Question

69. Solar Eclipse on Earth The sun has a Sun diameter of about 865,000 mi with a maxi- mum distance from Earth's surface of about Moon Earth 94,500,000 mi. The moon has a smaller diam- eter of 2159 mi. For a total solar eclipse to occur, the moon must pass between Earth and NOT TO SCALE Umbra 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, Funda- mental 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 Earth's surface was 225,745 mi and the far- thest 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?

Answer 1

Ans.

a) ( See from the figure). The diameter of the sun will be equal to AB'. The maximum distance of Earth from sun is equal to AC. The diameter of the moon is equal to DE'. We want to calculate the maximum distance between moon and Earth that is the value DC.

Applying similar triangles law to triangle ABC and DEC.

》 AB/DE = AC / DC

AB = 865000/2 (radius of the moon)

AC = 94500000, DE = 2159/2 ( radius of moon)

Putting the above values and calculating for DC, we get

DC = 235867.63 miles.

b) A total solar eclipse cannot occur every time the moon is between Earth and Sun. Here we calculated the maximum distance that is required for a solar eclipse to occur. If the distance is greater than this distance, solar eclipse wouldn't occur. However, if the distance is less than this distance, the total solar eclipse can occur.