOVA , The HistoryMakers (a digital archive of oral histories featuring African-Americans and preserved at the Library of Congress ), Big Think, and Duke University's news outlet, The Chronicle . Petters

1140-785: The first Belizean to receive the Caribbean American Heritage Award for Excellence in Science and Technology. In 2012 he became a fellow of the American Mathematical Society and the first Belizean American to be Grand Marshal of the Central American Day Parade in Los Angeles , where he received honors from the mayor and from the Confederation Centroamericana (COFECA). Petters was recognized by Mathematically Gifted & Black as

1178-427: The mathematical theory in [AP13] to help develop a practical diagnostic test for the presence of dark substructures in galaxies lensing quasars; classify the local astrometric (centroid) and photometric curves of an extended source when it crosses fold and cusp caustics due to generic lenses; predict the quantitative astrometric curve's shape produced by Galactic binary lenses. The classified local properties of

Petters - Misplaced Pages Continue

1216-413: The nearest solar-type stars . The European Space Agency's Gaia Mission , launched in 2013, applies astrometric techniques in its stellar census. In addition to the detection of exoplanets, it can also be used to determine their mass. Astrometric measurements are used by astrophysicists to constrain certain models in celestial mechanics . By measuring the velocities of pulsars , it is possible to put

1254-553: The past 50 years, 7,435 Schmidt camera plates were used to complete several sky surveys that make the data in USNO-B1.0 accurate to within 0.2 arcsec. Apart from the fundamental function of providing astronomers with a reference frame to report their observations in, astrometry is also fundamental for fields like celestial mechanics , stellar dynamics and galactic astronomy . In observational astronomy , astrometric techniques help identify stellar objects by their unique motions. It

1292-572: The probability densities of random time delay functions, lensing maps, and shear maps in stochastic microlensing and determined a Kac-Rice type formula for the global expected number of images due to a general stochastic lens system. The work forms a concrete framework from which extensions to more general random maps can be made. In two additional papers, he and Aazami found geometric universal magnification invariants of higher-order caustics occurring in lensing and caustics produced by generic general maps up to codimension five. The invariants hold with

1330-519: The question, "What is the universe made of?", systematically created a framework of stability and genericity for k-plane gravitational lensing. The book drew upon powerful tools from the theory of singularities and put the subject of weak-deflection k-plane gravitational lensing on a rigorous and unified mathematical foundation. Following his 1991–2001 body of mathematical lensing work, Petters turned to more astrophysical lensing issues from 2002 to 2005. In collaboration with astronomers, he applied some of

1368-465: The same term [REDACTED] This disambiguation page lists articles associated with the title Petters . If an internal link led you here, you may wish to change the link to point directly to the intended article. Retrieved from " https://en.wikipedia.org/w/index.php?title=Petters&oldid=1226320959 " Categories : Disambiguation pages Disambiguation pages with surname-holder lists Hidden categories: Short description

1406-431: The sky so they could track their movements. This can be dated back to the ancient Greek astronomer Hipparchus , who around 190 BC used the catalogue of his predecessors Timocharis and Aristillus to discover Earth's precession . In doing so, he also developed the brightness scale still in use today. Hipparchus compiled a catalogue with at least 850 stars and their positions. Hipparchus's successor, Ptolemy , included

1444-566: Was conducted while he was a professor of business administration at Duke's Fuqua School of Business (2008–2017). Petters also served the Government of Belize as chairman of the Council of Science Advisers to the prime minister of Belize (2010–2013). Petters has received numerous awards and honors. He was won an Alfred P. Sloan Research Fellowship in Mathematics (1998), and a CAREER award from

#285714