They appear very solid. The truth is, if you took all the matter within our bodies, the actual stuff, neutrons, protons and electrons, and compressed them into one place so that all the space between molecules and atoms is removed, the speck of actual matter you would have would be so tiny you would need magnification to see it. The distances between electrons and the nucleus of an atom is very relative to the vast distances between the heavenly bodies in our solar system. The thing that gives a sense of solidity to physical objects is the fact that on an atomic level they are moving at tremendous rates of speed. Like the blades of a fan, the movement gives the look of a much larger object than the fan blades themselves.
Television is a even better analogy.
The cathode ray at the back of the picture tube runs through the cycle lighting up the screen with such rapidity that the illusion of movement is given. In actuality, the thing that gives the sense of solidity to the physical world is our senses. Yoga philosophy perceives reality differently than science and our modern conception of reality. Here in the west, we start out there in the world of matter and perhaps try and work inward to learn about consciousness and existence. In yoga philosophy they begin with consciousness and the mind and go out through the senses to the world of manifestation.