It’s all about the precision of the experiment, which is a function of the instruments used and the object being investigated. I highly recommend you to check out the source link below. As they write there:
Observations made with ESO’s Very Large Telescope have for the first time revealed the effects predicted by Einstein’s general relativity on the motion of a star passing through the extreme gravitational field near the supermassive black hole in the centre of the Milky Way. This long-sought result represents the climax of a 26-year-long observation campaign using ESO’s telescopes in Chile.
There is a lot more actual science to be had there, so again, check it out. 🙂
Now read this: Zombie stars: A few words on how to read NASA (and others)
Credit for illustration: ESO/M. Kornmesser
Source of the illustration: http://eso.org/public/news/eso1825/