When I was in school, I saw the solar system in a 2-dimensional plane like this:
When we look at the solar system in static 3D, we will definitely think about the existence of a hypothetical invisible field that holds the planets and the sun from falling, called ether, like the animation below:
The view of the existence of ether is actually just an illusion and will change when we include the fourth dimension, namely motion, in the solar system simulation, so it will look like this.
Of course, the solar system's helical motion isn't entirely accurate, as the planets' actual tilt around the sun is 60 degrees. So, the most realistic depiction of the solar system's motion is something like this.
It's very complicated, isn't it?
So, is the Earth floating, flying, or falling? I prefer to use the words "thrown" and "bound" by the sun's gravity, which also moves with the galaxies thrown around in this vast universe.
Perhaps someday this explosion will turn into a Big Crunch, and everything will return to its original state, only to explode again, forming a new universe. And so on, endlessly.