If the Space Shuttle is always falls toward the center of the earth, how does it get to outer space? If something accelerates, doesn’t it go faster and thus have its speed increase?
The second question first: no, an object can accelerate without going faster. In fact, a stopping object is accelerating! If an accelerating object can speed up or slow down, it can certainly maintain a constant speed. If you swing a ball around in a circle on a string, that ball is accelerating all the time but its speed isn’t changing.
Now the first question: for the space shuttle to reach orbit, it needs an additional force in the upward direction. It obtains that force by pushing exhaust gas downward so that the exhaust gas pushes it upward. During the time when it’s heading toward orbit, it’s not falling because it has an extra upward force on it. However, the Space Shuttle can leave its orbit and head off into outer space by traveling faster than it normally does. It acquires this increased speed by firing its rocket engines again. Its usual speed keeps it traveling in a circle near the earth’s surface. If it went a bit faster, its path wouldn’t be bent downward as much and it would travel more in a straight line and away from the earth. It would still be falling toward the earth (meaning that it would still be accelerating toward the earth), but its inertia would carry it farther away from the earth. If the Shuttle had enough speed, it would travel to the depths of space before the earth had time to slow its escape and bring it back.