# How have the duration of the martian day changed in the past?

There is a panspermia theory which claims that life might have begun on Mars and I currently read a post that the human circadian rhythm is closer to the martian day length (about 25h) than the day length of Earth. I know from cave experiments that human circadian rhythm is much more complicated, but let's ignore that part and try to disprove this day length theory with physics.

I know from wikipedia that

A century ago, the average day was about 1.7 milliseconds shorter than today,[1] while in the late Neoproterozoic about 620 million years ago a day had only about 21.9±0.4 hours.

So the days on Earth slowed down significantly in the last few billion years. If this slowing down is constant, then about 4 billion years ago (when life began) a day was 10.5 hours long. I tried to find similar data about Mars, but had no luck. Can anybody help?

• Wow! It's interesting! What is all this thing? Is our planet rotating around itself more slowly as the time passes? Why? What is the physical explanation? If the angular velocity decrease, the momentum of inertia increases, for keeping the angular momentum constant. So, does the Earth become bigger in radius? I read sometime that the Earth become more flat, s.t. the equatorial radius increases. But, won't you tell us more details? – Sofia Dec 26 '14 at 22:54
• That the human circadian rhythm is longer than a human day has probably something to do with the theory of synchronized oscillators. It's much easier to synchronize an oscillator by reset than by phase comparison, but for that the oscillator has to run slightly slower than the synchronizing signal. That's a guess, of course, and I would leave it to the biologists and biophysicists to fill in the blanks. The slowing of the planet is not constant, it was much faster in the past when the moon was much closer and the tidal coupling much stronger, but you are roughly in the right ballpark, anyway. – CuriousOne Dec 26 '14 at 22:54
• @Sofia: The angular momentum is constant, but the moon is slowly moving away. This tidal coupling won't stop until the day will have the length of one month and both the moon and the earth will be tidal locked. In reality the sun will go trough its red giant phase first and destroy both before that happens. – CuriousOne Dec 26 '14 at 22:56
• @CuriousOne: Brrrrr! Our Sun will become giant red? And what about us? Where shall we go, given this curse of being limited to the light velocity? 4 light years distance to $\alpha$ Centauri. And who says that it has habitable planets? Aaaaaau! This is why I asked if there is some chance that Asimov's "jumps" be true. – Sofia Dec 26 '14 at 23:08
• @CuriousOne The gradual eating of the Sun means the Earth will be uninhabitable in only one billion year ;) – Thriveth Dec 27 '14 at 2:22

It's easier to dispel this with biology and geology than with physics.

That our circadian rhythms are 25 hour long is based on research done in 1962 that was later found to be faulty. For more recent research, see, for example, Czeisler, et al. (1999), "Stability, precision, and near-24-hour period of the human circadian pacemaker," Science 284.5423 : 2177-2181 and Wright, et al. (2001) "Intrinsic near-24-h pacemaker period determines limits of circadian entrainment to a weak synchronizer in humans," Proceedings of the National Academy of Sciences 98.24 : 14027-14032. The human circadian rhythm is very close to 24 hours long.

There are a number of records throughout the ages of the variation in the length of day on Earth, many of which were biological in origin. Since Wells (1963), "Coral growth and geochronometry," Nature 197 : 948-950, scientists have looked for and found a number of tidal rhythmites in rock formations that exhibit two or more of daily variations, monthly variations, and yearly variations. These rhythmites are the primary evidence for the secular variations in the length of day. Many of these tidal rhythmites are corals. Corals were well-adapted to the < 23 hour long day in the Carboniferous, just as they are well-adapted to the 24 hour long day today. Evolution has resulted in dinosaurs, birds, and mammals since the Carboniferous. Is it any surprise that evolution has adapted to the 1+ hour increase in the length of day since then, or the changes in the length of day that precede the Carboniferous?

What about length of day on Mars? Mars is dead, and has been for a long time. It has no biology, no plate tectonics, no oceans, no tides. There are no records of the variation in the length of day on Mars. There are only simulations, and simulating beyond a few multiples of 50 million years (the Lyapunov time of the solar system) is always a bit dubious.

• Mars is dead? No biology? But I heard that water was found on it. It has also an atmosphere, hasn't it? Though, it is dead? Water and atmosphere generate life. Don't they? And what are those simulations? What is that? – Sofia Dec 27 '14 at 11:43
• I understood that Mars is the 1st candidate for "terra-forming". – Sofia Dec 27 '14 at 11:45
• @Sofia - The strong consensus view is that Mars is dead and has been for a long, long time. Water in solid and gaseous form exists on Mars. Water in liquid form? Mars is too cold and its atmospheric pressure is too low. There are some claims of intermittent flows of liquid water on Mars, but these are highly contested. – David Hammen Dec 27 '14 at 12:52
• it is so interesting what you say. I would give you much more than 1 point if the system would permit. – Sofia Dec 27 '14 at 13:18