In one of my physics classes, the term escape velocity was used. As you know, it refers to the speed needed to break free from a massive body's gravity. I was wondering why such a velocity needs to be attained. Since the greater the distance from the object, the less the gravity, less force would be needed at larger distances to cancel gravity. So why wouldn't the force (e.g. thrust) need to only cancel out gravity's force? For example, why can't a person escape Earth's gravity at 1 m/s with an acceleration of 0 m/s^2 (thrust canceling gravity)?
If you shoot a gun into the air, the bullet will eventually fall back to Earth. That's because gravity acts on the bullet the whole time it's in the air. However, if you can increase the velocity, eventually the bullet can escape the pull of Earth's gravity and that's about 25000 mph. Satellites and the space station are only going about 17000mph and so they stay in orbit. You can calculate the escape velocity for any body by calculating the velocity that would be reached if an object dropped in from infinity.