Zero Point Leet Seconds

While computing certain round-trip times, here is a number I came across that is not easy to forget: It takes light 0.1337 seconds to travel the length of the Earth's equator via vacuum or air. Let me repeat that. It takes light "zero point leet" seconds to travel once around the equator.

We are going to ignore practical considerations regarding how light would actually follow a curved path around the Earth's equator via vacuum or air. This allows us to find the minimum amount of time that any signal must take in order to complete a round trip around the Earth. Despite the lack of practicality, this is an interesting result because it provides us a theoretical limit for the shortest time interval between sending a signal and receiving it after it has made a complete trip around the world.

The equatorial radius of the Earth is about 6378.137 km. The equatorial circumference of the Earth then is about 40075 km. The speed of light in vacuum is 299792.458 km/s by definition. The speed of light in air is about 299705 km/s. Therefore, it takes light about 40075/299792.458 seconds in vacuum and about 40075/299705 seconds in air to travel once around the equator. Both values can be written as 0.1337 seconds accurate up to 4 decimal places.