scholarly journals Spherical trigonometry of the projected baseline angle

2008 ◽  
pp. 115-124
Author(s):  
R.J. Mathar
Keyword(s):  
Line Segment ◽  
Position Angle ◽  
Baseline Length ◽  
Spherical Trigonometry ◽  
Baseline Vector ◽  
Stellar Interferometer ◽  
Celestial Sphere ◽  
The Right ◽  
Circular Line ◽  
High Diffraction

The basic vector geometry of a stellar interferometer with two telescopes is defined by the right triangle of (i) the baseline vector between the telescopes, of (ii) the delay vector which points to the star, and of (iii) the projected baseline vector in the plane of the wave front of the stellar light. The plane of this triangle intersects the celestial sphere at the position of the star; the intersection is a circular line segment. The interferometric angular resolution is high (diffraction limited to the ratio of the wavelength over the projected baseline length) in the two directions along this line segment, and low (diffraction limited to the ratio of the wavelength over the telescope diameter) perpendicular to these. The position angle of these characteristic directions in the sky is calculated here, given either local horizontal coordinates, or celestial equatorial coordinates.

A Device to Determine Position Rapidly Without Calculation

1956 ◽  
Vol 9 (1) ◽  
pp. 11-16
Author(s):  
Leo Randić
Keyword(s):  
Sidereal Time ◽  
Outer Circle ◽  
The Earth ◽  
Geographical Latitude ◽  
The Difference ◽  
Celestial Sphere ◽  
The Right ◽  
Right Ascension ◽  
Nautical Almanac

The problem of the determination of the observer's position on the Earth can be most easily solved in terms of the equatorial coordinates of the observer's zenith. From Fig. 1, in which the inner circle represents the Earth and the outer circle the celestial sphere, it can be seen that the zenithal point on the celestial sphere is its intersection with the prolongation of the radius to the observer's position. The geographical latitude of the observer is equal to the declination of the observer's zenith, and the geographical longitude is equal to the difference between Greenwich sidereal time (G.S.T.) and the right ascension of the observer's zenith. We can obtain G.S.T. by interpolation from a nautical almanac or directly from a separate watch or clock set to keep sidereal time.

scholarly journals TRIGONOMETRIA ESFÉRICA APLICADA NA ASTRONOMIA DE POSIÇÃO

2018 ◽  
Vol 10 (2) ◽  
pp. 60-67
Author(s):  
Christian Luz Pelissari de Oliveira ◽  
Fernando Pereira de Souza
Keyword(s):  
Education Program ◽  
Research Work ◽  
Spherical Geometry ◽  
Fundamental Relation ◽  
Spherical Trigonometry ◽  
Time System ◽  
Celestial Bodies ◽  
Law Of Cosines ◽  
Celestial Sphere ◽  
Mathematics And Physics

The present article is the result of a research work of the Degree in Mathematics in the scope of the Tutorial Education Program -PET. The work deals with concepts of Spherical Trigonometry, which has several fields of applications between mathematics and physics, related to cartographic problems, navigation and astronomy. The goal is to explore problems of astronomy applications of celestial bodies by making use of trigonometry concepts in the sphere to study positions and directions of stars in terms of a celestial sphere. In order to reach this objective, the article presents concepts of a smaller distance between two points in the sphere, a triangle of position that is the spherical triangle, the fundamental relation known as law of cosines, the Celestial Sphere, its elements, its coordinates in the equatorial system, horizontal system and time system. Thus, the work seeks to encourage students and teachers to work on Spherical Geometry in the classroom

scholarly journals The structure of the Milky Way based on unWISE 3.4 μm integrated photometry

2021 ◽  
Vol 507 (4) ◽  
pp. 5246-5263
Author(s):  
Aleksandr V Mosenkov ◽  
Sergey S Savchenko ◽  
Anton A Smirnov ◽  
Peter Camps
Keyword(s):  
Milky Way ◽  
Position Angle ◽  
Solar Radius ◽  
Complex Model ◽  
Wide Field ◽  
Large Set ◽  
Shape Structure ◽  
The Galaxy ◽  
External Galaxies ◽  
Celestial Sphere

ABSTRACT We present a detailed analysis of the Galaxy structure using an unWISE wide-field image at $3.4\,\mu$m. We perform a 3D photometric decomposition of the Milky Way taking into account (i) the projection of the Galaxy on the celestial sphere and (ii) that the observer is located within the Galaxy at the solar radius. We consider a large set of photometric models starting with a pure disc model and ending with a complex model that consists of thin and thick discs plus a boxy-peanut-shaped bulge. In our final model, we incorporate many observed features of the Milky Way, such as the disc flaring and warping, several overdensities in the plane, and the dust extinction. The model of the bulge with the corresponding X-shape structure is obtained from N-body simulations of a Milky Way-like galaxy. This allows us to retrieve the parameters of the aforementioned stellar components, estimate their contribution to the total Galaxy luminosity, and constrain the position angle of the bar. The mass of the thick disc in our models is estimated to be 0.4–1.3 of that for the thin disc. The results of our decomposition can be directly compared to those obtained for external galaxies via multicomponent photometric decomposition.

Interpolation Processes in the Perception of Real and Illusory Contours

Perception ◽  
1997 ◽  
Vol 26 (11) ◽  
pp. 1445-1458 ◽  
Author(s):  
Karl R Gegenfurtner ◽  
Joel E Brown ◽  
Jochem Rieger
Keyword(s):  
Line Segment ◽  
Spatial Configuration ◽  
Relative Length ◽  
Interpolation Process ◽  
Illusory Contours ◽  
Low Contrast ◽  
Line Segments ◽  
Significant Difference ◽  
Presentation Time ◽  
The Right

The spatial and temporal characteristics of mechanisms that bridge gaps between line segments were determined. The presentation time that was necessary for localisation and identification of a triangular shape made up of pacmen, pacmen with lines, lines, line segments (corners), or pacmen with circles (amodal completion) was measured. The triangle was embedded in a field of distractors made up of the same components but at random orientations. Subjects had to indicate whether the triangle was on the left or on the right of the display (localisation) and whether it was pointing upward or downward (identification). Poststimulus masks consisted of pinwheels for the pacmen stimuli or wheels defined by lines. Stimuli were presented on a grey background and defined by luminance or isoluminant contrast. Thresholds were fastest when the triangle was defined by real contours, as for the pacmen with lines (105 ms) and the lines only (92 ms), slightly slower for corners (118 ms) and pacmen (136 ms), and much slower for the amodally completed pacmen (285 ms). For all inducer types localisation was about 20 ms faster than identification. In a second experiment the relative length of the gap between inducers was varied. Thresholds increased as a function of gap length, indicating that the gaps between the inducers need to be interpolated. There was no significant difference in the speed of this interpolation process between the pacman stimuli and the line-segment stimuli. About 40 ms were required to interpolate 1 deg of visual angle, corresponding to about one third of the distance between inducers. In a third experiment, it was found that processing of isoluminant stimuli was as fast as for low-contrast luminance stimuli, when targets were defined by real contours (lines), but much slower for illusory contours (pacmen). The conclusion is that the time necessary to interpolate a contour depends greatly on the spatial configuration of the stimulus. Since interpolation is faster for the line-segment stimuli, which do not elicit the percept of an illusory contour, the interpolation process seems to be independent of the formation of illusory contours.

scholarly journals The shadows cast by buildings and towers in cities and by montains in the countryside

2003 ◽  
Vol 25 (1) ◽  
pp. 62-73 ◽  
Author(s):  
João Luiz Kohl Moreira
Keyword(s):  
Geographic Region ◽  
The Sun ◽  
Spherical Trigonometry ◽  
Specific Knowledge ◽  
Teachers And Students ◽  
Fundamental Astronomy ◽  
Astronomical Object ◽  
Shadow Cast ◽  
Celestial Sphere ◽  
Shadow Projection

ABSTRACT Often astronomers of the Observatório Nacional are asked about how the shadow cast from a building or a tower to be built will impact crowded areas; in which way they would interfere with the wellfare by depriving population from sunlight. The same problem arises when agronomers plan areas for cultures when topographical accidents may cast shadows in a geographic region. My colleages usually answer these questions by delivering spherical trigonometry formulae and the sun equations of movement, and therefore they transfer the responsability of the conclusions back to the engineers and agronomers. What we didn’t realize is the possible and even probable difficulties that these professionals could be facing, since fundamental astronomy and astronomical object positioning knowledge is needed to figure out how the sun moves in the celestial sphere. Shadow projection and its mapping on a ground plan also requires specific knowledge. This paper intends to introduce solutions that will offer professionals, teachers and students conditions of better understanding this problem and, possibly, at least in some cases, bypass the need for quering astronomers.

New explanation of opposite position angles in red and blue wings of spectral lines

2020 ◽  
Vol 499 (1) ◽  
pp. 1499-1505
Author(s):  
N A Silant’ev ◽  
G A Alekseeva ◽  
Yu K Ananjevskaja
Keyword(s):  
Inclination Angle ◽  
Azimuthal Angle ◽  
Symmetry Plane ◽  
Position Angle ◽  
Accretion Disc ◽  
Spectral Lines ◽  
Polarization Angle ◽  
Central Plane ◽  
Line Radiation ◽  
The Right

ABSTRACT We consider the emission of resonance line radiation from rotating circular accretion disc with the progressive increasing height (the inclined ring). Our theory can also be applied to the rotating spot-like sources of resonance radiation. We assume that the atmosphere of inclined ring is homogeneous. In this case, the every part of ring emits the radiation with the wave electric field oscillations perpendicular to plane $(\boldsymbol{nN^{\prime }})$, where ${\boldsymbol{n}}$ is the direction to a telescope and $\boldsymbol{N^{\prime }}$ is the normal to considered local surface of a ring. Geometrical consideration shows that the radiation polarization angle χ (frequently denoted as position angle or PA) depends on the inclination angle α of the ring relative to the central plane of accretion disc, the inclination angle θ of the central plane of accretion disc with the normal $\boldsymbol{N}$, and on azimuthal angle φ of radiating part on the ring. The right and left parts of a ring according to the symmetry plane $(\boldsymbol{nN})$ give rise to opposite polarization angles. For rotating accretion disc, due to Doppler’s effect, this means that polarization angles have opposite signs in the red and blue wings of emerging spectral line radiation. Such behaviour is observed in many objects.

Investor-State Dispute Settlement under NAFTA Chapter 11: The Shape of Things to Come?

1998 ◽  
Vol 35 ◽  
pp. 263-290
Author(s):  
J. Anthony VanDuzer
Keyword(s):  
Free Trade Agreement ◽  
Dispute Settlement ◽  
Trade Agreement ◽  
Minimum Standards ◽  
The North ◽  
State Behaviour ◽  
Nafta Chapter 11 ◽  
To Come ◽  
The Right

SummaryRecently, there has been a proliferation of international agreements imposing minimum standards on states in respect of their treatment of foreign investors and allowing investors to initiate dispute settlement proceedings where a state violates these standards. Of greatest significance to Canada is Chapter 11 of the North American Free Trade Agreement, which provides both standards for state behaviour and the right to initiate binding arbitration. Since 1996, four cases have been brought under Chapter 11. This note describes the Chapter 11 process and suggests some of the issues that may arise as it is increasingly resorted to by investors.

What face familiarity feelings say about the lateralization of specific entities within the core system

2019 ◽  
Vol 42 ◽  
Author(s):  
Guido Gainotti
Keyword(s):  
Temporal Lobe ◽  
Memory System ◽  
Core System ◽  
The Core ◽  
Memory Traces ◽  
Specific Memory ◽  
Target Article ◽  
Temporal Structures ◽  
The Right

Abstract The target article carefully describes the memory system, centered on the temporal lobe that builds specific memory traces. It does not, however, mention the laterality effects that exist within this system. This commentary briefly surveys evidence showing that clear asymmetries exist within the temporal lobe structures subserving the core system and that the right temporal structures mainly underpin face familiarity feelings.

Study of charge transfer in FeTi

1983 ◽  
Vol 41 ◽  
pp. 296-297
Author(s):  
J. Taft∅
Keyword(s):  
Charge Transfer ◽  
Charge Distribution ◽  
Electron Scattering ◽  
Periodic System ◽  
Electron Distribution ◽  
Scattering Amplitude ◽  
Transition Elements ◽  
Hartree Fock ◽  
Cscl Structure ◽  
The Right

It is well known that for reflections corresponding to large interplanar spacings (i.e., sin θ/λ small), the electron scattering amplitude, f, is sensitive to the ionicity and to the charge distribution around the atoms. We have used this in order to obtain information about the charge distribution in FeTi, which is a candidate for storage of hydrogen. Our goal is to study the changes in electron distribution in the presence of hydrogen, and also the ionicity of hydrogen in metals, but so far our study has been limited to pure FeTi. FeTi has the CsCl structure and thus Fe and Ti scatter with a phase difference of π into the 100-ref lections. Because Fe (Z = 26) is higher in the periodic system than Ti (Z = 22), an immediate “guess” would be that Fe has a larger scattering amplitude than Ti. However, relativistic Hartree-Fock calculations show that the opposite is the case for the 100-reflection. An explanation for this may be sought in the stronger localization of the d-electrons of the first row transition elements when moving to the right in the periodic table. The tabulated difference between fTi (100) and ffe (100) is small, however, and based on the values of the scattering amplitude for isolated atoms, the kinematical intensity of the 100-reflection is only 5.10-4 of the intensity of the 200-reflection.

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