scholarly journals Deriving and testing the great circle theory

2021 ◽  
Vol 6 (5) ◽  
pp. 16-24
Author(s):  
Reeya Bansal
Keyword(s):  
Great Circle

Charts for Great Circle Sailing

1885 ◽  
Vol 20 (501supp) ◽  
pp. 7991-7991
Author(s):  
Richard A. Proctor
Keyword(s):  
Great Circle

From Littoral to Ozone: On Mike Pearson’s Contributions to Indian Ocean History

2019 ◽  
Vol 2 (1) ◽  
pp. 12-24
Author(s):  
Edward A. Alpers
Keyword(s):  
New York ◽  
Indian Ocean ◽  
Great Circle ◽  
Historical Scholarship ◽  
The Indian Ocean ◽  
Seminal Article

In this article I examine two of Michael Pearson’s most important contributions to our understanding of Indian Ocean history: the concept of the littoral, which he first articulated in his seminal article on “Littoral society: the case for the coast” in The Great Circle 7, no. 1 (1985): 1-8, and his comment in The Indian Ocean (London and New York: Routledge, 2003, p. 9) that “I want it to have a whiff of ozone.” Accordingly, I review Pearson’s publications to see how he has written about these two notions and how they have influenced historical scholarship about the Indian Ocean.

Empirical Estimation of Shortest Route Length along U.S. Interstate Highways Based on Great Circle Distance

2021 ◽  
pp. 036119812110152
Author(s):  
Nawei Liu ◽  
Fei Xie ◽  
Zhenhong Lin ◽  
Mingzhou Jin
Keyword(s):  
Linear Regression ◽  
State Level ◽  
Distance Matrix ◽  
Great Circle ◽  
The State ◽  
Empirical Estimation ◽  
Interstate Highways ◽  
Shortest Route ◽  
Route Length ◽  
Great Circle Distance

In this study, 98 regression models were specified for easily estimating shortest distances based on great circle distances along the U.S. interstate highways nationwide and for each of the continental 48 states. This allows transportation professionals to quickly generate distance, or even distance matrix, without expending significant efforts on complicated shortest path calculations. For simple usage by all professionals, all models are present in the simple linear regression form. Only one explanatory variable, the great circle distance, is considered to calculate the route distance. For each geographic scope (i.e., the national or one of the states), two different models were considered, with and without the intercept. Based on the adjusted R-squared, it was observed that models without intercepts generally have better fitness. All these models generally have good fitness with the linear regression relationship between the great circle distance and route distance. At the state level, significant variations in the slope coefficients between the state-level models were also observed. Furthermore, a preliminary analysis of the effect of highway density on this variation was conducted.

scholarly journals Equatorial ionospheric disturbance observed through a transequatorial HF propagation experiment

2006 ◽  
Vol 24 (5) ◽  
pp. 1401-1409 ◽  
Author(s):  
T. Maruyama ◽  
M. Kawamura
Keyword(s):  
Large Scale ◽  
Ionospheric Disturbance ◽  
Great Circle ◽  
Rate Of Change ◽  
Spatial Distance ◽  
Propagation Path ◽  
Multiple Signal Classification ◽  
Radio Broadcasting ◽  
Equatorial Plasma Bubbles ◽  
Propagation Experiment

Abstract. A transequatorial radio-wave propagation experiment at shortwave frequencies (HF-TEP) was done between Shepparton, Australia, and Oarai, Japan, using the radio broadcasting signals of Radio Australia. The receiving facility at Oarai was capable of direction finding based on the MUSIC (Multiple Signal Classification) algorithm. The results were plotted in azimuth-time diagrams (AT plots). During the daytime, the propagation path was close to the great circle connecting Shepparton and Oarai, thus forming a single line in the AT plots. After sunset, off-great-circle paths, or satellite traces in the AT plot, often appeared abruptly to the west and gradually returned to the great circle direction. However, there were very few signals across the great circle to the east. The off-great-circle propagation was very similar to that previously reported and was attributed to reflection by an ionospheric structure near the equator. From the rate of change in the direction, we estimated the drift velocity of the structure to range mostly from 100 to 300 m/s eastward. Multiple instances of off-great-circle propagation with a quasi-periodicity were often observed and their spatial distance in the east-west direction was within the range of large-scale traveling ionospheric disturbances (LS-TIDs). Off-great-circle propagation events were frequently observed in the equinox seasons. Because there were many morphological similarities, the events were attributed to the onset of equatorial plasma bubbles.

Great Circle Sailing (Graphic Solution)

Navigation ◽  
1968 ◽  
Vol 15 (1) ◽  
pp. 53-61
Author(s):  
WILLIAM M. FRASER
Keyword(s):  
Great Circle ◽  
Graphic Solution

scholarly journals Advertisments concerning the quantity of a degree of a great circle in English measures

1676 ◽  
Vol 11 (126) ◽  
pp. 636-637
Keyword(s):  
Great Circle

Some while since an account was given concerning the quantity of a degree of a great circle, according to the tenour of a printed French discourse, entitled De la Mesure de la Terre.

scholarly journals Formulæ for computing the longitude at sea

1837 ◽  
Vol 3 ◽  
pp. 332-333
Keyword(s):  
Spherical Surface ◽  
Great Circle

These formulæ, in which the longitude and latitude of two points in a spherical surface, together with the arc of the great circle intercepted between them, are supposed to be given, furnish the means of determining the longitude of any other point in that circle, from its latitude.

A Discussion on global tectonics in Proterozoic times - Palaeomagnetic evidence for a Proterozoic super-continent

1976 ◽  
Vol 280 (1298) ◽  
pp. 469-490 ◽  
Keyword(s):  
North American ◽  
Mantle Convection ◽  
Great Circle ◽  
Prominent Feature ◽  
Time Data ◽  
Polar Wander ◽  
Late Precambrian ◽  
Palaeomagnetic Data ◽  
The Baltic ◽  
Global Tectonics

The Precambrian apparent polar wander (a.p.w.) curve for Africa is now defined in a general way from ca . 2700 million years (Ma) to Palaeozoic times, and is compared here with palaeomagnetic results from other Precambrian regions. Loops present in the African and North American a.p.w. curves between 2000 and 1000 Ma can be matched in size and shape, and when superimposed show that the AfroArabian and North American regions were in continuity at this time. Data from other Gondwanaland continents are reviewed and seem to be consistent with the SmithHallam reconstruction to ca . 2100 Ma for South America, to ca . 1800 Ma for India, and possibly for Australia back to ca . 2100 Ma. The a.p.w. curve from the Baltic and Ukrainian Shields can be matched with that from Africa and North America such that there was crustal continuity prior to 1000 Ma with the Gothide and Grenville mobile belts in great-circle alignment. The limited palaeomagnetic data from the Siberian Shield do not allow it to be placed uniquely with respect to the other land masses but are consistent with a position in juxtaposition with the Baltic-Ukrainian Shields such that massive anorthosites and ca . 1000 Ma mobile belts are in alignment with those from elsewhere. The palaeomagnetic evidence is consistent with a model in which the bulk of the Precambrian shields were aggregated together as a single super-continent during much of Proterozoic times, the most prominent feature of which is a great circle alignment of massive anorthosites (2250-1000 Ma) along a belt which also became a concentrated zone of igneous intrusion by rapakivi granites and alkaline intrusions, and culminated in generation of long linear mobile belts at 1150 ± 200 Ma and thick graben sedimentation. The predominance of this feature during much of the Proterozoic suggests that a simple mantle convection system pertained during this time. The proposed super-continent is not greatly different in form from the later shortlived super-continent Pangaea, formation of which may have involved relatively minor redistribution of the sialic regions in late Precambrian (probably post-800 Ma) and Palaeozoic times.

Geographical interpretation of measurements of average phase velocities of surface waves over great circular and great semi-circular paths

1964 ◽  
Vol 54 (2) ◽  
pp. 571-610
Author(s):  
George E. Backus
Keyword(s):  
Spherical Harmonics ◽  
Rayleigh Waves ◽  
Seismic Station ◽  
Great Circle ◽  
Explicit Formulas ◽  
Phase Velocities ◽  
Rapid Accumulation ◽  
Generalized Spherical Harmonics ◽  
Geographical Position ◽  
The Difference

ABSTRACT If the averages of the reciprocal phase velocity c−1 of a given Rayleigh or Love mode over various great circular or great semicircular paths are known, information can be extracted about how c−1 varies with geographical position. Assuming that geometrical optics is applicable, it is shown that if c−1 is isotropic its great circular averages determine only the sum of the values of c−1 at antipodal points and not their difference. The great semicircular averages determine the difference as well. If c−1 is anisotropic through any cause other than the earth's rotation, even great semicircular averages do not determine c−1 completely. Rotation has negligible effect on Love waves, and if it is the only anisotropy present its effect on Rayleigh waves can be measured and removed by comparing the averages of c−1 for the two directions of travel around any great circle not intersecting the poles of rotation. Only great circular and great semicircular paths are considered because every earthquake produces two averages of c−1 over such paths for each seismic station. No other paths permit such rapid accumulation of data when the azimuthal variations of the earthquakes' radiation patterns are unknown. Expansion of the data in generalized spherical harmonics circumvents the fact that the explicit formulas for c−1 in terms of its great circular or great semicircular integrals require differentiation of the data. Formulas are given for calculating the generalized spherical harmonics numerically.

Variation in Degree of Hornblende Grain Alignment within two Boudinage Structures

1971 ◽  
Vol 8 (1) ◽  
pp. 144-149 ◽  
Author(s):  
W. M. Schwerdtner ◽  
P. M. Sheehan ◽  
J. C. Rucklidge
Keyword(s):  
Inverse Relationship ◽  
Finite Strain ◽  
Great Circle ◽  
Preferred Orientation ◽  
Grain Alignment ◽  
X Ray ◽  
Fabric Diagrams ◽  
Principal Directions

The degree of preferred orientation of hornblende in two boudinage structures is analyzed by means of an X-ray texture goniometer. Relative values of reflected intensity for {110} are plotted on the stereographic net, and contoured at convenient intervals. As in conventional fabric diagrams for hornblende, {110} define a great-circle girdle whose breadth reveals the density of unimodal grouping of [001].The density of grouping of [001] varies throughout both boudinage structures. It decreases with increasing extension in structure A, and seems to have a similar trend in structure B, where the determined variation in degree of grain alignment is of doubtful statistical significance.The inverse relationship between the degree of preferred orientation and the magnitude of extension may be attributed to rotation of the principal directions of finite strain during syntectonic crystallization. Alternatively, reorientation of strained grains by annealing recrystallization may have produced the inverse trend.

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