Icarus, a few things for you to consider
"We just put Sir Isaac Newton in the driver's seat"-Astronaut Jim Lovell, Commander Apollo 13
Its all about gravity...
As I understand it we circled the earth gaining speed and used a figure 8 thru space to gravity shoot around the moon into a stable orbit.
A
"figure of 8" is a very simplistic way of looking at it., You see this often in diagrams of Apollo. Those diagrams assume the observer already takes into account the shifting frame of reference as the moon moves around in its orbit.
This is a more accurate representation...
...but even it has its limitations. The orbits were much, much closer to both the moon and the earth than this diagram indicates, and while the scale of the Earth/Moon sizes look about right, the moon is about 10 times further away (about 30 earth diameters instead of about 3 as shown here). This means the curved orbit is much more
"stretched" and much straighter. This is why the moon appears straight ahead even though it isn't precisely..
Also, The Apollo 11 mission lasted 8 days... that is more than a quarter of full revolution of the Moon in its orbit around the earth. The moon moved a lot further in its orbit than the diagram shows. Apollo 17 lasted 12 days; between 1/3 and 1/2 of a lunar revolution.
If you want a more accurate mental picture of what the orbits and the TL trajectory look like, try to imagine this
The Earth is a basketball.
The Moon is a tennis ball, placed 24 feet away
Wrap a piece of string a few times clockwise around the basketball, and then run it over to the tennis ball and wrap it counter-clockwise around that. The string represents the height of the orbits above the earth and the moon and the TL trajectory.
We leave Earth's orbit at what speed? Traveling directly toward the moon?
"No, not
directly. A spacecraft on any trajectory away from the earth after leaving orbit follows a path that is curved by the earth's gravity. As the spacecraft moves further away from the earth, the earth's gravitational influence lessens. If it is on a trans-lunar trajectory, as it approaches the moon, the influence of lunar gravity increases.
All the while, the Moon is moving so as it gets closer, the spacecraft is continuously being pulled in an ever-changing direction towards the moon