James' World 2

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You know how it goes: You’re trying to get some shut-eye in your bunk after a long shift of scraping samples of prebiotic material from red rocks in Utopia Planitia, and before you know it, your alarm bell rings. And then you see it woke you up a full 477 microseconds early!

Life on Mars is tough. Figuring out the exact time isn’t much easier.

Even on the larger end of the timescale, Martian chronometry is not exactly simple; the planet takes about 687 Earth days to go around the sun, making calendrical coordination with Earth pretty hairy. It also spins on its axis—completing one Mars day—in 24 hours, 39 minutes, and 35 seconds (to distinguish this period from an Earth day, we call it a “sol,” referencing the Latin word for the sun). Keeping track of your schedule on Mars would be different than doing so on Earth. But still, at its core, it would just be a matter of conversion.

Building an accurate Martian clock, on the other hand, can be very tricky, depending on how accurate you want it to be. When you start to slice time into smaller and smaller bits, the problem concerns not only engineering but also fundamental physics. That’s because the flow of time on milli- and microsecond scales is affected by relativity, gravity and orbital mechanics, which can vary radically from world to world.

The good news is that a pair of physicists did all the associated mathematical heavy lifting for Mars and published their results on December 1 in the Astronomical Journal. With their help, we can fine-tune our Martian timepieces.

It was Albert Einstein who really first got this ball rolling. Among many other things that emerged from his special theory of relativity, he postulated that time does not necessarily flow the same for two independent objects. The most commonly used example of this is how a clock runs more slowly when it is moving relative to an observer. The effect is pretty small until that motion nears the speed of light, whereupon it can get very large.

But there’s another twist to relativity: besides relative motion, gravity affects time’s flow as well! The stronger the gravity, the slower a clock will tick relative to some observer far away, where the gravitational effects are weaker. Both of these phenomena can affect us on Earth: GPS satellites, for example, orbit far above Earth, where gravity is weaker, so their clocks run faster than those on the surface. But the satellites’ rapid orbital motion also slows their clocks. Combined, these effects cause their clocks to tick about 38 microseconds faster than ones on the ground. This profoundly affects their accuracy in mapping, throwing them off by about 10 kilometers per day. Think about how angry you’d be if your smartphone’s map app was off by a kilometer or so after only a half hour of use. Happily, GPS takes all this into account, so the positional accuracy it calculates is pretty high. But this situation just shows how important relativity can be

What does this have to do with the Red Planet? Well, for one thing, while Mars is a rocky world like our own, it’s much smaller, about a tenth the mass of Earth. Its surface gravity is some three times less than what we feel at home. So on Mars, I’d only weigh about 65 pounds (29 kilograms)! I bet my knees and back would feel a lot better about that.

But this also means a clock on Mars feels less gravity than one on Earth, so it will run faster. And unfortunately, plugging this into Einstein’s equations to calculate that advancement is no easy task.

First, you have to define what the average surface of Mars is. After all, if you’re on a mountain, you’re farther up from the average elevation than you’d be if you were in a valley, where you’d feel a different amount of gravitational force.

But you can’t just average between the highest peaks and lowest valleys to arrive at some clear median. Oh, no. Just as a world can have varying surface elevation, it can also have a varying subsurface composition, with some regions being denser (and thus having greater local gravity) than others. Still, factoring this in alongside things like a global rotation rate and the influence of any massive orbiting moons, it’s possible (though difficult) to determine the average surface for any given world.

We did this properly for Earth in the late 20th century—and thanks to our extensive robotic orbital reconnaissance, we’ve done it more recently for Mars, too. Once calculated, Mars’s average surface can be used to gauge gravity’s influence on clocks anywhere on the planet.

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