Cool question! Forgive my lazy approaches to citation and linking below. I didn't have much time, and ran into the realization that you and I are probably the

Cool question! Forgive my lazy approaches to citation and linking below. I didn't have much time, and ran into the realization that you and I are probably the only HN users who will ever read this. > concrete observations No, certianly not. As far as I remember all of the early tests of post-Newton/pre-GR but "relativity compatible" gravitation were motived by sketched-out systems in Einstein's 1907ish-1912ish writings, with the observations and experiments taking place years later. > base his theory of GR on The entire programme of Einstein gravitation started from purely theoretical considerations, starting with thoughts about accelerated bodies in special relativity and relativistic ballistic bodies (which aren't accelerated beyond the initial impulse: c.f. Newton's cannonball (1728) -- ignoring friction a cannon ball's descent back to the ground is free-fall so the motion in free-fall must therefore be inertial, and in fact the whole trajectory up and down, or into orbit, or out to infinity after it is shot out of the cannon must be inertial <https://physics.weber.edu/schroeder/software/NewtonsCannon.html https://physics.weber.edu/schroeder/software/NewtonsCannon.h...>). General Relativity certainly didn't spring fully formed from Einstein's mind -- it took about eight years for him to develop the ideas and mathematics along the way. "Doc" references below are to translations of his early papers at https://einsteinpapers.press.princeton.edu/vol2-trans https://einsteinpapers.press.princeton.edu/vol2-trans (It's also handy to see how interested in diffusion and dissipation -- and thermodynamics more generally -- he was before his famous Brownian motion paper, 1905, Doc 16.) Relativity, 1905 (Doc 24 ("Does the inertia of a body depend on its energy content?")) First articulation of equivalence principle (observers in free-fall are in inertial motion), 1907 (Doc 47, "On the relativity principle and the conclusions drawn from it"; this is practically a short textbook and is awesome in total, but for your question the relevant bit is in part V, starting at the bottom of p. 301 (direct link because pagination is often weird on the site) <https://einsteinpapers.press.princeton.edu/vol2-trans/315 https://einsteinpapers.press.princeton.edu/vol2-trans/315>). A choice quote: from the end of part V §19: 'There exist "clocks" that are present at locations of different gravitational potentials and whose rates can be controlled with great precision: these are the producers of spectral lines. it can be concluded from the aforesaid that the wave length of light coming from the sun's surface, which originates from such a producer, is larger by about one part in two million than that of light produced by the same substance on earth.' (Footnote 1 is also interesting for noting that his initial thinking was about a uniform gravitational field, which does not exist in nature, and thus he was forced into assuming that his thinking also applied in a more realistic gravitational field; this was well before he started developing the mathematics of General Relativity in 1911-1915 and of course also before Schwarzschild 1915). Such a small spectral shift was untestable in 1907; it took until 1959-1960 (Pound-Rebka experiment, "Apparent Weight of Photons") and the 1970s (Harfle-Keatin and Gravity Probe A) to demonstrate and measure the effects of Earth's gravitational time dilation. Now we advance a few years to 1911: https://einsteinpapers.press.princeton.edu/vol3-trans https://einsteinpapers.press.princeton.edu/vol3-trans and in particular Doc 23, "On the influence of gravitation on the propagation of light" There is a lot of interesting stuff in that paper, including an early rough estimate of the deflection of light around the sun and Jupiter. However it's important to note that there are no tensors and no (pseudo-)Riemannian geometry in the 1911 paper: the theory with those (and the general covariance and curved spacetime they encode) was still about four years away. His light deflection estimates were illustrative of generic effects in any sort of principle-of-relativity-compatible gravitation (again, he was personally in no position to be thinking about a geometric theory, not yet having started learning differential geometry) rather than serious predictions, let alone existing observations that he needed to capture. It is really only after 1912 that Einstein begins developing a description of gravitation in terms of curved spacetime. By then there were several observations (motivated by Einstein's pre-GR work!) showing that Newtonian gravitation becomes inaccurate near the sun, with Newton's formulation (and also Poisson's and Gauss's and other equivalents) proving difficult to adapt via correcting terms. So: SR first; then thoughts about accelerated v freely-falling observers where relativistic effects are expected, including some thought experiments and some sketches that could be weakly checked by astronomy; becoming convinced that non-Euclidean geometry could represent some of these effects; then learning (and developing) relevant mathematics; then GR; then modelling systems and predicting behaviours using GR; then early precision astronomical and eventually (and sadly, posthumously) laboratory tests of those. It's possible to imagine that astronomical discoveries could come before a fully non-Newtonian theory of gravitation. Let's omit General Relativity and the early work in the 1920s-1930s, the theoretical developments of General Relativity from the 1950s&1960s, and more (thanks to computers) in the 1980s, but keep the dates of astronomical discoveries. We then wonder how what we realized were "manifestly relativistic" astrophysical systems would have been dealt with by theoreticians. The "Newtonian gravitation needs to go" trigger would probably have been clearly non-Keplerian orbits like pulsar+other binaries (Hulse-Taylor, 1970s; the orbit is contracting/speeding up) precision studies of stellar orbits in the Milky Way's central parsec (1990s; there is an unseen compact mass distorting the innermost stars' orbits), or could have come as late as the discovery of PSR J037-3039 (a two-pulsar binary, 2003) or PSR J30337+1715 (a pulsar a close binary with a white dwarf and with another white dwarf orbiting the central pair, 2007, which has been used to test the strong equivalence principle). However, in our history, predictions of "highlight" aspects of these astronomical oddities date from early work with GR in the 1920s and 1930s. Another trigger could be compelling evidence for the non-ballistic trajectories of distant galaxies, which started racking up in the 1990s. Einstein and others toyed with an accelerated expansion in the late 1920s-1930s (that other galaxies were distant was freshly discovered then), and rejected the idea for want of astronomical evidence. In all of these, with some thought, a pattern would emerge: in all these systems there are orbits or trajectories which appear to reach velocities comparable to the speed of light. Corrections in powers of v/c might seem obvious. However, with our real history, Einstein was doing this in about 1916 or so, because it was easier to calculate orbital evolutions that way, and the approach was (allegedly) easy to extract from (or trace back to) GR. I wish I had a handy reference for that. Perhaps some proper historian of relativity will update <https://en.wikipedia.org/wiki/Post-Newtonian_expansion#Uses https://en.wikipedia.org/wiki/Post-Newtonian_expansion#Uses>. Likewise linearized gravity captures the speeding-up of orbits implying the loss of non-electromagnetic energy radiated out of the binaries/triples/central parsec as gravitational waves. It is somewhat easier to relate to GR than expansions in v/c. But what form would early theories take when thinking about the decay of the Hulse-Taylor orbit?