Also: Apophis will be moving immense distances along an elliptical orbit before it gets close to Earth again. A one mm difference in its trajectory now might well make a significant difference in 20 years - significant enough to miss us. Or steer the rock into us.
“Or steer the rock into us.”
That’s my issue.
I don’t have the math on me right now, but the kinetic energy of a satellite going 6 miles per second is enormous. It would be like using a nuclear weapon.