General Relativity
A discussion of General Relativity is not really necessary here, but basically it says that gravity is caused by the warping of spacetime due to the presence of mass. The moon orbits the earth because the earth bends spacetime around itself. As far as the moon is concerned, it is traveling in a straight line.
Whether a spaceship is orbiting a planet, in freefall toward the planet, or moving at a constant speed in open space, its occupants will feel weightlessness. Also, in the spaceship, moving at a constant speed is not distinguishable from not moving at all. Note that an object can only be thought of as moving relative to some other object – without that reference, the idea of motion is meaningless.
A change in motion, however, is another matter. If the spaceship accelerates, decelerates, or changes direction, its occupants would feel the inertial change. A change in direction is considered an acceleration, even if the object is still moving at the same speed. An acceleration is a change in the direction and/or magnitude of its momentum vector. The experience of gravity on a planet is considered to be equivalent to an accelerating reference frame. Experientially, with no visual external reference, there is no difference between being on the surface of a planet and being in spaceship undergoing constant acceleration.
Those points are probably intuitive enough, but here is where it gets less so. Relative to the planet, an object in freefall accelerates as it falls, and an object in orbit changes direction, yet as far as it is concerned, it is not accelerating – it is not feeling any inertial change. The apparent acceleration is due to the bending of spacetime around the planet, not to an external force acting on it. In this view, gravity is not actually a force as such – it is only an effect of warped spacetime.
Then there are the warped spacetime effects of space contraction and time dilation – something for further exploration for those interested.
