It may not entirely have been gravity we were breaking with our expensive rockets or even our stepping feet. Theory suggests everything moves in a linear motion along a trajectory through space that is bent by mass. Though, physics' calculations requires a reconciliation of the two.
The simplest way to explain bended space is to imagine a large mattress covered in a thick quilt. It can be black if it helps. The surface represents the plane on which our planets revolve around the sun. Let some massive objects, like bowling balls, represent the planets and sun. The dip in the mattress caused by their sheer mass is bended space. The planets move linearly (straight) through space. It's just that the space is now bent, giving the "sense" of elliptical motion.
To prove this, we assume light, with linear motion, can be bent by mass. We know it is subject to some force because of black holes, which are said to be so massive, that not even light can escape it. Anyway, either light has mass (which actually may be the case) or it follows the curve in space, so says Einstein's warped space corollary in his General Theory of Relativity.
Now we can't really observe this in a laboratory test. Nothing we have has enough mass to produce any measurable influence on the path of light. Light may bend slightly around me, but it's nothing any of our instruments can detect.
So to test this theory, astronomer Arthur Eddington used the sun as his massive object and set to observe the stars around its edge. Of course, the sun's own brightness mutes the light from other stars, so Eddington waited for a solar eclipse to run his experiment.
The results showed that the stars appeared out of their usual position, as the light which allows them to be seen was distorted by the sun and made them appear elsewhere.
Gravity, or the attraction of bodies to each other, still can exist, though. Warped space simple is a way to explain gravitation. Well, it's either that or gravitons.
