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.

The sun's parallax would be 180 degrees, greater than which you can't get.  so a. would be your anwser