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# hw3 - Eric Couillard Astro 142 11 February 2008 Homework#3...

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Eric Couillard Astro 142 11 February 2008 Homework #3 1.a. At the very beginning of the trip, depending on to what degree of accuracy you measure their paths, they are parallel. It would depend on what kind of a map you looked at in order to determine whether or not they were parallel. A 3D map would show their routes as both traveling to the same flat along the sphere, where a 2D map would show both lines curving (eventually.) So at first they are parallel. b. However, because north is a point on the globe, in order for two people to approach it from different areas, there's no way they could remain parallel. After a few hours of air travel, looking at their positions on a 2-dimensional map would show that they were curving slightly. This is due to the fact that the shortest distance between two points on a sphere is a great circle, or a circle with the center of the sphere as its center. Because both of these points are going along one of these great circles to the North Pole, both will curve towards it. So after a few hours of travel they would not be parallel. c. Their paths will not meet until they hit the North Pole, because their great circles both meet at the same point (the north pole.) Parallel lines eventually converge in spherical geometry. d. Yes they do. This is because the Earth is so huge relative to human beings that when you are close to the ground is not obvious that the Earth is spherical.

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