YA USA hardback library book. 1960s or before. Very Heinlein YA type story, but not one of his books.
I distinctly remember the opening chapter. A young man is playing baseball. Maybe a college or minor leagues. He is in the field (baseman or outfielder.) A high popup is hit. He takes one look at it, then looks down to the spot where his is going to run to catch it. One of the coaches yells at him (like all coaches do to all players trying to catch a popup.) "Keep your eyes on the ball!!") He never looks up. He reaches the spot he had picked out, raises his mitt and catches the ball. The coach then says something like "Sorry I forgot you don't need to keep your eyes on the ball."
- He can instantly plot trajectories in his head once he sees an object in flight. This is the gimmick of the story.
Later he goes to space/rocket ship pilot training school. He does very well. Nearing graduation, he is doing his final "solo" flight on the moon. He is flying with an antagonistic instructor in the unpowered co-pilot station, but the instructor is only an observer/hands off unless there is an emergency or safety issue.
The school administration is concerned because he does not follow piloting instructions/orders if he knows they are wrong, so they have rigged the test. While he is coming in for the final landing of his test, he notices the instructor is focusing on the viewport/window watching the landing base, so he starts paying a little more attention to the ships on the landing field.
He notices a rocket ship take off (this should not be happening, while someone is landing) and starts slowing his rocket ship to "land under" the other ship. More or less giving the other ship the right of way and clear the airspace above it, to let it finish taking off.
The instructor tells him to fly over the other ship, to the other side of the field and land there. He refuses, saying something like, "when the other ship sees us, in nearly all instances, the launching ship will maneuver away from us, so if I fly over we will be on a collision course."
The instructor tells him again to follow orders, but he refuses. The instructor declares an emergency, and says "My ship" while flipping a toggle to put his station in control. The young man immediately slams his hand on the toggle to switch it back to his station, hitting it so hard the toggle breaks and cannot be switched back.
He brings the ship down under the other ship and lands it safely. Later, one of the admins reviewing the incident comments that the fuel expended matched what it would have been if the launching ship had not interfered with his landing.
It turns out that the launch was rigged. The ship was not going to maneuver, so the instructors orders would have worked, but would have cost much more fuel. I'm pretty sure fuel usage counted in your final grade for the flight.
I believe he was thus expelled or flunked from the school for failing to follow orders.
Sometime later (couple years) he is still living and working on the moon (not sure what capacity.) A rocket ship flying in space above him has a rocket engine failure. One of the four main engines quits firing thus the ship will have uneven thrust causing it to drift toward the failed engine. The ship could not just shut the opposite engine down for balanced thrust, because two engines would not slow it down enough for a survivable crash. Three engines would be enough for a survivable crash.
The ship had already reported the failure, so everyone knew it was going down on three engines, but lost communications once it when it went below the horizon.
Due to his ability to plot trajectories once he has seen something, he knows that everyone else's plot of the crash location will be wrong. IIRC, he sees that the ship is rapidly spinning to equalize/balance the thrust, and reduce the drift, and will closely maintain it original heading. No one will listen to him (a flight school wash out) and are heading to the wrong location.
He heads to the location he had calculated, and gets there just in time to bring oxygen to the occupants before theirs runs out.
