Every depiction I have seen shows the Eclipse path of totality travel Eastward from Oregon. Why Doesn't the path travel Westward from South Carolina as the Earth rotates Eastward? Shouldn't the Totality follow the Path of the Sun?
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1$\begingroup$ Question for the student: what is changing about the Earth-moon-sun geometry over time other than the angular orientation of the Earth? $\endgroup$– dmckee --- ex-moderator kittenCommented Aug 19, 2017 at 16:02
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3 Answers
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The answer posted by Sammy Gerbil is quite wrong. The passage of the eclipse from west to east has nothing to do with the sun overtaking the moon in the sky.
Sammy does correctly point out that, as viewed from above, the moon is circling the earth in a counterclockwise direction. And that means it is travelling from west to east. It is in fact travelling quite fast: about 2200 mph in fact (relative to a fixed earth), as you can verify by some simple computations. And that is also how fast its shadow is traveling.
The rotation of the earth however, being in the same direction, tends to counteract the motion of the shadow, by around 800 mph at the latitude of the eclipse. So the effective speed of the shadow across North America was close to 1400 mph, from west to east.
There is a very good animation of this on the Wikipedia website from which you can see at once that I have calculated this correctly: https://en.wikipedia.org/wiki/Solar_eclipse_of_August_21,_2017
EDIT: interesting that if you could rev the earth up to reduce the day to 11 hours, then the totality of an eclipse could last almost all day.
answered Aug 23, 2017 at 4:21
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$\begingroup$ My explanation is not incompatible with yours. In your explanation the line between the Sun and the Earth is stationary, in my explanation the Earth is stationary. The Sun overtaking the Moon as they both cross the sky from E to W is the same as the Moon passing between the Earth and the Sun in a W to E direction as the Earth rotates. $\endgroup$ Commented Aug 23, 2017 at 21:18
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$\begingroup$ My first instinct was to explain the eclipse in terms of leverage and parallax, exactly as you explained it @sammygerbil. But then I couldn't justify the high speed at which the shadow traveled from west to east. The explanation which I have posted here is very different (it seems to me) from the way I tried to explain it at first. $\endgroup$ Commented Aug 23, 2017 at 21:31
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$\begingroup$ I found the Wikipedia visual after I'd already come up with the math. And the visual totally shows the geometry of what's happening. It's the absolute speed of the moon relative to the orbital (not rotational) speed of the earth which explains everything.. $\endgroup$ Commented Aug 23, 2017 at 21:33
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$\begingroup$ Which animation are you referring to? I don't see one which shows the Sun-Moon-Earth geometry or the orbital motion of the Earth. $\endgroup$ Commented Aug 23, 2017 at 22:44
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$\begingroup$ Sorry, it's not a geometrical diagram. It's the visual graphic in the right-hand column that shows pictorially the shadow racing across the country, while pointing with a grey line to the position of the sun. $\endgroup$ Commented Aug 23, 2017 at 22:57
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As Earth orbits the Sun, the Sun appears to move to the east against the background stars by about 1°/day --- completing its apparent route around the ecliptic in about 365 days.
As the Moon orbits the Earth, the Moon appears to move to the east against the background stars by about 12°/day --- completing its apparent route around the sky in about 30 days.
During a solar eclipse, the Moon "overtakes" the Sun against the background stars, traveling from the Sun's west side to its east side over the course of roughly 1/12 day = 2 hours.
When you are observing totality, people to your west have seen totality already, but people to your east have not seen totality yet.
Earth's rotation, which causes the Sun, the Moon, and all the stars to move from east to west at a rate of approximately 360°/day, is a distraction. Think instead about the apparent motion of the Sun and Moon compared to the distant background stars.
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Like the Sun, the Moon travels from east to west across the sky. However, the Moon travels slightly slower than the Sun, because of its rotation around the Earth.
Looking down from above the north pole, the Moon orbits anticlockwise, the same direction as the Earth rotates. But because its rotation period is much longer - about 27 days compared with 1 day for the Earth's rotation - this makes only a small difference to its speed across the sky.
As the Sun overtakes the Moon in the sky, the shadow of the Moon travels from west to east.
answered Aug 19, 2017 at 16:43
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1$\begingroup$ You can't compare the moon's rotation with that of the spin of the Earth. You should be comparing it to the sun's rotation in the sky over the course of a year. $\endgroup$ Commented Aug 23, 2017 at 4:48
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$\begingroup$ @JohnathanGross What difference would that make to my explanation? $\endgroup$ Commented Aug 23, 2017 at 21:27
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1$\begingroup$ From the Earth's perspective, the Sun, the Moon, and the rest of the night sky are traveling roughly the same speed westward with an angular velocity of about 360 degrees/day. The sun moves relative to the sky at a rate of 360 degrees/year while the moon travels across the sky at a rate of 360 degrees/month. $\endgroup$ Commented Aug 23, 2017 at 22:01
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1$\begingroup$ @sammygerbil if it helps to understand, the main issue as I see it is the sentence ending "this makes only a small difference to its speed across the sky." This sentence gets the physics 100% backwards, because in fact if the rotation period of the Moon about the Earth was, let's say, a million days, rather than 27 days, then you would see an eclipse every day for several days as your rotation brought you into the umbra and out again on a daily basis. $\endgroup$– CR DrostCommented Aug 24, 2017 at 20:38
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$\begingroup$ In fact one can get a good approximation for the duration of the eclipse from onset to totality by approximating the size of the Sun as 0.5° and then computing 0.5° · (27 days / 360°) as this duration. $\endgroup$– CR DrostCommented Aug 24, 2017 at 20:39