Because of conservation of angular momentum, the Earth (and everything else) will continue to travel in the direction it is rotating unless acting on by an outside force.
Think about a spinning ice-skater. She will keep spinning in one direction, and keep spinning in that direction, and keep spinning in that direction. The only things which will slow her down are friction with the ice against her skates or when she opens her arms out and redirects herself.
The same thing is happening with the Earth except there is no ice, and there are no arms. There are a few things which are slowing down the rotation of the Earth. Gravitational interactions with the Moon and the Sun are slowing it down ever so slightly. The Sun will die out long before we slow down enough that we're not rotating relative to it (like the Moon is to us). That means that the only thing which could cause us to go retrograde (as mathman said) would be a huge (and I mean huge... as big as Mars at least) asteroid impacting us in the correct position and direction to blow off our angular momentum.
To visualise this, think of the skater again. To slow her spin down (and hurt her, I'm sure) you put a big block off to the side. She spins into it, and it stops the spin (and she gets a huge bruise probably)
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The above was taken from a astronomy board.
And from my knowlege of physics and math, I concur with this. The only way the sun will rise from the west is if the Earth reverses its direction of rotation around its axis. This is not the same as revolution around the sun.
The issue of the sun rise on Mars is a little confused here. Retrograde motion is a "quirk" of the difference in orbits of mars and earth. The sun rise on mars did not, and will not change change its position, barring some catrostrophic metor impact. Retrograde motion is the percieved motion of mars as seen from earth.
Here is the
Nasa webstie explaining retrograde motion
So retrograde motion is what we percieve mars to be doing from our position on earth. so a planet cannot really undergo retrograde motion, it is better thought of as what we "see" mars doing. and this happens every 26 months to our pecieved view of mars from earth.
Hope this helps, so don't worry about the apoclypse anytime soon, at least from the sun rising in the west.
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