Suppose we get a rope that's about 40,000 kilometers long, and tie it snug around the Earth's equator (imagine a perfectly spherical and solid earth). Now let's add just 10 meters of slack to the rope and distribute it around the planet so that the rope is equidistant from the surface at all points (vertically).
How much space is between the rope and the Earth's surface? Before solving numerically, take a ballpark guess - can you fit a mountain under the rope? Walk underneath it? Can you even slide a sheet of paper between the rope and the Earth's surface?