However, during the Great American Eclipse this past August 21st, the shadow of
ID: 3281145 • Letter: H
Question
However, during the Great American Eclipse this past August 21st, the shadow of the Moon and the Earth's surface tracked from the Pacific Northwest coast of the continental United States, diagonally across the country to the Atlantic coast near Charleston, South Carolina. So the Moon's shadpw moved from West to East.
1.) Explain why, even though the moon rises in the East and sets in the West, the eclipse shadow tracked in the opposite direction from Wesdt to East. Include a diagram to illustrate the geomoetry.
2.) Use your knowledge of rotational motion to show, mathematically, why this is the case and compute the speed that the Moon's shadow tracked across the globe from West to East. Use the following information:
Distance from Earth's cetner to the Moon's center at lunar perigee: 361438 km
Distance of the Eath-Moon barycenter from the center of the Earth: 4670 km
Period of the Moon's orbit: 27 days
Period of the Earth's rotation: 24 hours
(Note: the barycenter is the point about which the Earth-Moon system rotates. It is also the center of mass of the Earth-Moon system)
Explanation / Answer
The sun rises inthe east and sets int he west. This mainly happens because the earth rotates CCW viewed from the north pole. It spins such that the Sun appear on the eastern horizon first and track west. Now interestingly viewed from this location (North Pole), in the outer location the moon also appears to move in a CCW motion as it obits the Earth. It is this CCW motion of the moon that mainly causes, its shadow during a total solar eclipse to move across Earth's surface from west to east.
The Glint of sun (reflected flash) moves from west to east. If you are vieweing from a satellite, you can see that moving from east to west, exactly opposite to the movement of earth. Now earth moves from west to east in one particular frame of reference. In the same frame of reference you will see the Sun's glint moving from east to west.
If you are on the same satellite, during a total solar eclipse you would see that the moon's shadow move across the Earth's surface but in the opposite direction.
To Summarize ...
Because the moon moves to the east in its orbit at about 3400 km/.h and Earth rotates to the east at 1670 km/h at the equator. So the lunar shadow moves to the east at (3400-1670) = 1730 km/h velocity near the equator. (relative motion and relative velocity). You cannot keep up with the shadow of the eclipse unless traveled at Mach 1.5.
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