The time dilation issues of GPS satellites are handled by computers through a combination of software algorithms and hardware compensation mechanisms. Here's a brief overview of how these issues are addressed:
Special and General Relativity Considerations: According to Einstein's theories of special and general relativity, time runs slower in stronger gravitational fields and at higher velocities. As GPS satellites are in motion and experience weaker gravity compared to the Earth's surface, these relativistic effects cause their onboard atomic clocks to run slightly faster relative to clocks on the ground.
Clock Corrections: To account for the time dilation effects, the GPS satellites are equipped with highly accurate atomic clocks that are regularly synchronized with the ground-based clocks. The satellites continuously transmit timing signals indicating the precise time according to their onboard clocks. These signals are received by GPS receivers on Earth, which compare them with the local time.
Relativistic Algorithms: The GPS receiver's software includes sophisticated algorithms that factor in the time dilation effects predicted by relativity. These algorithms compensate for the difference in time between the satellite clocks and the receiver's clock due to the relativistic time dilation. By applying these corrections, the GPS receiver can determine the accurate time and calculate the precise position.
Ephemeris Data: The GPS satellites also broadcast ephemeris data, which includes information about the satellites' precise orbits and clock corrections. GPS receivers utilize this data to determine the satellite's position accurately. The ephemeris data is updated regularly to account for the changing positions and clock corrections of the satellites.
By combining these techniques, GPS receivers can mitigate the time dilation effects and accurately calculate the position and time for navigation purposes. The incorporation of precise relativistic algorithms and constant updates from the satellites ensures that the GPS system remains highly accurate despite the time dilation experienced by the satellites.