"Alternatively (and more likely) we would have decided the idea simply doesn't work."

No, we would just keep beating on it until it works. It's a myth that science always precedes engineering. It's a very regular drift, and worst case scenario, if they just couldn't work it out, they'd build several ground stations in known locations, derive corrections as those drift, and upload corrections into the system periodically. (Similar things are done today: https://en.wikipedia.org/wiki/Differential_GPS )

Even with the science that we have, there's still fudge factors and empirically-determined values we have to use anyhow, because the Earth is not homogeneous and we have to take its slightly-lumpy gravity field as a given, not something we can "scientifically" determine. (Of course we "use science" to determine the lumps, but the lumps themselves are simply a given.)

Given the choice between trial and error engineering and science backed engineering I much prefer the latter. That does not mean doing engineering without the science is impossible just so much harder. They both go hand in hand, nothing mythological here. Advancements in one leads to ideas in the other and vice-versa.

"Given the choice between trial and error engineering and science backed engineering I much prefer the latter."

That's not the question; the question is, are we forced to give up engineering if we don't have "the science" yet?

And the answer is an objective "no", from abundant past human history. There's this myth sold that science always precedes engineering that is very, very popular. I'm not even sure where it's coming from. Oral history in primary education, maybe. But it's a myth that engineers themselves can ill afford.

The vast majority of practical programming is programming running way, way ahead of the "science", which occasionally takes point samples of how 10 college sophomores behave under a certain limited experiment.

We just overbuild until we have the science and the manufacturing capacity to back it up. Every once in a while I hear some civil engineering fan comment about how the roman aqueducts are still standing because they built a huge margin of safety into them (because they couldn't do the calculations, not because they wanted them to last a thousand years)

Maybe it's because for instance there were exactly zero engineers working with radio waves before Maxwell and Hertz, or zero engineers working with semiconductor transistors before, basically, Brattain, Bardeen and Shockley. Electromagnetism and electronics happen to come straight from science labs. You could check also Idk... chemical synthesis, polymer science... nuclear physics?

I don't understand why would you come up with such "objective" statements unless you really think it's not necessary to know anything about the history of science and engineering to have a strong opinion about them.

> Maybe it's because for instance there were exactly zero engineers working with radio waves before Maxwell and Hertz

Well, humans have been crafting optical lens way before Maxwell ;). And even way before [1] Descartes and Newton decided to study light.

For everything out of reach of our senses, like the examples you gave, we need formal science. But for everything humans can see, smell or touch, we're pretty good with empirical observations : chemistry, fluide dynamics, genetics and mechanics where comonly used way before formal science was even a thing.

[1]: https://en.m.wikipedia.org/wiki/Nimrud_lens

Isnt the more relevant question "does engineering benefit from (basic) science?"

Possibly amended to include "to a degree that justifies the spending"

> And hence have discovered GR in the process.

Fascinating to wonder how modern physics community worldview would be different, if GR had gone [empirical anomaly -> new theory], and ended up in the same place rather than [thought experiment -> empirical proof]. (IAN a historian of physics - forgive me if I have that wrong.)

> Alternatively (and more likely) we would have decided the idea simply doesn't work.

I don't think that's true. Consider the Bell Labs guys who won the Nobel Price for Microwave Background Radiation, who were just trying to remove the noise their antenna was receiving.

Bell Labs and the CMB is nice example! At the same time, it unfortunately doesn't give us any intuition about how many times somebody doing engineering had less tenacity or experience and gave up instead of ending up with a Nobel Prize. :)