Question

A total solar eclipse is a rare phenomenon that happens at the same location once in about 200 years. During this phenomenon, the Moon passes directly in front of the Sun as seen from Earth. Given the visible diameter of the Moon is very close to the visible diameter of the Sun, the Moon covers the Sun completely and the part of Earth in the Moon’s shadow plunges into darkness during the daytime. The average shadow of the Moon on Earth is about 200 km wide and it slowly travels across Earth during the eclipse day. On August 21st 2017, this rare phenomenon occurred in the US. Below are the data about the eclipse. Answer the questions below. (The photo above shows the Sun in Franklin, NC, about 5 minutes before the total solar eclipse in 2017). a. The 2017 total solar eclipse started on Monday August 21 in Madras, Oregon at about 10:20 am (Pacific daylight time) and ended in Columbia, South Carolina at 2:44 pm (Eastern daylight time). Estimate the average speed of the Moon’s shadow moving across the United States and compare it to the speed of sound in air (340 m/s). Indicate any assumptions that you made. b. During the same total solar eclipse in Franklin, North Carolina, the Moon cast on Earth a circular shadow with a diameter of about 109 km. The total solar eclipse in Franklin lasted for 2 minutes and 30 seconds. Estimate the speed of the Moon’s shadow moving across Franklin. Compare this answer with the answer in part a. and try to explain any discrepancies.

Answer 1

a)In the first case the average speed of the Moon's shadow moving across the United States=Diameter of Moon's shadow/Time for which the eclipse lasted.

The time for which the eclipse lasted=4 hours and 24 minutes=((4*60)+24)*60 seconds=15840 seconds.

The diameter of the Moon's shadow=200 km=200000 m.

Therefore the required speed=200000/15840=13 m/s.

This value is much smaller than the speed of sound in air.

b)In the second case the average speed of the Moon's shadow=109 km/(2*60+30) sec=109000/150=727 m/s.

This speed is larger than the speed in the first case and is a clear indication of the fact that the speed of the Moon's shadow varies with the latitude and longitude of the particular place on Earth at which it is calculated.