What factors determine the timing of a solar eclipse?

[arabianights]

I observed the eclipse from Washington DC area yesterday. I have a few questions.

from the eclipse map and youtube clips ppl uploaded, the eclipse starts in Oregon and sweep across states.

questions:
1. I know Earth rotate around itself from west towards east every 24 hrs, is this the main reason ppl on the west coast see the eclipse first?
2. which direction moon rotate around earth? I assume also west towards east?
3. it took around 1 hour and half for the totality max region sweep through continental US. 1720UTC ~ 1845UTC. is this mainly corresponding to Earth's rotational speed or moon's?

 

[mathman]

1. yes
2. i don't know
3. Earth's rotation

 

[Bandersnatch]

1. yes
2. i don't know
3. Earth's rotation

I'm pretty sure two of those answers are wrong, mathman!

1. I know Earth rotate around itself from west towards east every 24 hrs, is this the main reason ppl on the west coast see the eclipse first?

Think about the following: The Earth rotates from west to east, and yet the sun rises in the east and sets in the west. Shouldn't it be the same with the eclipse, if it's mainly due to Earth's rotation?

2. which direction moon rotate around earth? I assume also west towards east?

Like most bodies in the solar system, it 'revolves' (=orbits, as opposed to 'rotates' = spins on its axis) anticlockwise - the same way Earth rotates, and the same way Earth+Moon revolve around the Sun.

3. it took around 1 hour and half for the totality max region sweep through continental US. 1720UTC ~ 1845UTC. is this mainly corresponding to Earth's rotational speed or moon's?

Think about the following: There are roughly 3 time zones (3 hour difference) between Oregon and South Carolina. The time zones are the direct result of Earth's rotation.
And yet, it took ~1.5 hours for the eclipse to travel the distance. Not only that, but it traveled opposite way than the Sun.
This should be sufficient to doubt the direct complicity of Earth's rotation.

It's best to draw it all out.

As shown above, there are three rotational components affecting the position of the point of total eclipse on Earth's surface. All the components are anticlockwise rotations, but they cause different directions and magnitudes of displacement of the point of totality.

We will not concern ourselves with trying to calculate the magnitude of each effect here, just figuring out the directions of displacement they cause.

Let's split the situation into three cases, in each case we'll pretend that only one rotational component exists. The actual displacement can be obtained by adding all three contributions together.
The pictures are simplified and not to scale. Everything is assumed to happen in one plane, and the shadow is a point. But none of those simplifications should affect our conclusions.

First case:

The Earth and the Moon are stationary both w/r to each other and w/r to the Sun. The Moon casts a permanent shadow along the dashed line to the left. As the Earth rotates under it between initial time T0 and some later time T1, the shadow moves from East Coast (EC) towards the West Coast (WC).
(the magnitude of this effect is easy to estimate, as it's always 15 degrees longitude per hour, regardless of latitude)

Second case:

The Earth and Moon are not revolving around the Sun, nor is the Earth rotating. The Moon is revolving around Earth. As the Moon moves anticlockwise in its orbit, the shadow cast along the dashed line is sweeping eastwards across Earth's surface.

Third case:

The Moon does not orbit the Earth, and the Earth does not rotate. The Earth and Moon system moves as a whole in its orbit around the Sun. The shadow of the Moon sweeps westwards across the Earth's surface.

Calculating the magnitude of the latter two effects would require some trigonometry (be my guest).

But since only case 2 results in the shadow moving eastwards, we can say with certainty that it is that effect which is dominant. Furthermore, since the first effect (Earth's rotation) causes the shadow to move westwards at a rate of approx. 1 width of continental USA per ~3 hours (~45 degrees longitude difference between Oregon and South Carolina coasts at 15 degrees/hour), and the actual shadow moved in the opposite direction twice as fast, we can estimate that the second effect (Moon's revolution) must be at least 3 times larger in magnitude (the rotating surface is 'chasing' the moving shadow).

The last effect is likely small - while orbital velocity around the Sun is ~30 times higher than orbital velocity of Moon around Earth, the orbital radius is also 400 times larger in the former case, so the resultant angles should be very small.

 

[stefan r]

Calculating the magnitude of the latter two effects would require some trigonometry (be my guest).

You can skip the trig calculation and just use the synodic period. Wikipedia: 29.5 days or 708 hours. The sun/moon are about 1/2 degree or 30 minutes of arc. 360 degrees times two is comes to around 720. 708/720 is around one hour. It took 1.5 hours from start of eclipse to totality.