What holds earth steady as it rotates on its axis

I think it's the gravity net around the earth. 

Hope this helped! 

Kepler's law and Newtons laws explains this very well. If we could just stop the Earth for a moment relative to the sun and then allow it to freely move it would fall into the sun. But the earth was born from a ring of material that was moving around the sun on a stable orbit. So after the debris coagulated to form the earth, this initial orbital energy was retained. Hence the earth is moving on a stable orbit of fixed radius. Look up Kepler laws the period of revolution of a body squared is proportional to the distance between the sun and the body cubed.