# Calculate Accuracy of GPS?

by godtripp
Tags: accuracy
 P: 54 Hello, I need to calculate how accurate a GPS system is using only Special Relativity and a very basic knowledge of GR (without tensors...which is limited). I'm not sure where to begin however... where does the uncertainty in the measurement come from? How can I calculate the size of the uncertainty of a GPS position? Any references or insight would be GREATLY APPRECIATED. Thanks PF, J
 P: 604 You can pretty much calculate the discrepancy using the following equations and quantities- Time dilation due to gravity (GR)- $$d\tau=dt\sqrt{1-\frac{2M}{r}}$$ where $M=Gm/c^2$ Time dilation due to velocity (SR)- $$d\tau=dt\sqrt{1-\frac{v^2}{c^2}}$$ Quantities required- Earth's mass Earth's (mean) radius satellite's altitude satellite's velocity

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