I dont know that book, but it should not be all that complicated, as long as you have two observers on different parts of the earth.
Lets say, an astronomer in London watches the night sky and writes in his notebook “On April 17th, the moon passed just 0.1 degrees over the start Alpha Centauri”.
On the same day, an astronomer in Cape Town notes the same thing, only he sees the moon and the star 0.8 degrees apart.
Sometime later those two men meet and compare notes.
They now draw a small circle representing earth, and mark London and Cape Town at their appropiate places on that circle. They also draw a straight line from the earth to Alpha Centauri.
Now, all they have to figure out is where exactly on (or near) this line they have to place the moon so that there is a 0.7 degree angle between the lines moon-London and moon-Cape Town. Once they got that, they have a true-to-scale map of the earth-moon system in front of them.
Imagine you’re standing in a room with an overhead light on a ceiling painted with stars. You want to know the distance to from the centre of the room. You could walk to opposite corners and look the light. It looks different with respect to the background stars, because you’re at a different angle. From both the corners of the room you take a picture and compare them. From the way the stars look, you can find the angle between the lines from the light to the corners. Then measure the distance between the corners. you can now draw a line from the light straight down to get a right-angle triangle. using some simple geometry to calculate the hight of the light. It works basically exactly the same with the moon instead of a light, just with bigger distances and smaller angles.
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