Calculate Accuracy of GPS?

1. godtripp

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

2. stevebd1

686
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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