This is the simple physics problem where human intuition generally fails. If you thought out of the solar system, then congratulations! It is easy (provided that you do have enough strength, and apply the best methods) to throw the ball out of this solar system. If you wonder how, then following discussion clariﬁes it.
Throwing to the Sun
The speed of the earth around the sun is around 30 km/s. The ball being on the earth is also moving around the sun with the speed 30 km/s. So, if we throw the ball at 30km/s in the direction opposite to the earth’s motion, then the speed of the ball relative to the sun will become zero. This means that the ball will fall straight to the sun because of sun’s gravitational force.
So, we need to throw the ball at 30 km/s to hit the sun !
Throwing out of Solar System
Now, to throw the ball out of the solar system, we need to throw the ball with the velocity equal to the escape velocity of the sun, since the entire solar system is under the sun’s gravitational field.
The escape velocity is the function of distance distance from the sun.
Since the earth is at a distance of 149.6 million kilometers from the sun, the escape velocity for the solar system initiated from Earth’s orbit can be obtained as 42.13 km/s. We need to give this speed to the ball if the earth was at rest. But earth’s speed is itself 30 km/s.
Thus, we need to throw the ball with the speed 12.13 (i.e. 42.13 – 30) km/s in the direction of earth’s motion to escape from the solar system.
So, we need to throw the ball at 12.13km/s to escape from the solar system!
This is signiﬁcantly lower than 30 km/s required to hit the sun. Therefore, it is easy to throw the ball out of the solar system.
But remember, throwing at random directions won’t work. The best way to hit the sun is to throw in the direction opposite to earth’s motion, and the best way to escape the solar system is to throw in the direction of earth’s motion.