How does Gravitational Time Dilation affect us?

The phenomenon of gravitational time dilation affects nearly every one of us in our day to day lives. Without an understanding of this changing of time the GPS system which we all use in our everyday lives would fall apart and cease working. To understand why this happen you need to know what the GPS system consists of and how it works

What is GPS?

Ideas and statistics from http://en.wikipedia.org/wiki/Global_Positioning_System

GPS stands for “Global Positioning System” and is an American system which uses a constellation of 24 satellites to allow you to locate your position on the Earth’s surface to an accuracy of about 10-20 metres. For global coverage a constellation of 24 satellites is required with the current constellation consisting of 31 providing redundancy in the system in case of individual satellite failures.

Each satellite contains within it a highly accurate atomic clock and the satellite broadcasts that time out continuously along with its precise position in space and the approximate positions of the over satellites. Your GPS receiver on the ground picks up the signal from 3 satellites and can use this information to calculate its position.

How does GPS work

Images taken from http://en.wikipedia.org/wiki/Global_Positioning_System

Your GPS receiver compares the time in the signal from a satellite from its own onboard time and (knowing the speed of light) can calculate how far away it is from the satellite. It therefore knows a locus of point around the satellite. It can then compare the locus for one satellite with the locus of another it knows it is on the points where the loci overlap, as shown below.

As you can see in the zoomed in section in the bottom right of the diagram the overlap results in a circle of points where the receiver is. By repeating this process again for a third satellite the position can be narrowed down further, as shown below.

This results in two possible points where you could be, with a GPS designed for land use picking the one closer to the surface of the earth. As long as the atomic clocks on the satellites stay accurate the positioning system will work

How does Gravitational Time Dilation affect GPS?

1. Ideas from http://en.wikipedia.org/wiki/Gravitational_time_dilation#Experimental_confirmation and http://en.wikipedia.org/wiki/Global_Positioning_System

As covered earlier on in the website time runs slower the stronger the gravitational potential you are in. Therefore, from our point of view, the clocks on the satellites will run fast and will no longer be accurate, and this has very sever effects on GPS.

Although the effects of gravitational time dilation only results in the clocks running 30 nanoseconds fast per minute, the fast transfer time for signals from the satellite to the earth’s surface mean that the 30 nanoseconds is quite a large percentage error. Thus the 30 nanosecond error results in an error in the position of 7-9 m.

Over the course of a day this will build up to an error of approximately 10 km which renders the system utterly useless. The US army therefore has to constantly monitor the system and update the clocks on the satellites to counteract the fact they run fast and ensure that the world continues to run smoothly.

Loci of points around two GPS satellites showing possible position of the GPS receiver

Third locus of possible locations of receiver around a GPS satellite and points of intersection with locus of points from first two satellites