Why does a Solar Eclipse move from West to East, whereas the sun moves from East to West??

On 22nd July, 2009 we witnessed the longest Solar Eclipse in the 21st century, which will stay unchallenged till June, 2114. Early yesterday morning when i was glancing through the paper I noticed the path of the Solar Eclipse through various parts of India.

The Eclipse first became visible at 5:28 am at the eastern coast near Gujrat, and then left India at 10:42 am from over the North-Eastern part of India. Nothing seemed fishy to me at first, but then my dad posed me a question.. That the sun moves from east to west, then why so does the solar eclipse move the other way round..??
Hmmm..Intersting!! So I decided to look it up.. (Given that I had nothing else better to do. )

Now, first how does the Solar Eclipse take place. In the lamest terms, amongst all the randomness of the celestial motion of the earth, moon and sun; now and then, the three bodies line up together in a straight line. When the moon comes in between the earth and the sun and hides our good ‘ole sun…Walla..we have a Solar Eclipse!!!
When the moon blocks the sun partially, its a partial solar eclipse. Instances when it shadows it completely (like in our case on 22nd July), its called a Total solar eclipse.

Now the question at hand…
The Earth revolves around the Sun from West to East. (surely, because this motion gives us the apparent sensation the the sun is moving the other way round. i.e., East to West.)
The moon revolves round the Earth from West to East as well. (Watch Moonrise on successive nights and you’ll see that it rises later each day as the Earth’s rotation needs more time to ‘catch up’ with the Moon in its orbit. )
The Moon orbits at a velocity of 1 km/sec, thus its shadow also moves at the same velocity. However the Earth is also rotating around its axis in the same direction with almost 0.5 km/s at the equator, slower with approaching poles. As a results near the equator Moon’s shadow advances about 500 meters per second.
The easiest example to understand this is, assume to cars are moving in the same direction, at the same speed. They appear stationary to each other.
Now a case when one is at 20 km/hr and the other at 40 km/hr. Now from the perspective of the faster car, the other car is moving backwards.

Similarly, even though Earth and the Moon are moving in the same direction (West to East), the relative velocity of the Moon is higher, it advances with respect to Earth.

Now there are various exceptions to this case, but this much is enough for my curiosity. If you are interested more, have a look at this link.. Mechanics of Solar Eclipses.

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