# Why is the Accuracy in the measurement of Time so important in GPS?

I read in a physics book that

Without clocks of extreme accuracy, the Global Positioning System (GPS) that is now vital to worldwide navigation would be useless.

What would be effects on navigation of less accurate clocks in the context of GPS?

• Voting to reopen. The question is perfectly clear and can be answered in detail - less accurate clocks in the GPS system would lead to less precise position measurements. I have edited the question to replace "doubt" by the more usual "question". Sep 4, 2023 at 7:36

GPS works by determining the distance between the GPS receiver and a number of GPS satellites (usually at least 4). From these distances (and the known positions of the satellites) the GPS receiver can calculate its position very precisely.

The distance calculations made by the GPS receiver depend on multiplying the speed of the radio waves emitted by the satellites (which is basically the speed of light) by the time difference between when a signal was emitted by a satellite and when it was received by the receiver. So if the GPS clocks were less accurate then the GPS receiver would not be able to measure these time differences so accurately, and its position calculation would also be less accurate.

A rough idea of how accurate the clocks must be can be found by multiplying a notional time difference by the speed of light. If the GPS clocks were only accurate to within $$1$$ microsecond ($$10^{-6}$$ seconds) then in that time light travels $$300$$ metres, so GPS position measurements would only be accurate to within a few hundred metres. In practice the clocks in the GPS system need to be at least $$10$$ times more accurate than this.

Actually, it is necessary for clocks to be both extremely accurate and precise in order for GPS to work at all.

What your handphone is doing by accessing GPS is to ask the satellites what the times on the satellites are. If you cannot have extremely accurate times on the satellites, then when you are seeking the times on the satellites, each one gives you a time that you cannot trust, then you cannot work backwards to know where it is, and thus your own position is of great uncertainty.

Similarly, if the precision of the time pieces are bad, then even if the GPS clocks are very accurate, the uncertainties will also be huge, and then you will, again, not know where you are.

Just to be a bit more clear GPS receivers/phones/'handphones' never asks for anything from GPS - its receive only - period (unless the US DOD included a receiving package on the satellites and that would be secret/sensitive/TS and just for military - it does seem pretty clear that GPS can deliver encrypted one way messages on one of the carriers to all military specific S/N's of receivers and groups. That would be sensitive and never revealed on purpose). Normally DSP/Defense Support Program satellites would just be used - although in time of 'more then normal' conflict the US Military is constantly running low on bandwidth

The closest You get from a GPS transmitting is a bad design accidently leaking the L/O (Local oscillator) that couples and transmits a faint signal at the offset of the L/O through the RX/receiving antenna. If a receiver had amazing signal/noise performance (likely with the help of super cooling) and DF/direction finding they could sent a missile to all consumer receivers being used by the enemy behind the front line

That's specifically why EMCON/Emission Control exists in the military - even some receive only equipment needs to be shut down even though its a "transmission only" device if the front end leaks too much from the local oscillators(s)