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From my bookish knowledge all planet revolve around the sun in anticlockwise direction and electron also moves in the anti clock around the nucleus. Is there any specific reason behind the stability of anticlock wise direction?

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Clockwise and counterclockwise depend on which direction you're looking from. – Alan Rominger Jan 25 '14 at 21:17
    
Related: physics.stackexchange.com/q/72656/2451 , physics.stackexchange.com/q/7819/2451 and links therein. – Qmechanic Jan 25 '14 at 21:24
    
It should be noted that, with respect to Earth Neptune and Venus revolve in clockwise direction. – Vinaykumar Jan 25 '14 at 21:27
    
@VINAY they rotate, not revolve, in the opposite direction. – David Z Jan 25 '14 at 22:18
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Electrons don't revolve anticlockwise around nuclei. – DumpsterDoofus Jan 25 '14 at 23:22

all planet revolve around the sun in anticlockwise direction

Says who? People in the northern hemisphere, if we lived in the southern hemisphere and looked at the solar system from beneath then we would find that all of the plannets would revolve in the same direction but it would be the clockwise direction.

electron also moves in the anti clock around the nucleus.

Electrons can move in clockwise and anti-clockwise directions. And barring the outer shell will move equally in both directions.

Chirality does play an important role in chemistry. Drugs may behave drastically differently than its enantiomer (mirror image molecule).

In physics most things would be unchanged if it were a mirror image of itself, the weak force being an exception. Where a left spin electron behaves differently than its right spin counterpart.

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What does it mean to say electrons move in some direction around a nucleus? – Richardbernstein Mar 8 at 3:30

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