What would happen if the Moon blew up?

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I'm developing a plot in which the Moon gets blown up. But I am not sure about the possible results of such a cataclysmic event. I'm thinking about particles of the moon forming into a ring around the Earth, tidal waves stopping altogether and more asteroids entering the Earth's atmosphere. That's about it.

What would be the scientific implications of the Moon getting destroyed?

Thank you all in advance.
 
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Short answer: it would be very very bad.
You will want to get specific about what you mean by "blow up" though.

It's a topic that occupies some minds more than others:
http://www.spaceanswers.com/solar-system/what-would-happen-if-we-blew-up-the-moon/

If you just want to dismantle the Moon to make rings:
http://io9.com/5931098/using-the-roche-limit-to-put-a-ring-around-earth

To the specifics:
A dust ring may form from explosion bits that manage to find themselves in orbits within the Roche limit for the Earth. It may be pretty when it occludes stars or the Sun.

No tides - sure. Tidal waves, properly called Tsunami's, would still happen since they are not caused by tides.
The Moon only has a slight affect on the meteroid rate. You can work out the probability of the Moon intercepting some substantial lump of stuff heading our way by working out how much of the sky it blocks.
 
at least a fraction of (pi * r_e)^2 / 4 pi (d_m)^2 of the moon would be expected to crash on the Earth directly.
(r_e is radius of the earth, d_m distance of the moon).
this is 6.7*10^(-5) times the mass of the moon. About as massive as a 140 km diameter asteroid (with the density of the moon).
I don't think we can survive that.
 
Simon Bridge said:
No tides - sure. Tidal waves, properly called Tsunami's, would still happen since they are not caused by tides.
There wouldn't be lunar tides but there would still be tides caused by the sun.

The moon is a major influence on the Earth’s tides, but the sun also generates considerable tidal forces.

http://oceanservice.noaa.gov/education/kits/tides/tides06_variations.html
 
Over time the Earth's Rotation and Axis Tilt would also fluctuate as both are currently stabilized by the moon. Seasons would become unpredictable.