Astronomers decided to observe a total solar eclipse from an airplane flying east along the eclipse strip at a speed of 900 km / h.

Astronomers decided to observe a total solar eclipse from an airplane flying east along the eclipse strip at a speed of 900 km / h. The eclipse took place near noon at 60 ° latitude and its total phase on Earth lasted 5 minutes. How many minutes did it take aboard the plane?

The duration of the eclipse will increase as many times as the speed of movement of the lunar shadow relative to the observer slows down. The speed of the lunar shadow relative to the center of the Earth is close to the orbital speed of the Moon (1 km / s); The rotation speed of the earth’s surface at 60 ° latitude is 0.25 km / s. This means that their relative speed is 1 – 0.25 = 0.75 km / s.
An observer on an airplane moves relative to the Earth’s surface at a speed of 900 km / h = 0.25 km / s, therefore, its speed relative to the center of the Earth is 0.25 + 0.25 = 0.5 km / s. This means that the lunar shadow is catching up with it at a speed of 1 – 0.5 = 0.5 km / s. Hence the duration of the eclipse by plane: T = 5 min · 0.75 / 0.5 = 7.5 min. Such long-term eclipses from the Earth’s surface can be observed only in the equatorial region.

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