In this blog post, we’ll explore how GPS works, how it calculates our location, and how GPS satellites provide location information anywhere on Earth.
GPS is a technology we’re very familiar with in our daily lives, whether it’s the police tracking a suspect’s location or using smartphone navigation. Here’s a scene from Dan Brown’s novel ‘The Da Vinci Code’. Sophie and Langdon are hiding in a restroom. Sophie decides to help Langdon escape; she takes the tracking device from the left pocket of his coat, places it inside a bar of soap, and throws it toward a passing trailer. The police mistakenly believe Langdon has boarded the trailer and chase after it in vain, allowing Langdon and Sophie to escape the Louvre Museum safely. How were the police able to track Langdon’s location using the tracking device? The principle behind it lies in GPS.
GPS (Global Positioning System) is a satellite navigation system that calculates a user’s location using signals transmitted by satellites.
Can a location be determined using just one satellite? Unfortunately, no. This is because the distance information provided by a single satellite alone corresponds to countless possible locations at that exact distance. As the number of satellites increases, the overlapping locations narrow from an area to a line, and then to a single point.
To understand the optimal number of satellites, we must first understand the concept of dimensions. Dimensions are defined by the number of directions in which an object can move independently. This is because knowing how far and in which direction an object has moved from a reference point allows us to determine its position.
In one dimension, an object’s position can be determined simply by knowing how far it has moved forward or backward. In two dimensions, information in two directions—forward/backward and left/right—is required. So, what about three-dimensional space? All three directions—forward/backward, left/right, and up/down—are necessary. Since the space we inhabit is three-dimensional, information regarding all three of these directions is required to calculate a position.
Therefore, four satellites are required to calculate an exact position in three-dimensional space, as information is needed regarding the reference point as well as the forward-backward, left-right, and up-down directions. However, by utilizing the fact that the user is on the Earth’s surface, the Earth itself can serve as a reference plane, meaning that, in theory, a position can be calculated using only three satellites. However, actual GPS systems use a total of four satellite signals. The additional satellite is used to correct for time errors that occur during the transmission and reception of signals; it helps determine a more accurate position by calculating the time it takes for light to travel.
Now, let’s look at how the distance information received from the satellites is calculated. In this section, you’ll see why the Pythagorean theorem and trigonometric functions—which you learned in middle school math—are important.
Triangulation is a method of calculating the coordinates and distance of a given point using the properties of triangles. Given two reference points, if you measure the angles formed by the base and the other two sides of the triangle formed by the unknown location and the two reference points—and know the lengths of the sides—you can calculate the coordinates and distance using the law of sines and other formulas.
For example, let’s assume we are measuring the distance from the beach to a ship out at sea. An observer measures angles α and β from two fixed points, A and B, respectively. If the distance l between A and B is given, or if the coordinates of the two points are known, the coordinates of the ship at point C can be calculated using the properties of similar triangles and the law of sines, and the distance d from the beach to the ship can also be determined. GPS operates on the same principle.
It calculates the location of an object on Earth by combining the positions of the satellites with the distance information measured from them.
Currently, the GPS system consists of approximately 31 operational satellites; of these, generally 24 or more form the core operational system, while the rest serve as backups or provide performance enhancements. These satellites orbit the Earth along multiple orbital planes and are designed so that multiple GPS satellites can be observed simultaneously from anywhere in the world. This ensures a stable signal from at least four satellites, providing more accurate location information. GPS satellites are powered by solar panels.
Take a moment to look up at the night sky. If you see a particularly bright, moving dot, it might be a GPS satellite calculating your location.
