General relativity
In addition to special relativity, there is also a general theory of relativity which goes beyond special relativity to incorporate the effect of gravity. This explains why:
Data from GPS satellites have to be adjusted in order to give accurate positional data. (There is also a smaller'—'but still significant'—'effect due to special relativity.)
Starlight near massive objects. This was famously observed during a solar eclipse by Arthur Eddington in an experiment that confirmed one of Einstein's predictions.
There is a precession of Mercury's orbit by about 43 arcseconds per
century. It was the successful explanation of this phenomenon by general relativity which led to its widespread acceptance.
Light from distant stars is redshifted, an observation which led to the conclusion that the universe is expanding.