Gravity in space exists, but is very weak.
Sure! Gravity is everywhere. The effect diminishes with distance, but it never goes away.
So the term "zero-g" is a misnomer. What really happens to astronauts (or satellites) is they fall sideways as they're falling toward the planet, a setup that keeps them in orbit and feeling weightless.
Where the space station roams, some 250 miles (400 kilometers) up, the force of gravity is about 90 percent what it is here on the surface.