Modern Astronony works by making up a mechanism or interaction as the explanation and then considering it to be the true cause until it is shown to be impossible or unlikely. Hardly any of it is experimentally determined.
What experiments did Stephen Hawking conduct on the universe before coming up with his theory of the metric expansion of space?
No, it absolutely does not work like that. Science works now like it always has. Theories are formed which explain observations and generally have predictive powers. Future observations are checked against that theory, if observations don't match then the theory is amended or, if needed, discarded. Thousands of years ago we probably did think the world was flat because if you look out to sea you do just see a flat horizon. But that is not a sufficient observation to conclude definitively you live on a flat earth. Other shapes, like a sphere for example, can look flat locally if they are big enough. This is not your "eyes playing tricks on you" any more than merging perspective lines are your eyes playing tricks. Your visual acuity is only so good. A small enough curve and a straight line are not distinguishable.
The famous stick experiment can be explained in two ways, a close sun or a curved earth.
Your response is "the earth is flat, ergo the explanation must be a close sun". That is not a rational.
What experiments have you done to determine whether that is the correct explanation? If you haven't done any then it is you who have made up something (a close sun) because it reinforces your flat earth belief and are assuming it to be true without trying to verify it in any way.
A distant sun has been long established in different ways, I'll leave you to Google how.
I can't sensibly talk about metric expansion of space. I did Google it and the Wiki article doesn't mention Hawking. Some of modern physics is, admittedly, highly theoretical. But they aren't just making up stuff. Take the fact that stars are moving apart. Clearly one cannot directly measure this, but if you understand spectroscopy (elements have different and consistent "signitures") and the Doppler effect (the apparent frequency of waves is altered by velocity) then you can work out that stars are moving away from us. Both of these concepts can be tested by experiment. We can't go and measure the velocity of a star directly but you can calculate it. Just like if you know the resting pitch of a sound source and drove it away from (or towards) an observer at a certain speed then the observer could measure the change in pitch and calculate the speed without directly measuring it. Experiments like this can be done to build confidence in the science behind all this which gives confidence in the conclusion that the stars are moving away from us.
You call things like this "rationalisation" simply because they don't fit in with your world view.
But you apply different standards to things which do. You say you don't, but your "shadow object" is made up. What experiments have you done to determine whether it even exists? You say "there's a shadow on the moon so there must be something which casts it". Fairly sound logic, but no less sound than "Doppler shift is observed in starlight so the stars must be moving away from us". Both start with an observation and result in a conclusion without direct observation of the explanation.
I will have a look at that Rowbotham chapter and I'll look at starting a thread about those experiments I mentioned, but if you claim you are an empiricist it seems strange that you have concluded the sun's distance or what the horizon is when these things can be so easily verified by experiment and I see no evidence that any experimentation has been done.