Galileo's Pendulum

How did the sauropods—the long-necked dinosaurs like Apatosaurus, Brachiosaurus, and Diplodocus that grew to be the largest land animals that ever lived—get so huge? The full answer to that question is complicated and interesting, involving a lot of science I don’t know. Come to think of it, the true answer involves a lot of physics I don’t know: calculating the compressive strength of bones, the fluid dynamics involved in getting blood from the heart up to the head, and so forth. So, I’ll leave unabashed sauropod snuggler Brian Switek to talk about the biological and reproductive aspects of the big dinosaurs, and address another hypothesis: that Earth’s gravity was noticeably weaker in the Mesozoic Era, the Age of Dinosaurs.

I first read about that hypothesis in Brian’s book, My Beloved Brontosaurus, but despite my intentions, I didn’t follow up until a series of tweets from baseball player Jose Canseco received widespread mockery last week. Here’s a sample of what Canseco posted to Twitter:

Gravity had to be weaker to make dinosaurs nimble

— Jose Canseco (@JoseCanseco) February 19, 2013

My theory is the core of the planet shifted when single continent formed to keep us in a balanced spin

— Jose Canseco (@JoseCanseco) February 19, 2013

The land was farther away from the core and had much less gravity so bigness could develop and dominate

— Jose Canseco (@JoseCanseco) February 19, 2013

It’s easy to mock Canseco for saying things like that, but let’s face it: every report, every column, every mockery only made fun of him without explaining what’s wrong with what he wrote. (Think of this post as my personal atonement for having done that.) While Canseco, based on his hostile response to Bill Nye, doesn’t seem to understand that scientific theories require evidence to back them up, some scientists had proposed weaker gravity as an explanation for big dinosaurs. Knowing why those scientists—and Canseco—are wrong is important. The question “how do we know Earth’s gravity didn’t change radically over 100 million years?” is a variation on the most important question we can ask about science: how do we know what we know?

Some preliminaries

I’m not sure exactly how much weaker gravity must be in either Canseco’s or the other hypotheses. We don’t need to be as extreme as Canseco thinks, though: he states the weight of Supersaurus to be about 200 tons. Current estimates place it closer to 40 tons: it was a pretty slender beast compared to its length! (In fairness, 40 tons is hardly skinny: the record-setting male African elephant was about 11 tons. Sauropods were still big animals.) To quote Brian, “Sauropods were weird from snout to tail.”

For the sake of argument, however, let’s assume the largest land mammal was as big as any animal can get: the 20-ton Paraceratherium, which lived in the Oligocene (about 23-34 million years ago). This is consistent with some earlier estimates, which means that gravity in the Jurassic Period (when Supersaurus lived) must have been about half what it is today, or something else must have been going on.

The weight of evidence (ha!) is that sauropods could and did get that big, not because of lower gravity or higher oxygen content, but because of their reproductive strategy. They were lighter than earlier scientists thought because they were very bird-like in bone structure and respiratory system, allowing them to survive under normal gravity and oxygen levels. Having started the discussion of weaker gravity, though, let’s carry it through to the end.

(Note: I still haven’t determined the source where weaker gravity is proposed, so I’m inferring its arguments from later papers. It’s evidently discussed in a later paper on the theoretical maximum size any mammal could be, but this one is unavailable to me without the appropriate academic credentials. However, here’s the citation: Economos, AC. The largest land mammal. Journal of Theoretical Biology. 1981; 89:211–215 .)

The gravity of the situation

Earth’s gravity—as with any planet, star, moon, asteroid, etc.—is determined primary by its mass and size. Mass is (roughly speaking) the amount of matter in the planet, and that’s something hard to change drastically: if you wanted to make gravity noticeably stronger, you’d have to add the equivalent mass of another planet or moon, something that can’t just happen spontaneously. While Earth is constantly being bombarded by tiny asteroid fragments and dust grains, and is also losing small amounts of its atmosphere to space, neither of those effects is very big. To my knowledge, nobody has proposed the idea that Earth was lighter in the past as a solution to dinosaur size anyway, so let’s leave it alone.

A somewhat more reasonable idea is that Earth shrank. (Again, Canseco didn’t propose this idea, so please don’t take this as a strawman argument. I’m covering many possibilities to be thorough!)  When Earth formed, its was molten rock, a completely different planet than it became subsequently. As it cooled and solidified, it would have contracted, shrinking by a noticeable degree. We see effects like that on the Moon and Mars, where the dramatic canyon Valles Marineris may have formed when the crust fractured, then grew bigger via erosion.

However, there are two strikes against that as an explanation. First, while the 65 million years since the last dinosaur is a long time by human standards, Earth has been around 4.5 billion years. The cooling-down period ended long before the colonization of land by animals, which itself happened long before the first dinosaur. The second problem is that, to double Earth’s gravity between Supersaurus and today, Earth would have had 1.4 times the diameter in the Jurassic. While that doesn’t sound like much, it translates to twice the surface area and nearly three times the volume of modern Earth. That’s a much bigger planet! (For the details of this calculation, see the note at the end of the blog post. For more about gravity, see my post on Le Petit Prince and the inverse square law.)

Blue plate tectonic special

Earth isn’t a perfectly smooth sphere, and its composition varies somewhat from place to place. That means both the density of rock and the gravitational force vary slightly around the planet. It’s not a huge variation, but it’s measurable and important if you work in a field where knowing precisely what direction is “down” is important. (To wit: if you’re trying to design a water system for a city, you’d better know how gravity will affect the flow of water, or else you might end up with stagnation or low pressure.)

A pair of satellites called GRACE (Gravity Recovery And Climate Experiment) flew in tandem around Earth, mapping tiny variations in Earth’s gravity. The result is a diagram called a geoid, one version of which is shown at right. In some places—such as the Himalayas, Andes, and ridges in the north Atlantic—the concentration of rock is much higher than normal, making the gravitational force that much stronger. Notice, though, that these spots don’t correspond exactly to continents, though they do correlate strongly to young mountain ranges (whether above or below water). Despite the appearance of the geoid, though, these fluctuations are pretty small, measured in tens of “milligals” or “milligalileos”. The average gravitational strength is 981 gals, so 50 milligals (0.05 gals) is relatively tiny.

During the Jurassic period, the continents had just broken apart from Pangaea, the supercontinent encompassing most of the land in the entire world. That meant that most of the landmass on Earth was still concentrated in one hemisphere. In his tweets, Canseco conjectured that this land concentration actually shifted the position of Earth’s core in compensation. A moment’s thought lets us dismiss the “compensation” argument: if the location of the continents made such a difference, wouldn’t it result in increased gravity rather than reduced? However, let’s take the hypothetical results at face value.

Earth’s interior is strongly differentiated, meaning that below the surface (the crust) there are distinct layers. The mantle is a region of rock heated until it behaves like plastic: mostly solid, but capable of flowing like a liquid under high pressure. The core consists of two regions: the molten outer core (made largely of iron and nickel) and the solid inner core. The temperatures are highest at Earth’s center, but because the pressures are also highest, the inner core stays solid, much like you can heat water far beyond its boiling point in a pressure cooker. To move that core around would require rearranging Earth’s interior pretty drastically. The crust is no more than 50 kilometers (30 miles) thick at most, which sounds like a lot until you realize that Earth’s average radius is 6371 kilometers. (I say “average” because Earth isn’t a perfect sphere.) Even with a relatively high concentration of crust on one side of the globe, you couldn’t shift the core very much: the forces aren’t strong enough.

The truth is that Earth’s tectonic plates, on which the continents rest, are always in motion, rearranging themselves very slowly over tens of millions of years. Yet the Moon reliably orbits, which wouldn’t be true if plate tectonics made a huge difference to Earth’s gravity. In fact, there’s another sign Earth’s gravity hasn’t changed much in the last 100 million years: the Moon is actually moving away from Earth, albeit very slowly. If Earth’s gravity had doubled since the time of the sauropods, we would expect the opposite effect.

So?

Admittedly, this may seem like using a sledgehammer to crush a gnat. I’ve expended a lot of words and diagrams to combat a few short tweets from a baseball player, which he may or may not have thought very carefully about. However, as with many far-out “what if?” ideas, the real answers are known by science, and can be tested. Canseco, to his credit, did hypothesize something that’s testable; that his ideas are wrong doesn’t make him any worse than many others who have postulated such things over the centuries. While it’s doubtful he’ll read either my post or Brian’s companion post on sauropod anatomy, the answers are out there, if he wants to know. Inquisitiveness is part of science; being open to new knowledge (and I certainly learned a lot writing this post!) allows us to move from naive speculation to a deeper understanding of our world.

Notes on the physics

The strength of gravity at the surface of Earth, which tells how much a falling object accelerates, is determined by Newton’s law of gravity:where g is the acceleration, G is Newton’s constant (just a number that tells us the strength of gravity), and R is Earth’s radius. If we assume Earth’s mass stays the same, for the reasons I mentioned earlier, then changing gravity is a matter of changing Earth’s size and/or its shape.

Let’s consider a change just in size first, so Earth maintains its spherical shape. What we care about is the ratio of gravity now to gravity then, and what that means for the change in size:If gravity now is twice what gravity was then, the ratio is 2, and the radius then would have to be √2 = 1.41 times larger than Earth’s radius today. Earth’s surface area goes like the square of the radius, soIn words: double the gravity now implies double the surface area of the planet then.

If Earth’s mass isn’t distributed evenly, as in the Canseco conjecture, we can still use Newton’s law of gravity, adding up the effect of all the bits of mass to get the net effect at a position on the surface. (That’s a large part of the construction of the geoid I mentioned earlier.)