Home » Random Bubbles » The mountains and the sea, Part 2

The mountains and the sea, Part 2

Ah, GPS!  What would we do without it?  Those satellites tell us exactly where we are. That’s what they do, isn’t it?

Well, not exactly.  In fact, the only thing a GPS satellite does is tell you what time it is up there.  For that to tell you where you are, two things are required: two perfectly synchronized clocks, one in the satellite and one in the receiver, and a way to tell exactly how long the signal from above takes to get to you.  The clocks in the satellites are atomic clocks; they’re be accurate for many millennia.  The clocks here are quartz clocks, like your fancy wristwatch; they’re cheaper and you can easily reset them if they get off, something you can’t do to the satellite clocks.  The satellites just send out regularly timed strings of pseudo-random numbers.  The necessary calculations to figure out where we are all done down here.  The receivers generate the same, and then compare the signals to get the lag.  Since we know the speed of light, which is the same as radio waves, calculating the precise distance is easy peasy.

A little sidebar of interest: you know those equations Einstein came up with you thought were only good for bombs and nuclear reactors?  Without them, GPS wouldn’t work worth a damn.  You see, the satellites orbit at about 12,000 miles, far enough for them to be moving significantly faster that anything on the surface of the earth.  So fast, in fact, that time actually slows down for them relative to the earth.  If you don’t take that into account, you’ll end up thinking you’re in the middle of the ocean somewhere.

Cool.  There are enough satellites (27) so that you can get at least 3 or 4 from anywhere on the planet, and can thus pinpoint your location by trilateration.  But there are issues.  The military, which originally developed GPS, also wanted to know the elevations as well as horizontal location.

Remember sea level?  Our lumpy egg of a planet drove us to turn that into an abstract surface, where all points on it had the same gravitational potential.  An easy way to think of that is to think of a surface where an object weighs exactly the same, no matter where it is (yes, if you want to lose weight, just climb a mountain).  This surface is called the geoid, and is less lumpy than earth as a whole, but lumpy all the same.  GPS gives you the actual surface of the earth, but you have to adjust that to sea level to get a useful elevation.  Shouldn’t be a problem, right?

Wrong.  Since the geoid is irregular, there’s no easy way to model it for the computers to work with.  The best we could do was a smoothish egg, kinda-sorta where we thought sea level was, but often significantly different.  What to do?  It turns out that traditional ways of measuring elevation, with spirit levels, was very, very good at arriving at the geoid.

Years ago, I worked as a land surveyor when the military was just developing GPS.  The Defense Department sent out memos to surveyors everywhere, requesting us to set up our receivers at known elevation points every chance we got, and report the official elevation along with the what the GPS receiver thought the elevation was.  It wasn’t too long before an accurate model of the geoid was available.

Now you know what that little flat box does when you tell it to go to Grandma’s house, by the mountains or the sea.

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s