Actually, gravitational force does not depend on an atmosphere at all. All things that have mass enact a gravitational force on all other things with mass around them. Perhaps you are imagining being out in open space and being able to float. The reason that you can float in open space is that you are sufficiently far away from big things like the sun and the earth that would otherwise pull you in. The gravitational force that is exerted by an object like the sun or a planet (or anything) decreases fast with distance. So as you move far away, you can't feel the gravity pulling you in anymore.

So in short, gravity exists by itself--even in a vacuum. But on an interesting side note, although gravity doesn't depend on the atmosphere, the atmosphere does depend on gravity. Gravity is actually the force that keeps gaseous molecules close to the surface of planets and that's why planets have atmospheres!

Not at all, the gravitational force between two objects depends on the amount of mass both objects have, and the distance between them. The larger the masses, the larger the force, and the larger the distance, the smaller the force. The Sun has a mass of about 333,000 times the mass of the Earth! So the Sun and the Earth both feel the same amount of gravitational force pushing them toward each other, but the Earth is affected way more by the force than the Sun is, because the Earth has much less mass. Atmosphere has nothing to do with it, although if you're in space outside the Earth's atmosphere, you're definitely farther from the Earth than if you were on the ground, so you would feel less gravitational force from the Earth.

No, gravity does not depend on an atmosphere. Gravity creates atmospheres, by holding gas close to the surface of planets (or stars), but atmospheres are not needed for gravity. The movies that you have seen that have things floating in space until atmosphere is added are wrong (yes, I have seen them).

Actually, gravity doesn't have anything to do with the atmosphere. Everything in the universe experiences a gravitational force from every other thing in the universe. The force gets weaker as you get farther away so we only usually feel the force from the earth. This was first theorized by Newton in the late 1600's and was proved by over a hundred years later by Henry Cavendish. Cavendish discovered that even two ordinary lumps of metal attract each other (but only very slightly). (Cavendish Experiment)