GPS - my final offering

If you are still with me - you only have to endure one more post on GPS related information. 
OK... you really didn't have to breathe that sigh of relief now ;-)

Last time I wrapped up the basics on how GPS achieves the seemingly miraculous job of using a constellation of satellites to have you know where on Earth you are.  But it seems I left you with a bit of a problem... the location you are getting reported is too inaccurate. OK, so you should know what city you are in, and maybe what side of the tracks you are on.  But if you don't already know this, GPS accuracies are not likely the biggest of your problems!

So what is wrong?  Several things:  Leap seconds, Einstein and more Einstein.

What, you ask, the heck, is a leap second????  First off, let me get the disappointment done with early.  What I know is limited... so you will just have to Wikipedia this for the gory details.  Bottom line:  just as every now and then calendars are adjusted with an extra day (leap years), so is our time occasionally in need of a minor tweak.  Every so often, Earth standard time is nudged by a second.  Keeps the time bean counters happy, or something like that.  But unfortunately for the makers of GPS satellites, their atomic clocks are not adjustable.  So each time we nudge time by a second, the GPS time and Earth time deviate by another second.  We currently have something like 24 leap seconds since this practice was started.  If we did not adjust for this, just accounting for Earth's rotation, we would be off by 6-7 miles or so. 
So now we adjust for this, and we are quite a bit closer to the mark.  But still off...   so let's go visit Einstein.

Who doesn't know Einstein?  I mean really.  But many don't know much about what he brought to the physics world.  Something about relativity, speed of light and energy. 
We will ignore the ever famous E = mc squared.  But the speed of light and relativity are very important to GPS.  Radio signals travel at the constant speed of light. And that is how we generally know how long the Satellite signals should take to travel from the Satellite to where we are.  I say generally - because I lied.  Again.  The speed of light is NOT constant.  It is constant only in a true vacuum, as in space.  But it tends to change speeds a little in an atmosphere, and also tends to bend a little as it goes though some of the atmosphere's layers.  This is akin to when you are looking into a pool and things look a little distorted.  Same thing happens to these Satellite signals.  Again, more corrections need to be layered in if we really want to be accurate!    Closer still... but there are 2 more effects that we need to address if we want accuracy that will help us navigate as drive the streets.

In Einstein's Special theory of Relativity, among its many implications, is that as you travel relative to another object at any significant speed, your clock slows down.  Time just happens slower for you.  And while our Satellites are zipping along pretty darn fast, the effect is minor.   But still just big enough that we need to account for the change in the speed of the clock on the Satellite.

Later Einstein published his General Theory of Relativity.  Very complicated - but again, I'll bottom line it for you.  Gravity curves space-time.  And our GPS satellites are experiencing slightly different gravity than you and I are here on the surface.  So the space-time they are zipping past has a slightly different curvature than you and I do, and this too, translates into a clock that ticks a little faster than ours on the surface. 

So when we account for Time dilation (Special theory of Relativity), Time contraction (General theory of Relativity), speed of light and its refraction through the atmosphere, and leap seconds - we now have a very accurate GPS position estimate. 

And that little box sitting on your dash?  The one you just take for granted.  It does all of this - just so you don't get lost making the wrong turn somewhere!