As a physics undergrad, I was taught about how empirical evidence eventually backed up Einstein’s theory of general relativity, and how it’s held up strongly over the last 100 years. From wikipedia’s article on “tests of general relativity” (link):
Henry Cavendish in 1784 (in an unpublished manuscript) and Johann Georg von Soldner in 1801 (published in 1804) had pointed out that Newtonian gravity predicts that starlight will bend around a massive object. The same value as Soldner’s was calculated by Einstein in 1911 based on the equivalence principle alone. However, Einstein noted in 1915 in the process of completing general relativity, that his (and thus Soldner’s) 1911-result is only half of the correct value. Einstein became the first to calculate the correct value for light bending.
The first observation of light deflection was performed by noting the change in position of stars as they passed near the Sun on the celestial sphere. The observations were performed in 1919 by Arthur Eddington and his collaborators during a total solar eclipse, so that the stars near the Sun could be observed. Observations were made simultaneously in the cities of Sobral, Ceará, Brazil and in São Tomé and Príncipe on the west coast of Africa.
The result was considered spectacular news and made the front page of most major newspapers. It made Einstein and his theory of general relativity world-famous.
These days we are pretty comfortable with the theory, and interpret certain astrophysical phenomena as being caused by Einstein’s equations describing light-bending around massive objects. Examples:
Einstein’s ring (link)
Einstein’s Cross (link)
The article continues, though:
Considerable uncertainty remained in these measurements for almost fifty years, until observations started being made at radio frequencies. It was not until the 1960s that it was definitively accepted that the amount of deflection was the full value predicted by general relativity, and not half that number.
Looking into it further makes for a good read. If you have the time, this pdf is worth checking out.
Some quotes from the introduction:
Specifically it is alleged that a sort of data fudging took place when Eddington decided to reject the plates taken by the one instrument (the Greenwich Observatory’s Astrographic lens, used at Sobral) …
… Eddington employed a brilliant, as perhaps somewhat misleading, public relations
campaign to stampede scientists and the public into accepting his thesis …
The article mentions this book, which I plan on reading.