Tables of Solid Angles: I. Solid Angle Subtended by a Circular Disc

1963 ◽  
Vol 17 (82) ◽  
pp. 207
Author(s):  
J. W. W. ◽  
A. V. H. Masket ◽  
W. C. Rodgers
Keyword(s):  
Solid Angle ◽  
Circular Disc ◽  
Solid Angles

Reply by author to Dr. LaFehr

Geophysics ◽  
1977 ◽  
Vol 42 (4) ◽  
pp. 877-877
Author(s):  
Shri Krishna Singh
Keyword(s):  
Closed Form ◽  
Solid Angle ◽  
Short Note ◽  
Circular Disc ◽  
Closed Form Expression ◽  
Gravitational Attraction ◽  
Form Expression ◽  
Practical Usefulness ◽  
Solid Angles ◽  
Classic Paper

It is difficult to include all references when dealing with a subject so well studied as the gravitational attraction of a circular disc. Although the practical usefulness of Nettleton’s paper can not be denied by anyone, it nevertheless gives no details (except for some references) of the computation of solid angles subtended by a disc from which his graphs (Geophysics, 1942, Figure 4) result. My short note deals with (in what I consider an easy way of) obtaining a closed form expression for the solid angle. For applications of the result the reader would do well to look up Nettleton’s classic paper.

GRAVITATIONAL ATTRACTION OF A CIRCULAR DISC

Geophysics ◽  
1977 ◽  
Vol 42 (1) ◽  
pp. 111-113 ◽  
Author(s):  
Shri Krishna Singh
Keyword(s):  
Cross Sections ◽  
Solid Angle ◽  
Vertical Component ◽  
Circular Disk ◽  
Circular Disc ◽  
Gravitational Attraction ◽  
Exploration Seismology ◽  
Solid Angles ◽  
The Cross

The vertical component of gravitational attraction [Formula: see text] of a circular disk is of some interest in geophysics since it can be used to obtain attraction of 3-D bodies whose parallel sections are circular and also since the solid angle Ω subtended by a disc at any point is proportional to [Formula: see text] at the same point (Ramsey, 1940, p. 36). Solid angles may be needed in some diffraction calculations in exploration seismology (see, e.g., Hilterman, 1975). It is clear, however, that in calculation of attraction from 3-D bodies, approximation of the cross‐sections by a polygon (Talwani and Ewing, 1960) has wider application.

Dimensions of plane and solid angles and their units in the International System of Units (SI)

2020 ◽  
pp. 26-32
Author(s):  
M. I. Kalinin ◽  
L. K. Isaev ◽  
F. V. Bulygin
Keyword(s):  
Solid Angle ◽  
International System ◽  
International Committee ◽  
Plane Angle ◽  
Arc Length ◽  
Weights And Measures ◽  
International System Of Units ◽  
System Of Units ◽  
In Series ◽  
Solid Angles

The situation that has developed in the International System of Units (SI) as a result of adopting the recommendation of the International Committee of Weights and Measures (CIPM) in 1980, which proposed to consider plane and solid angles as dimensionless derived quantities, is analyzed. It is shown that the basis for such a solution was a misunderstanding of the mathematical formula relating the arc length of a circle with its radius and corresponding central angle, as well as of the expansions of trigonometric functions in series. From the analysis presented in the article, it follows that a plane angle does not depend on any of the SI quantities and should be assigned to the base quantities, and its unit, the radian, should be added to the base SI units. A solid angle, in this case, turns out to be a derived quantity of a plane angle. Its unit, the steradian, is a coherent derived unit equal to the square radian.

Viewing the World from Different Angles: Plato’s Timaeus 54E-55A

Apeiron ◽  
2013 ◽  
Vol 46 (3) ◽  
pp. 244-269
Author(s):  
Ernesto Paparazzo
Keyword(s):  
Present Article ◽  
Solid Angle ◽  
Alternative Interpretation ◽  
Plane Geometry ◽  
A Value ◽  
Solid Geometry ◽  
The World ◽  
Euclid’S Elements ◽  
Solid Angles ◽  
The Universe

Abstract The present article investigates a passage of the Timaeus in which Plato describes the construction of the pyramid. Scholars traditionally interpreted it as involving that the solid angle at the vertex of the pyramid is equal, or nearly so, to 180°, a value which they took to be that of the most obtuse of plane angles. I argue that this interpretation is not warranted, because it conflicts with both the geometrical principles which Plato in all probability knew and the context of the Timaeus. As well as recalling the definitions and properties of plane angles and solid angles in Euclid’s Elements, I offer an alternative interpretation, which in my opinion improves the comprehension of the passage, and makes it consistent with both the immediate and wider context of the Timaeus. I suggest that the passage marks a transition from plane geometry to solid geometry within Plato’s account of the universe.

A comparison of two windowless x-ray detector designs on VG HB501 STEMs

1988 ◽  
Vol 46 ◽  
pp. 672-673
Author(s):  
A. W. Nicholls
Keyword(s):  
Energy Range ◽  
Solid Angle ◽  
Low Energy ◽  
Original Design ◽  
X Ray ◽  
Solid Angles

Windowless X-ray detectors are routinely used on VG HB501 STEMs allowing detection of all elements from B upwards (fig 1). The original design for the HB501 built by Link Analytical had a theoretical solid angle of 0.077sr but recently a new design has appeared with a solid angle of 0.181sr. In order to compare these two designs it would be useful to develop a test that could be carried out on the microscope column that would accurately characterise the performance of the detector in the low energy range (<1keV) as well as at higher energies. Recently there has been much interest in characterising X-ray detector microscope systems using the peak to background (P' B) ratio from specially prepared evaporated Cr films. As an extension to this method this type of specimen has-been used to look at the ratio of effective detector solid angles and also the low energy area by comparing CrK to CrL intensities in order to fully characterise the detectors on VG HB501 STEMs.

Absorption corrections for AEM Analysis of thin-film and sphere samples with large-solid-angle x-ray detectors

1989 ◽  
Vol 47 ◽  
pp. 206-207
Author(s):  
Nuri A. Zreiba ◽  
Thomas F. Kelly
Keyword(s):  
Thin Film ◽  
Solid Angle ◽  
X Rays ◽  
Ray Optics ◽  
X Ray ◽  
Plane Parallel ◽  
Recent Advances ◽  
Absorption Correction ◽  
Solid Angles ◽  
Sphere Geometry

Recent advances in x-ray detectors for TEM and STEM instruments have resulted in large increases in the solid angle that these detectors subtend with respect to the sample. These solid angles of order 0.2 steradian mean that x rays emitted into a cone of semi-angle equal to 15° will be intercepted by the detector. Since the conventional absorption correction for x-ray analysis assumes that all detected rays are parallel, we chose to examine whether divergent x rays could change the absorption and fluorescence corrections significantly and should therefore be taken into account.This paper will focus on the effects of such changes on the absorption correction of thin specimens. Two specimen geometries will be considered, namely the usual plane parallel slab and the sphere geometry. Sphere geometries are of interest because they are currently used in the evaluation of the efficiency of x-ray detectors, the results of which are to be presented in the X-ray Optics and Microanalysis Conference in Poland this summer.

scholarly journals FORTRAN PROGRAM FOR CALCULATING THE SOLID ANGLE SUBTENDED BY ONE CIRCULAR DISC AT ANOTHER.

1967 ◽  
Author(s):  
I. R. Williams ◽  
A. M. Craig, Jr. ◽  
C. L. Thompson
Keyword(s):  
Solid Angle ◽  
Fortran Program ◽  
Circular Disc
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