Total Solar Eclipse ... How, Why, When .. using 16 Feb 1980 eclipse example.

 

How? I suspect you mean why.

Well, first you got the direction of the Moon incorrect. Viewed from above the North Pole, everything (Earth & moon) revolves and rotates counterclockwise. It travels across the sky east to west because the Earth is rotating on a daily basis.

The moon orbits Earth from west to east. It travels at 2290 miles per hour to the east which makes the shadow move to the east.

EDIT: Summary.

The moon's speed dominates, moving the shadow to the east 2290 mph. However, the Earth's rotation subtracts quite a bit from that motion by moving the shadow to the West 700 mph. Finally, the Earth's orbital velocity adds back in a little bit westward 410mph.

In the end, it moves eastward at 2000 mph.

Detail…

Drawing a picture of this viewed from above the North Pole with some vectors, showing all of the relevant speeds, it turns out that the moon's orbital speed is the dominant factor here. The speed of the eclipse across the US is very close to 2,000 miles per hour. That is, it travels 2500 miles in 1 hour and 14 minutes. See sources below…

You could stop there and say that's close except that the Earth's daily rotation is in the opposite direction at about seven hundred miles an hour this would give us a 1590 mile per hour shadow. So we've got 410 miles per hour to account for.

Lastly, if you look at the geometry of the Sun-Moon-Earth and then consider the Earth's orbital velocity of 67000 miles per hour, you see that this motion moves the shadow to the west[edit was east]. I'm sure there's some trigonometric black magic [edit actually similar triangles] that can be done to account for that additional 410 miles per hour, but I didn't bother with it.

……….

I got the start time of the eclipse at two locations from here by finding zip codes on a zip code map first:

A solar eclipse is coming to America. Here’s what you’ll see where you live.

I got the distance the eclipse travels from here:

Distance Calculator

… EDIT 2. …

P.S.

The ground speed at a latitude is = equator.speed * cos(latitude)

More accurate numbers:

Earth dia = 7917.5 mi (Google)

Earth circum = d * pi = 24,873.6 mi.

Equator speed = 1036.4 mph

St Louis latitude = 38.6270 (Google)

Speed of St Louis = 809.66 mph

Moon speed = 2288 mph (Cool Cosmos, Cal Tech)

2288 -809.6 = 1,478.34 mph difference.

A total eclipse of the sun is one of the most awe-inspiring natural phenomena in the world, so be sure to make your plans to see it well in advance!