Diagrams are not the only way of seeing the route to the moon.
One of the interesting things that came up when I was looking at my satellite image comparisons was in using Stellarium to look at where the terminator line should be at the time an Apollo photograph was taken, or to use that Stellarium view of Earth from the moon to work out a time for a photograph.
The further away the Apollo missions were from the moon, the least like the Stellarium view of Earth the photographs are in terms of the shape of the lit portion of the surface, and this gradually changes over translunar coast until there is an exact match.
The explanation is, of course, simple. In the early part of the mission, they are not on the moon, they are pointing towards where the moon will eventually be when they get there, and quite obviously this gives a different view of the Earth in space. The fact that this view of Earth changes gradually to become the same as the Stellarium depiction is yet another clue to the fact that are in space following a trajectory that will put them on a lunar intercept.
You can see the same effect in reverse with pictures of Earth on the way home, and also by comparing the view of the moon from Earth with photographs of the receding moon taken during trans-earth coast. These views start by showing areas not visible from Earth (after the far side TEI burn) and with a lunar phase obviously different to the terrestrial view. The closer they get to Earth, the more like the view from Earth the lunar photographs are.
The evidence Heiwa needs to see how the Apollo trajectories work are all in those photographs. No equations necessary, just joined up thinking.
