The Fixer said:
What size of astroid would it take to absolutely obliterate earth? What impact would it have on our solar system if us or any planet in solar system was fcuked off the map so to speak??
It absolutely depends.
Theoretically, one asteroid the size of a pea could destroy the Earth, and one bigger than the Moon wouldn't.
To destroy the Earth, the size isn't important, but the amount of energy released. For example, if somebody threw a ball bearing at you, it wouldn't particularly damage you, yet if the same ball bearing was shot out of a high speed gun, it would do some damage. Obviously, the gun is giving the ball bearing energy.
As far as absolutely obliterating the Earth, we would need to measure the sum total of the energy taken to gravitationally collapse the matter that makes up the Earth, compared with the energy released when the asteroid hits us.
To save you the physics/maths, we'd be talking about something bigger than Mars to do that, travelling at 1000 km per second (we need something about 60% the mass of the Earth). The fastest asteroid that we've found went on an orbital velocity of around 30km/s.
Interestingly, we've been hit by a planet before not far off of the size of Mars. We call it Theia, and it hit us before we cooled down about 4.5 billion years ago. There used to be an excellent video show casing this called the "Ultimate Rube Goldberg Machine" but Ch4 has blocked it on copyright grounds. This somewhat explains it:
The remains of the Theia then started orbiting around the Earth, pulling millions of rocks that had just been ejected into space right into it, like a vacuum cleaner sucking up dust. This is what the Moon is, and why there are so many impact craters on it. It's the remnant of a several billion year old collision of Theia with the Earth.
I find it quite cool to look at the Moon and realise that it's a rock floating 240,000 miles away that was formed 4,500,000,000 years ago.