Solve each problem. Solar Eclipse on Mars (Refer to Exercise 67.) The sun...

Solve each problem.

Solar Eclipse on Mars (Refer to Exercise 67.) The sun’s distance from the surface of Mars is approximately 142,000,000 mi. One of Mars’ two moons, Phobos, has a maximum diameter of 17.4 mi. (Source: World Almanac and Book of Facts.)

(a) Calculate the maximum distance that the moon Phobos can be from Mars for a total eclipse of the sun to occur on Mars.

(b) Phobos is approximately 5800 mi from Mars. Is it possible for Phobos to cause a total eclipse on Mars?

(Reference Exercise 67)

Solar Eclipse on Earth The sun has a diameter of about 865,000 mi with a maximum distance from Earth’s 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 moon’s umbra (shadow) to reach the surface of Earth. (Source: Karttunen, H., P. Kröger, H. Oja, M. Putannen, and K. Donners, Editors, Fundamental Astronomy, Fourth Edition, Springer-Verlag.)

(a) Calculate the maximum distance 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 Earth’s 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?