The understanding that time is affected by gravity comes from Einstein's theory of general relativity, which was formulated and developed over a century ago. The theory has been extensively tested and validated through various experiments and observations.
One of the key predictions of general relativity is that the presence of a massive object, such as a planet or a star, can cause a curvature of spacetime in its vicinity. This curvature affects the motion of objects and the flow of time.
The most famous experimental confirmation of time dilation due to gravity came from the Pound-Rebka experiment conducted in 1959. In this experiment, gamma-ray photons were emitted from the top of a tower and detected at the bottom. Due to the difference in gravitational potential between the top and bottom, the photons had to climb out of the gravitational well, causing them to lose energy. This energy loss was observed as a change in the frequency of the photons, which is a manifestation of time dilation.
Another well-known confirmation of time dilation due to gravity is the measurement of the precession of the orbit of Mercury. Mercury's orbit deviates from what would be predicted by classical Newtonian physics. General relativity successfully accounts for this deviation by considering the curvature of spacetime caused by the Sun's gravitational field.
Additionally, the phenomenon of gravitational redshift has been observed. When light travels out of a gravitational field, such as from the surface of a massive object to a region of weaker gravity, it loses energy and its wavelength becomes longer. This shift towards the red end of the electromagnetic spectrum has been measured and confirms the time dilation predicted by general relativity.
Overall, these experimental confirmations and observations provide strong evidence for the influence of gravity on the flow of time, supporting the notion that time is affected by gravity as described by Einstein's theory of general relativity.