How does a spacecraft enter Earth's atmosphere? If Earth whirls around the center of our galaxy at some 220 kilometers per second, how can a spacecraft, which is much slower, enter Earth's atmosphere when returning from Mars for example?
 A: Because when you hear mission control mention a spacecraft's velocity, which may be well below the speed the Earth is actually moving at through the galaxy, the velocity in question is actually it's velocity relative to Earth, not it's actual velocity which will be much higher. i.e. all velocities are relative to the Earth's frame of reference.  
Although it would have been funny if the first object in space had, once it had left the Earth's atmosphere, suddenly appeared to zoom off at enormous speed having dropped to an actual velocity of only a few thousand miles per hour...  
A: It all comes down to the fact that we are moving too.

How can the bird drop down and catch the worm, if the earth and the worm are moving so quickly. It can because the tree, the bird, and the air are moving at the same speed, cancelling out.
If we launch a spacecraft from Mars to the earth, the spacecraft is zooming around the sun at the same speed Mars does. This is about the same speed that the earth zooms around the sun, so it almost completely cancels out.
