Yes, you are correct. Some satellites equipped with atomic clocks need to account for the effects of both general and special relativity to maintain accurate timekeeping. This is because the satellites are influenced by both the Earth's gravitational field and their relative motion at high velocities.
The two main relativistic effects that impact the satellite clocks are:
Time Dilation due to Gravitational Field: General relativity predicts that clocks in a stronger gravitational field will tick more slowly compared to clocks in a weaker gravitational field. Since satellites orbiting the Earth experience a weaker gravitational field compared to clocks on the Earth's surface, their clocks run slightly faster from the perspective of an observer on the surface.
Time Dilation due to Relative Velocity: Special relativity predicts that clocks moving at high velocities relative to an observer will appear to tick more slowly when viewed by the observer. The satellites, moving at high speeds relative to the Earth's surface, experience this time dilation effect.
These relativistic effects are not just theoretical; they have been experimentally confirmed and are essential for accurate GPS (Global Positioning System) operations. The GPS system relies on precise timekeeping to calculate the distances between satellites and receivers accurately.
If the relativistic effects were not taken into account, errors would accumulate, and the GPS system's accuracy would decrease significantly over time. To prevent this, GPS satellites are equipped with atomic clocks, and they continuously adjust their clock rates to compensate for the effects of time dilation due to both their motion and the Earth's gravity. These adjustments ensure that the clocks on the satellites remain synchronized with clocks on the Earth's surface, allowing for precise and reliable GPS navigation. The recalibration typically occurs every 24 hours or as needed to maintain accurate timing.