Is There Gravity In Space?

If you've seen footage from the International Space Station or any of the space shuttle missions, you know that astronauts float around as they orbit the Earth. Why is that? Is it because the gravitational force on them is zero in space? (Or nearly zero?) The truth is that the strength of the gravitational attraction is only slightly less than it is on Earth's surface. So how are they able to float? Well, they aren't floating - they're falling, along with the space station. They don't crash into the Earth because they have a huge orbital velocity. So as they accelerate towards the Earth, the Earth curves away beneath them and they never get any closer. Since the astronauts have the same acceleration as the space station, they feel weightless. It's like being in a free-falling elevator (without the disastrous landing).