How Much Does Time Dilate for the ISS Astronauts?

One of those nifty facts Einstein discovered in his Theory of Relativity is that the force of gravity affects time. The more gravity, the slower time progresses until time appears to a stop in a black hole from the perspective of an outside observer. This natural phenomenon is known as Gravitational time dilation.

Spacetime Curvature

Experimental proof for this phenomena came with the Pound-Rebka Experiment in 1959. Later, scientists would fly aircraft over the Chesapeake Bay carrying an atomic clock, to further prove the clock in the air ran faster than one on the ground.

So this begs the question, How much longer have astronauts on the International Space Station lived compared to us on the ground?

Lucky me for living in the Information Age that a quick google search found someone had already done the math:

I considered the ISS speed v as 8000 m/s or 0.00002667c (c is the speed of light). Then I calculated the epsilon factor as epsilon = sqrt ( 1 – v^2 / c^2 ) = 0.9999999996443555 Finally I applied the epsilon factor to the ISS orbit time (3013 days * epsilon) and found out that the resulting difference is 0.0925 seconds.

That means that time inside the ISS has so far been about one tenth of a second slower than the time down here on earth.

Waitaminute, slower? That doesn’t grok with gravity slowing down time. A closer look at the above math reveals it is calculating the effects of velocity on time. As objects approach the speed of light, their relative time slows down. This fact fuels an interesting thought experiment known as the Twin Paradox, where one twin goes on a light speed journey and the other stays on Earth. For the traveling twin only a few moments pass during the journey, but for the twin on Earth, it has been decades.

ISS Science Officer Ed Lu independently confirms the ISS math, concluding the astronauts age 0.007 seconds less than people on Earth. So these two sources have figured out how the ISS’s velocity slows down its relative time, but there’s no mention of gravity in their math.

If the ISS were to orbit the Earth at 1.5 times the Earth’s radius (5,900 miles or 9500 km) then the effect of velocity and gravity on time would cancel each other out. At orbits greater than 5,900 miles, gravity is stronger and speeds up time, below 5,900 miles, velocity is stronger and time slows. The ISS orbits 255 miles above the Earth at 8000 m/s, so time runs approximately 0.0000000014 percent slower.

Today, GPS satellites are adjusted to account for this distortion of space time, both for the effect of time dilation from their velocity (special relativity) and their reduced gravity (general relativity), when they are put into orbit. Armed with all the knowledge above, you might have some fun explaining why this PhD-holder has no idea what he’s talking about when he calls time dilation a myth and proposes putting an atomic clock on the ISS to disprove it.

Note: Programming geeks and other scientists concerned with time should bookmark the NIST: Time and Frequency Division, which maintains the time standard used in all clocks maintained by satellite.