2. Hong Kong is in the northern hemisphere. In March, the sun’s declination is a

Question

2. Hong Kong is in the northern hemisphere. In March, the sun’s declination is about 0 degrees. At local noon in Hong Kong, in March, the sun reaches an angle of elevation of about 68 degrees. At this time, it is 4:24am in Greenwich, England. What is the latitude and longitude for Hong Kong? Assuming a spherical Earth with radius 3960 miles, write the position of Hong Kong in spherical coordinates.

3. Given latitude 13.80N, longitude 100.50E for Bangkok, Thailand, and latitude 40.70N, longitude 74.00W for New York, United States, determine the time difference between occurrences of local noon at these two locations (write in hours and minutes). Also, given that the sun’s declination is about 0 degrees in March, compute the angle of elevation of the sun at noon in both New York and in Bangkok in March.

4. The shape of the Earth can be approximated by an ellipsoid with an equatorial radius of approximately 3963 miles and a polar radius of approximately 3949 miles. This means the distance from the center of the Earth to the equator is approximately 3963 miles (to any point on the equator) and the distance from the center of the Earth to both the North and South Poles is approximately 3949 miles. Because the distance to the poles is less than the distance to the equator, the Earth can be describe as an oblate ellipsoid.

Explanation / Answer

4.

A spheroid, or ellipsoid of revolution, is a quadric surface obtained by rotating an ellipse about one of its principal axes; in other words, an ellipsoid with two equal semi-diameters. If the ellipse is rotated about its major axis, the result is a prolate (elongated) spheroid, shaped like an American football or rugby ball. If the ellipse is rotated about its minor axis, the result is an oblate (flattened) spheroid, shaped like a lentil. If the generating ellipse is a circle, the result is a sphere. A spheroid has circular symmetry. Because of the combined effects of gravity and rotation, the Earth's shape is not quite a sphere but instead is slightly flattened in the direction of its axis of rotation. For that reason, in cartography the Earth is often approximated by an oblate spheroid instead of a sphere. The current World Geodetic System model uses a spheroid whose radius is 6,378.137 km (3,963.191 mi) at the equator and 6,356.752 km (3,949.903 mi) at the poles. The word "spheroid" originally meant "an approximately spherical body", admitting irregularities even beyond the bi- or tri-axial ellipsoidal shape, and that is how the term is used in some older papers on geodesy (for example, referring to truncated spherical harmonic expansions of the Earth.

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