Time dilation is a phenomenon predicted by both special relativity and general relativity, where the passage of time is observed to be different between two observers who are in relative motion or experiencing different gravitational fields.
In special relativity, time dilation occurs due to relative motion. When two observers are moving relative to each other, they will perceive the other's clock to be running slower compared to their own. This effect arises from the fundamental postulate of the constancy of the speed of light, which leads to the dilation of time intervals as velocity increases. This phenomenon has been experimentally verified and has practical implications, such as the need to account for time dilation in the Global Positioning System (GPS) satellites.
In the case of GPS satellites, they orbit the Earth at high speeds relative to observers on the ground. Due to their velocity, the satellites experience time dilation, and their onboard atomic clocks appear to run slightly faster compared to identical clocks on the Earth's surface. This effect arises because the satellites' motion causes them to experience less time than observers on the ground. To ensure accurate GPS navigation, this time dilation effect must be accounted for, or else errors in position calculations would accumulate.
In addition to the velocity-induced time dilation, satellites also experience gravitational time dilation as predicted by general relativity. The closer a clock is to a massive object, such as the Earth, the stronger the gravitational field it experiences. In accordance with general relativity, clocks in stronger gravitational fields will appear to run slower compared to clocks in weaker gravitational fields. This effect also needs to be accounted for in satellite-based systems like GPS, as the satellites experience weaker gravitational fields compared to observers on the Earth's surface.
In summary, both velocity-induced time dilation predicted by special relativity and gravitational time dilation predicted by general relativity are relevant for satellites. GPS satellites, in particular, experience both effects, and adjustments are made to their onboard clocks to ensure accurate timekeeping and precise navigation.