The satellite slow-down can be calculated using the formula: Δf/f = (1-v^2/c^2)^(1/2) - 1, where Δf is the change in frequency, v is the satellite's velocity, and c is the speed of light.
The relativity speed-up refers to the phenomenon where a satellite appears to be moving faster to an observer on Earth due to the effects of time dilation and length contraction.
Time dilation is a consequence of Einstein's theory of relativity where time appears to slow down for an object in motion relative to an observer. In the context of satellite slow-down, the satellite's clock will appear to run slower to an observer on Earth due to its high velocity.
The satellite's speed affects its frequency due to the Doppler effect. As the satellite moves closer to or farther away from an observer on Earth, the frequency of the signals it transmits will appear to increase or decrease, respectively.
Understanding satellite slow-down and relativity speed-up is crucial for accurately calculating and predicting the orbits of satellites. This knowledge is also important for ensuring the accuracy of GPS systems, which rely on precise timing and frequency signals from satellites.