**General Relativity in the Global Positioning System (GPS)**

Now we reach the culmination of everything on this site thus far. The original inspiration of this webpage is a paper titled “Relativity in the Global Positioning System” by a man named Neil Ashby. I have attached a copy of the paper: Ashby GPS.

In the paper, Ashby details the effects of Einstein’s general theory of relativity in the context of the GPS system. As it turns out, we would not even have such an amazingly accurate construct without taking relativity into account.

In the following sections, I will use knowledge we have previously covered, and tie it together with considerations to the global positioning system.

**Hey, Nobody is a Perfect Sphere**

The Earth is not a perfect sphere. It is bumpy, filled with pits, and even oblate (flattened at the poles and stretched at the equator) due to it’s rotation. As we will see, the shape of the planet affects clocks in orbit.

**Geoid Model**

To quote Wikipedia: “a geoid is a surface along which the gravity potential is everywhere equal and to which the direction of gravity is always perpendicular”. The link to their page on geoids can be found here. Below is an image of the geoid for Earth:

Above, we see Earth’s geoid. This is the shape we get if we imagine the entire surface of the planet to be water: the gravity of the landmasses would create this shape. The geoid helps us to account for variations in gravity across the planet. A mountain has more gravitational “pull” than a valley, and more dense rock will have a stronger pull than less dense.

The geoid is a way to calculate mean sea level, and allows for simplification when dealing with minute changes in gravitation. A great video about the geoid model for Earth is found below:

^{(PLEASE SEE “GR IN GPS IMAGE RESOURCES” PAGE FOR VIDEO SOURCE)}

Both the oblate shape of the Earth, and the Geoid model come in handy when talking about precision in the global positioning system.

**LET’S SEE HOW TIME DILATION AND FREQUENCY SHIFTING ARE ACCOUNTED FOR IN THE GPS SATELLITE SYSTEM!**