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The illusion that gravity is a force is created by the presence of mass. The presence of mass (lets say a planet in a vaccuum) , compresses the space-time around it giving the impression of force when the apparent geometric position of an object entering that field is relocated to the new location of that point in space.
If you had two non-moving objects in space (of course, very little truly doesn't move).But, you can have 2 objects relative to each other. For example I could hold a weight in the air.When I release the weight, it tends to fall towards Earth.Does your theory account for this tendency to for non-moving objects to start to move towards each other?However, in many senses, your theory is similar to the "rubber sheet" theory of gravity.