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METEORITICAL AND OTHER GREAT‐CIRCLE PROBLEMS *
Author(s) -
LEONARD FREDERICK C.
Publication year - 1953
Publication title -
meteoritics
Language(s) - English
Resource type - Journals
eISSN - 1945-5100
pISSN - 0026-1114
DOI - 10.1111/j.1945-5100.1953.tb01305.x
Subject(s) - great circle , equator , midpoint , meridian (astronomy) , mathematics , geometry , point (geometry) , continuation , latitude , geodesy , mathematical analysis , physics , geology , computer science , astronomy , programming language
In this paper, which is really a continuation of two previously published papers, the following great‐circle problems are solved: (1) to find the coördinates of the poles of a great circle: third and analytic method; (2) to find the coördinates of the common nodes of two given great circles: second and analytic method; (3) to find the equation of the great circle passing thru a given point in a given direction with respect to the meridian passing thru that point; (4) to find the inclination of a great circle to the equator, and the angular distance of a given point on the great circle from the given nearer equatorial node of the great circle; (5) to find the length of the projection of a given arc of a given great circle on the equator; (6) to find the equation of the great circle passing thru a given point and making a given acute angle with a given great circle; (7) to find the longitude of the equatorial node nearer to the midpoint of the arc of the great circle passing thru two given points; the inclination of the great circle to the equator; and the angular distance between the two given points; (8) to find ( a ) the angle between the meridian, and ( b ) that between the parallel of latitude passing thru a given point on a given great circle, and the great circle; and (9) to find the maximum difference between the hypotenuse and a side of a spherical right triangle, inclined to each other at a given angle, as they vary in length from 0° to 90°. Special cases of six of the forenamed nine problems— i.e ., nos. (1), (2), (4), (5), (6), and (9)—which are encountered in either meteoric or spherical astronomy, likewise are discussed. In an addendum, several errata in §13 of the second paper on great‐circle problems are corrected.