So you are not going to explain when a orbit becomes a trajectory?
How about point when it happens in this image:

It really is a funny picture. Earth is assumed fixed in space and a spacecraft leaves it one way or other - a force is applied, fuel is consumed and the spacecraft heads for the Moon at some speed/direction/time.
During the trip speed is slowed down most of the tiime due to Earth gravity and direction changes all the time. It seems correct. After a while speed increases due to Moon gravity and ... a gravity assisted kick or slingshot suddenly occurs, i.e. the direction is changed >360° while the speed increases and slows down and increases again - really magic. I explain at http://heiwaco.com/moontravel.htm why such a >360° turn cannot take place in space. It is my A, B, C, D why human space travel is not possible and my Challenge is so difficult to win.
According my calculations the spacecraft should either (a) crash on the Moon or miss the Moon and continue out in space, where Earth gravity would stop it and pull it back to Earth again where it would (b) crash on the Earth.
Thus the picture shows something that cannot happen in reality. Why do you refer to such nonsense? The picture is a fake!
Lets see your calculations. Then you can explain why Newton, Kepler and Einstein were wrong.
You failed to answer the other part of the scenario. What happens putting the spacecraft in the same orbit but avoiding encountering the moon? I am not talking about a flyby, but lets assume the moon and spacecraft will be on opposite sides of the Earth when apoapsis is reached.
Will it still crash on Earth?
Are you going to explain when an orbit becomes a trajectory?
My calculations you find at my popular website about space travel. It has >300 visitors/day!
Newton, Kepler and Einstein never investigated the problems of
human space travel and, if alive today, would probably fail the Heiwa
Challenge. Newton and Einstein had some ideas about gravity and Kepler and Einstein about orbits but none ever considered
human space travel.
What happens if you send a spacecraft straight up forgetting the Moon? Take a US InterContinental Ballistic Missile! It is sent up in space to say 1 600 km altitude, where it stops to drop down again by gravity on Moscow to explode and wipe out Putin & Co. Very naughty.
To send up something like an ICBM to 1 600 km altitude requires a certain amount of energy/fuel/force/speed applied and it takes a certain time say 10 minutes. Say that the max speed going up is 9 000 m/s, it is then 0 at 1 600 km altitude and then it becomes 9 000 m/s again, when dropping down into the atmosphere again where ... it is vaporized after about 10 minutes. Any student of the Heiwa
Challenge can do the calculations. They are basic
US Department of Nuclear War and Destruction says it is not true! A heat shield is fitted on the ICBM and the ICBM is not vaporized at re-entry. No, the atmosphere brakes the ICBM, when it drops almost vertically on Moscow and then BOOM - Moscow is vaporized.
Apollo re-entered almost horizontally, while ICBMs re-enter almost vertically but heat shields work anywhere ... in the sick minds of space re-entry experts. It is hilarious. Imagine all these US nuclear war generals doing ... nothing.
An orbit is the path of an object around another object in space. No fuel is required. If you apply a force to one object in orbit, it will leave the orbit and enter a trajectory going somewhere else.