Gravity has no range, so it will affect you. No matter how far you are from an object with mass. However, its effect does drop off quickly with distance. If you imagine that you were very very far from the Earth, and that the Earth was the only object with mass then while you would fall towards it the rate would be so slow you would probably not notice it.
Astronauts are in orbit around the Earth, same as the Moon. The Earth is in orbit around the Sun. The Sun is in orbit around the core of our galaxy. The reason they don’t hit whatever they are in orbit around is because they are moving so fast to the side that the curved surface moves downward as fast as they move downward.
