What Time Is It on Mars?

You know how it goes: you’re trying to get some sleep in your bunk after a long day of work scraping samples of prebiotic material from red rocks of Utopia Planitia, and before you know it, your alarm bell is ringing. And then you see that it woke you up 477 microseconds earlier!

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

Even on a longer time scale, Martian chronometry isn’t exactly simple; the planet takes approximately 687 Earth days to go around the sun, which makes calendar coordination with Earth quite tricky. It also rotates on its axis, completing a Martian day, in 24 hours, 39 minutes and 35 seconds (to distinguish this period from an Earth day, we call it “sol”, referring to the Latin word for the sun). Keeping track of your schedule on Mars would be different from what you would do on Earth. But ultimately, it would only be a question of conversion.

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On the other hand, building an accurate Martian clock can be very tricky, depending on the desired precision. When you start to slice time into smaller and smaller pieces, the problem involves not only engineering but also fundamental physics. Indeed, the flow of time on the millisecond and microsecond scale is affected by relativity, gravity and orbital mechanics, which can vary radically from one world to another.

The good news is that two physicists have done all the heavy lifting associated mathematical work 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 launched this project. Among other things from his theory of special relativity, he postulated that time does not necessarily flow in the same way for two independent objects. The most commonly used example is how a clock runs more slowly as it moves relative to an observer. The effect is quite small until this movement approaches the speed of light, after which it can become very significant.

But there is another particularity of relativity: besides the relative movement, gravity also affects the flow of time! The stronger the gravity, the slower the clock will run compared to a distant observer, where gravitational effects are weaker. Both of these phenomena can affect us on Earth: GPS satellites, for example, orbit well above Earth, where gravity is weaker, so their clocks run faster than those on the surface. But the rapid orbital movement of satellites also slows down their clocks. Combined, these effects cause their clocks to run about 38 microseconds faster than those on the ground. This profoundly affects their mapping accuracy, disrupting them by about 10 kilometers per hour. day. Think about how angry you’d be if your smartphone’s map app lags about a mile after just half an hour of use. Fortunately, GPS takes all of this into account, so the accuracy of the position it calculates is quite high. But this situation shows how important relativity can be.

What does this have to do with the red planet? Well, for one thing, even though Mars is a rocky world like ours, it is much smaller, about a tenth of the mass of Earth. Its surface gravity is about three times less than what we feel at home. So on Mars, I would only weigh about 65 pounds (29 kilograms)! I bet my knees and back would feel a lot better because of this.

But this also means that a clock on Mars feels less gravity than a clock on Earth, so it will run faster. And unfortunately, integrating this into Einstein’s equations to calculate this advancement is not an easy task.

First of all, we must define what the average surface of Mars is. After all, if you’re on a mountain, you’re further away from average altitude than if you were in a valley, where you would feel a different gravitational force.

But you can’t just average the highest peaks and lowest valleys to arrive at a clear median. Oh no. Just as a world can have varying surface altitude, it can also have varying subsurface composition, with some regions being denser (and therefore having greater local gravity) than others. Nonetheless, taking this into account as well as things like the overall rotation rate and the influence of any massive orbiting moons, it is possible (although difficult) to determine the average surface area of ​​a given world.

We did it well for Earth in the late 20th century and, with our extensive robotic orbital reconnaissance, we have also done it more recently for Mars. Once calculated, the average surface area of ​​Mars can be used to assess the influence of gravity on clocks anywhere on the planet.

But that’s not all. Mars orbits the sun further than Earth, which has two effects: The solar gravity felt by the Red Planet is reduced, so its clocks will run faster than Earth’s. Additionally, its orbit around the sun is slower than Earth’s, so its clocks will run even faster.

Worse, Mars’ orbit is elliptical (think a slight oval rather than a perfect circle), which means that sometimes the planet is closer to the sun than average (so it orbits faster and the clocks go slower) and sometimes it is further away (so it orbits slower and the clocks run faster).

The equations that cover all of this are fierce, to say the least. However, after some serious digital hooking up and calculations, scientists found that on average, a clock on Mars would run about 477.6 microseconds faster per day than a clock on Earth. But it’s really on average! The change in orbital distance and motion applies a variation of approximately plus or minus 113 microseconds over the course of a Martian year, meaning clocks can be ahead of Earth’s by between 364 and 590 microseconds per day.

It’s not much, on a daily basis. A typical human blink lasts about 165 milliseconds, or more than 300 times longer than the offset of the Martian clock! So it won’t affect your daily floor, but scientists regularly have to measure times much faster than that. Like GPS on Earth, these effects would be taken for granted by any future planetary explorer; for example, synchronizing terrestrial and Martian Internet connections would require this relativistic correction. And if we ever need to build a robust GPS for Mars, some variation of these calculations will need to be applied as well, lest users on the ground get lost in the red dust.

At some point – maybe not soon, but someday – humans may live on Mars and will need to synchronize their clocks with those on Earth. Until then, it shouldn’t be too difficult, relatively speaking.