Monday, August 14th, 2017

darkoshi: (Default)
This morning, I started wondering why the eclipse will be seen on the west coast before it is seen on the east coast.

I know that the earth spins counter-clockwise (towards the east) when looking at it from above the north pole. And that the moon travels around the earth in the same counter-clockwise direction. And that the earth spins relatively faster. It does a complete rotation (360 degrees) in 24 hours, whereas the moon only travels 1/28th of the way around the earth (360 / 28 ~= 13 degrees) during that time.

So how can the moon's shadow travel from west to east? Isn't the earth spinning into the shadow and out of it in a clockwise west to east direction (the same as it always spins), and so the shadow should appear to move from east to west, just like the moon appears to do in the sky?

According to the answer on PhysLink.com, it has something to do with the moon's orbital velocity being greater than the earth's. But according to this orbital velocity formula, it seems that anything closer to the earth (ie. the earth's surface) would have a greater orbital velocity than something further away (ie. the moon). So that answer seems to be wrong or badly worded, maybe. Of course, if we simply consider velocity, the moon does travel a further distance through space than the earth's surface does, in the same amount of time. But what does that have to do with the eclipse? If it were a race, the earth would still win, rotating faster than the moon revolves.

Here's another page (cached, as the original eclipse2017.org page isn't responding - the website must be swamped) that tries to answer the question. Some of the commenters on that page seem to have the same confusion as I do.

Here's another page (Washington Post) that tries to explain it. Again talking about the speed of the moon compared to the earth.

Watching the various NASA visualizations didn't explain it well to me, because of how the videos keep shifting perspectives. Even in this animation, it looks like the sun must be moving from behind the viewer, to make the shadow move like that.

I think I may finally sort of understand it, but my explanation doesn't match any of the answers I read. So it's probably wrong. But... as the moon moves across the sun from right to left (as seen from the earth while facing south), it's shadow as seen from the earth changes direction. First it points towards the west, then straight, then towards the east.
And while the moon itself, from the earth's perspective, doesn't move far in the sky (and due to the earth's rotation, even appears to be going to the west*), it's shadow moves much faster... that must be why the answers keep mentioning the speed of the moon.. they must be trying to say that the speed of the moon's shadow across the face of the earth matches the moon's speed in space. I suppose that is logical, even though it isn't very intuitive to me**.

* But the sun appears to move to the west faster than the moon, so the moon does still cross the sun from right to left, even though they are both moving to the west.

So the moon's shadow moves quickly from the west to the east.

Right? Maybe? Sort of?

** Because the moon doesn't move in a straight line, but rather circles the earth. And those x-thousand miles per hour it moves up in space only correspond to y-hundred miles down on the earth... Oh jeez, now I'll start doubting my above explanation again...

Ok, thinking about it more. The shadow moves west to east like I explained above, because the moon crosses the sun from west to east. The speed of the moon through space around the earth affects the speed of the shadow, but it's not a direct x = y equation. The faster the moon moves across the face of the sun, the faster the shadow sweeps across the land from west to east. Since the shadow is sweeping through an arc (sort of), the far end of the shadow will pass a different distance during that time, depending from how far away you measure it... which for us is based on the distance between the moon and earth. So the speed of the shadow depends on that distance, and on the speed of the moon's revolution, and on the speed of the earth's rotation, and the size of the earth, etc. And it is complicated more because the moon moves in an elliptical orbit, not just straight past the sun, etc.

Now it makes sense to me. If I'm wrong, feel free to tell me which of my logic is wrong.

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On a related topic, how long will totality last, across the U.S.? It will start on the west coast around 10:17am (1:17pm eastern time). It will end on the east coast around 2:48pm (eastern time). So for one and a half hours, the shadow will sweep across the country, from coast to coast.

Within that time period, based on the 3 to 4 hour time difference between the coasts, the earth only rotates about half the same distance.

But actually, the earth and the shadow are moving in the same direction... so if the earth weren't turning, the shadow would traverse the distance even faster.

2017/08/16 Corrected some words above. I was mixing up the words "right" and "left", even though I was visualizing it correctly. I'm used to thinking of the west coast as on the left side and the east coast on the right side. For the above, my perspective is from the center of the county looking south. So the west coast is on the right, not the left.
Although since the sun will be pretty high overhead during the eclipse, "left" and "right" aren't good words to use to begin with.