Friday, November 30, 2012

How many hours were in a dinosaur's day?

Real dinosaurs lived in a world that would have been different to ours in more than the obvious ways.

The 24-hour clock is locked into our mammalian biology, our technology and our culture. But it hasn't always been that way.

The length of an Earth day has been increasing slowly throughout most of the Earth's 4.5-billion-year history, says Dr Rosemary Mardling, mathematical scientist at Monash University, and it all has to do with the Moon.

"The reason is that the Moon is attempting to slow down the spin of the Earth. The Earth was spinning very much faster when the Moon was formed," says Mardling.

Back when the Moon was formed the length of an Earth day was a very brief two to three hours, and a much closer Moon was orbiting the Earth every five hours.

So how did the Moon slow us down? It has to do with gravitational force and the transfer of angular momentum.

"If someone was sitting on a chair that could spin and you tried to slow them down with your hand, they would slow down a little bit and you'd be flipped around a bit. You'd get some angular momentum."

And that's what is happening with the Earth-Moon system. Much like the hand interrupting the spinning chair, the gravitational pull of the Moon exerts a force on the Earth that transfers angular momentum from the spin of the Earth into the orbit of the Moon.

"In doing so, the Earth slows down a little bit and the Moon moves away from the Earth," says Mardling.

We can measure the speed of the Moon's retreat — reflective panels on the Moon allow for fine calibrations that show that it's currently moving away one to two centimetres a year.

We also know that the spin of the Earth is slowing.

"The spin down rate is very slow," says Mardling, "It's about two milliseconds per century. So the Earth's day is getting longer by a 500th of a second every century"

In the time of the dinos

So would the day length during the age of the dinosaurs have been 21 hours?

"The dinosaurs were around 100 million years ago, which at the current rate [of day lengthening] adds up to 2000 seconds, which is less than an hour."

But while the lengthening of the day adds up, "the spin down rate was probably greater in the past," she adds.

Geological evidence for increasing day length can help us pin this time down more accurately. Tidal records laid down in ancient estuaries can show daily, monthly and seasonal cycles in alternating deposits of sand and silt. They indicate that 620 million years ago the day was 21 hours, says Mardling.

Since the dinosaurs lived during the Mesozoic era, from 250 million years ago to 65 million years ago, day length would have been longer than 21 hours and probably closer to 23 hours.
At that time the Moon would have been closer to the Earth too. So the world the dinosaurs lived in would have been different to ours in more than the obvious ways, she says.

Earthquakes and day length

Significant earthquakes can also affect the length of the day, but only very slightly.
They do so be changing the Earth's "moment of inertia" which describes how mass is distributed inside the Earth. The principal of conservation of angular momentum means that a change to the moment of inertia results in a change to the spin rate.

"Imagine the Earth is made of lots of little bricks. You can measure the position of each brick and its position from the rotation axis of the Earth. If you squared that distance, multiplied it by the mass of the brick and then you added it all up over all the bricks, you would get the moment of inertia.
If you move the bricks around a little bit you get a different answer, and that's what can happen during some very large earthquakes.

The future

The Moon and Earth's celestial dance theoretically will take billions of years to end.

"This process finishes when the length of the day is the same as the length of the (lunar) month," says Mardling, who once worked this out to be around 45 (current Earth) days.

This means that the Moon will take 45 days to orbit the Earth and the Earth will take 45 days to complete a rotation that currently takes 24 hours.

"At that point the Earth will always show the same face to the Moon, as the Moon already does to us."

This will occur when the Moon has "spun down" the Earth, says Mardling.

"We spun down the Moon a long, long time ago because it is so much less massive than the Earth".
"However", says Mardling, "it's such a ridiculously long time away that by then the Sun will have become a red giant."

And if humans are still around then we'll have bigger things to worry about than day length.

Dr Rosemary Mardling is a senior lecturer at Monash University's School of Mathematical Sciences. She studies the dynamical evolution of stellar and planetary systems. Dr Mardling spoke to Kylie Andrews.

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