Solar Eclipse on Earth The sun has a diameter of about 865,000 mi with a maximum

Chapter 1, Problem 69

(choose chapter or problem)

Solar Eclipse on Earth The sun has a diameter of about 865,000 mi with a maximum distance from Earths surface of about 94,500,000 mi. The moon has a smaller diameter of 2159 mi. For a total solar eclipse to occur, the moon must pass between Earth and the sun. The moon must also be close enough to Earth for the moons umbra (shadow) to reach the surface of Earth. (Source: Karttunen, H., P. Krger, H. Oja, M. Putannen, and K. Donners, Editors, Fundamental Astronomy, Fourth Edition, Springer-Verlag.) (a) Calculate the maximum distance, to the nearest thousand miles, that the moon can be from Earth and still have a total solar eclipse occur. (Hint: Use similar triangles.) (b) The closest approach of the moon to Earths surface was 225,745 mi and the farthest was 251,978 mi. (Source: World Almanac and Book of Facts.) Can a total solar eclipse occur every time the moon is between Earth and the sun?