Time dilation is not an illusion, but rather a real and measurable phenomenon predicted by Einstein's theory of relativity. The effects of time dilation have been confirmed through numerous experiments and observations.
In the case of atomic clocks in satellites, their orbits are significantly different from those on the Earth's surface. Satellites orbit at high speeds and experience weaker gravitational forces compared to objects on the Earth's surface. Both of these factors contribute to time dilation.
According to the theory of relativity, time appears to run slower in a stronger gravitational field and in systems moving at high speeds relative to each other. The satellites in orbit experience both of these effects simultaneously.
The speed of the satellites affects time dilation due to the phenomenon known as "time dilation due to velocity" or "special relativistic time dilation." As satellites move at high speeds relative to observers on Earth's surface, time runs slightly slower for the satellites. This effect has been experimentally confirmed by comparing the rates of atomic clocks on satellites with those on the ground.
Additionally, the gravitational field experienced by the satellites is weaker compared to the surface of the Earth, leading to "gravitational time dilation" or "general relativistic time dilation." The closer an object is to a massive body, the slower time appears to pass. As the satellites are farther from the Earth's center, where the gravitational field is stronger, time runs slightly faster for them.
The combination of these two effects results in a measurable time dilation in the atomic clocks on satellites compared to clocks on Earth. The predictions made by Einstein's theory of relativity regarding time dilation have been confirmed with great precision through experiments and observations, including those involving satellite-based atomic clocks.