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Consider two points on the Earth: latitudes and longitudes (0,0) are the coordinates of ...
Consider two points on the Earth: latitudes and longitudes (?0?,?0?) are the coordinates of the observer, and (?P?,?P?) are the coordinates of the magnetic pole. The angle along the meridian lines between the north pole and the two points are 90???0? and 90???P?; the angle between the two meridian lines is ???=?P???0?. Angle D is the azimuth of the magnetic north pole from the position of observation. Angle ? is also shown in the figure. Now recall the equations of spherical trigonometry. From the law of cosines applied to the spherical triangle we get: cos?=sin?0?sin?P?+cos?0?cos?P?cos??, and from law of sin we have: sin??cos?P?=sinDsin?. (a) Using Rotation Matrices applied to the spherical triangle derive these equations. (b) From the known geographical coordinates of the North Magnetic Pole and of Hoboken, find the numerical values of angles I and D (in degrees) that magnetic field makes in Hoboken. (c) The measurements of early Cretaceous limestone in Italian Apennines at geographical coordinates ?0?=42.9? north, and ?0?=12.6? east yield the mean values of I=38? and D=313?. Find the present geographical coordinates of the location of (?P?,?P?) of what was the magnetic pole at the time of the formation of the sample. Where is that place located on Earth?