newtonian mechanics - How come the Sun's gravity can hold distant planets in orbit, but cannot rip humans off Earth?

The sun is strong enough to keep gas giants close, but why not people?

Answer

The Sun is keeping you close. After all, you are orbiting it just like the Earth. You don't fly off into space because the Earth and you experience the same acceleration due to the Sun's gravitational force, so you orbit together; this is sometimes called the equivalence principle.

If, however, you were floating near Earth but closer to the Sun, you would experience stronger gravity. You would be in a smaller orbit which would make you drift away from the Earth. You wouldn't fall into the Sun, though.

Edit: I forgot to say something about the outer planets, something which the other answers touch on but I think get wrong. First, we should speak of acceleration rather than force, because like I said earlier all objects at a given distance from the Sun experience different forces but the same acceleration.

You ask "how come the Sun is strong enough to keep the distant planets in orbit but I don't fall into it?". The important point is that you don't need such a huge acceleration to keep the planets in orbit, because they are far away and move very slowly.

But, the smallness of the acceleration isn't the reason you don't feel it. The reason is that you're in free fall around the Sun; even if you were zipping around kilometers from the Sun's surface, you would not feel the huge gravitational force, because it affects everything around you in exactly the same way (disregarding tidal effects).