The earth is moving dropkick it has massive inertia ... try calculating it.
If you fire stuff in space the earth does move fractionally but good luck measuring it you can only really calculate it because it's so small.
It's a standard calculation here:
http://en.wikipedia.org/wiki/Escape_velocityYou will note that is why launch sites are as close to the equator as possible and you will note for something as heavy as the Saturn V rocket you can calculate the recoil on earth
When the mass reaches the Andromeda galaxy the earth will have recoiled 500 m.
Lets take your stupidity down to a really kid stupid level you are on a car does throwing a ball from the car change it's speed?
Lets see if you can work that out or are you a little kiddy because it is the same situation.
To help here is an answer for the little kiddies of an iceskater throwing a ball
https://www.khanacademy.org/science/phys...r-throws-a-ballSo does the car speed change Marosz?
There is also a structural error in your drawing if that long pipe is also spinning with with the earth. If the right hand mass is going up the left one should be going down. If you doubt it draw the pipe and masses a bit earlier and then draw it a bit later if the explosion didn't happen. Notice the movements that would be preserved.
You show the left mass m going up it won't it will go down as the masses have spin inertia, basic physics. The right one probably won't go up like you have shown either but you would need numbers and sizes of pipe, m and explosion because technically it could go up, down or fly flat
