I noticed something interesting recently while reading about the history of navigation. It seems that determining one’s position on Earth is very much related to knowing the precise time, both historically and today, but for very different reasons.

In the Age of Discovery (around 1500-1600 AD), we did not have a good way of determining where you are on the open ocean. You need two measurements to pinpoint your location: latitude and longitude. Latitude gives your north-south position, and since this is perpendicular to (hence unaffected by) the rotational axis of the Earth, figuring it out was relatively easy. At the equator, the Sun should be directly above you when its at the highest point in the sky. As you go further north or south, this angle will change, and the deviation from the perfect 90-degree angle will determine your latitude. Of course, any astronomical object will work, as long as you know its current altitude angle at the equator. So with a sextant and a lookup table of equatorial altitude angles, you can figure out your current latitude pretty easily. Determining the longitude on the other hand, is a lot trickier, and for a very long time was the main roadblock to navigating effectively at sea.

Since longitude measures the east-west position, it runs parallel to the rotation of the Earth. This means that even if you are not moving longitudinally yourself, the Earth is taking you on the move relative to the stars anyway. People worked on this problem for a long time, and turns out it comes down to keeping track of some reference time accurately. First you would create a look up table of the altitude angles of some astronomical object at a reference location (say, the Greenwich Observatory) at various times. Out at sea, you can measure the local altitude angle of the same object, and if you also know the current time of the reference location, you can look up what the angle of the object is at the reference location. How much the two values differ will tell you how far east or west you are from the reference location, giving you the current longitude measurement.

These days we no longer use natural astronomical objects to determine our location. Instead we use artificial objects, namely the constellation of GPS satellites, and an entirely different principle of positioning. The pre-modern method, if we are to look at its core idea, is about figuring out how the local sky looks different compared to at some known reference location (the equator for latitude, the Greenwich meridian for longitude). This difference lets us calculate our deviation from the reference location, thereby locating us. The modern method of GPS positioning is much more direct, and dispenses with the need for any reference location. It relies on straightforward geometry.

On a flat surface, knowing the precise distance to three separate external points will uniquely identify a single point. Solving for the position like this is done via the method of trilateration. In 3D space, we just need the distance to one more point. The GPS satellites are the external points that we use to do this calculation. They are constantly orbiting the Earth, broadcasting their current position and onboard time. Knowing the precise time is crucial here. First, the time is used to figure out our distance to these satellites. The signals travel at the speed of light, and by timing the delay of receiving each signal, we can determine our distance to the signal sources. Second, because the satellites are further from the Earth’s gravitational field than us on the ground, time passes ever-so-slightly faster for them (about 38 microseconds per day). There is an extremely accurate atomic clock onboard every GPS satellites, which together with Einstein’s equation, help us compensate for this relativistic effect.

It seems strange to me that determining position, both 500 years ago and today, actually comes down to the problem of accurate timekeeping, for wildly different reasons. In the pre-modern era of navigation, time was essentially used to compensate for the rotation of the Earth, while in the modern era, time is used to measure distance and compensate for time dilation. In a sense it is poetic, that to know your place in the world first you must know the time.