## Saturday, June 8, 2013

Given my disappointment with the new Star Trek movie, it's nice to know there are still some legitimate (and non-fictional) bad ass space travelers out there. Canadian astronaut Chris Hadfield recently made headlines for an awesome video where he sings David Bowie's Space Oddity.

 In a karaoke battle of the Chrises, Hadfield would totally destroy Pine.1

While that video is awesome in its own way, I personally prefer how Hadfield explains cool science to the masses:

All this talk about astronauts and cool science reminds me of a question my physics buddy Kendall asked me to do:  How much extra time do astronauts gain by being in orbit?

According to Einstein's theory of relativity, time slows down as you move faster. Since the International Space Station (ISS) travels about 4.8 miles per second, Hadfield and the other astronauts on board should age somewhat slower than the rest of us.

Using the time dilation formula, we find that a person traveling at the speed of the ISS ages at a rate 0.000000033% slower than the rest of us. As our paper of the week demonstrates, even though this effect is tiny, it's still measurable if you've got a precise atomic clock.  After one year on the ISS,2 an astronaut would age 10 milliseconds less than a person at rest on the Earth because of special relativity.

As amazing as our above result is, it's not quite correct. The problem above illustrates the principle of special relativity, which Einstein discovered was the correct way to describe fast moving objects in the absence of heavy masses. Eleven years later, Einstein published his general theory of relativity, which explains how time dilates in a gravitational field. According to general relativity, time slows down as you move closer to heavy masses (i.e. people on Earth would age more quickly than people far away from its gravitational pull). At a height of 230 miles above Earth's surface, astronauts age 0.000000098% slower than objects without any heavy masses in the vicinity. After one year on the ISS, astronauts would age 31 milliseconds less than a person far away from any masses, but 1.8 milliseconds more than a person on the surface of the Earth.

[1] However, in a battle of the Kirks, I'm pretty sure this means Pine could take Shatner.
[2] Valeri Polyakov holds the record for the longest time on the space station with a time of 437.7 days.

Aaron Santos is a physicist and author of the books How Many Licks? Or How to Estimate Damn Near Anything and Ballparking: Practical Math for Impractical Sports Questions. Follow him on Twitter at @aarontsantos.