Latitude-Longitude SystemLos Angeles is located at 34.05° North latitude and 118.24° West longitude, and Rio de Janeiro, Brazil, is located at 22.90° South latitude and 43.23° West longitude (see figure). Assume that Earth is spherical and has a radius of 4000 miles.
(a) Find the spherical coordinates for the location of each city.
(b) Find the rectangular coordinates for the location of each city.
(c) Find the angle (in radians) between the vectors from the center of Earth to the two cities.
(d) Find the great-circle distance between the cities. (Hint: )
(e) Repeat parts (a)–(d) for the cities of Boston, located at 42.36° North latitude and 71.06° West longitude, and Honolulu, located at 21.31° North latitude and 157.86° West longitude.
This problem is an elaboration of Example 7 on page 611 of the textbook.
Assuming that the earth is a sphere of radius 3960 miles, Salt Lake City is located at 40.8 degrees North and 111.9 degrees West, and San Francisco is located at 37.8 degrees North and 122.4 degrees West, the great circle distance between Salt Lake City and San Francisco is ( ) miles.
Assuming that Sydney in Australia is located at 33.9 degrees South and 151.2 degrees East, and that you are flying from Salt Lake City to Sydney on a great circle course at 600 miles per hour, it will take you ( ) hours to get there.
The greatest great circle distance between any two points on earth is ( ) miles.
The antipodal point of Salt Lake City (i.e., the far point at which a line from Salt Lake City through the center of the earth pierces the surface of the earth) has a latitude of ( ) degrees( ) (enter North or South) and a longitude of( ) degrees ( ) (enter East or West).
Note: the geographic coordinates were taken from the internet, and were rounded to one tenth of one degree. Recall that ww expects your answers to be within one tenth of one percent of what it has been given as the correct answer. To be sure you want compute your answers, based on the data given here, a little more accurately than ww requires
