The GPS Satellite Clock Synchronization · AI Generator #GEN-591FC2ED

Physics

Problem

A GPS satellite orbits Earth at an altitude of

20{,}000\;\text{km}

with a velocity of

3{,}900\;\text{m/s}

relative to Earth's surface. The satellite's atomic clock is initially synchronized with an identical clock on Earth's surface. After the satellite completes exactly

10

orbits, by how much will the satellite clock differ from the Earth clock due to time dilation? (Ignore gravitational time dilation effects and consider only special relativistic effects. Use

c = 3.0 \times 10^8\;\text{m/s}

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