Gravity is ever-present in space, pulling objects into orbits around planets and the sun. It may be weaker at certain points of space, such as those that are far away from the sun, but it doesn't ever disappear entirely. The phenomenon of "weightlessness" experienced by astronauts is actually just a constant state of free fall. The astronauts are indeed being pulled towards Earth, but the high speed of the their spacecraft, which is moving sideways relative to Earth, opposes the gravitational force.
Why Are Astronauts Weightless?
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Key Facts In This Video
The moon orbits the Earth due to gravitational attractions. 00:37
The ISS orbits about 400 kilometers above Earth. 01:43
The high sideways velocity of astronauts orbiting the Earth causes them to "float" in a constant state of free fall. 02:38