Humble Pi: When Math Goes Wrong in the Real World

by Matt Parker

As the protoplanetary disk congealed and separated into the planets as we know them, the Earth was made with a certain amount of angular momentum, sending it flying around the sun, spinning as it goes. The orbit we ended up in gave us the length of the year, and the rate of the Earth’s spin gave us the length of the day. Except they don’t match. There is no reason they should! It was just where the chunks of rock from that protoplanetary disk happened to fall, billions of years ago. The yearlong orbit of the Earth around the sun now takes 365 days, 6 hours, 9 minutes, and 10 seconds. For simplicity, we can call that 365¼ days. This means that, if you celebrate New Year’s Eve after a year of 365 days, the Earth still has a quarter of a day of movement before you’ll be back to exactly where you were last New Year’s Eve. The Earth is tearing around the sun at a speed of around 30 kilometers every second, so this New Year’s Eve you will be over 650,000 kilometers away from wherever you were last year. So, if your New Year’s resolution was to not be late for things, you’re already way behind.