– guest-blogged by W. Kevin Vicklund
A little over four years ago, Ed blogged about a possible new explanation for how the dinosaurs went extinct (a second impact, in this case). A month later, in late December 2006, a guy named John L. posted a link to a crackpot alternative explanation (the author is a John Stojanowski, so it seems likely they are the same person). The argument was that Pangaea would have reduced gravity so much that the dinosaurs were able to grow to their immense sizes, and that the break-up of Pangaea killed off the dinosaurs because gravity returned to normal levels. Led by yours truly, the readership of Dispatches demolished the arguments put forth by John. Even ridiculously assuming Pangaea was covered primarily by plateaus towering 9 km over the livable surface, the most generous calculations showed that Pangaea could only have reduced gravity by 1%. In order to get the type of reductions John was requiring, Pangaea would have had to been a ball compressed to the density of the surface of a neutron star!
I recently found out that John decided to alter his explanation, suspiciously right after getting his tail whipped here.
More precisely, while not completely giving up on his original explanation, he added another component. The following is an excerpt from John’s addition:
The shift of the Earth’s solid inner core or both the solid inner core and the liquid outer core must be considered. With the consolidation of the continental land masses on a relatively confined surface area of the Earth, a shifting of the core away from Pangea within the equatorial plane could account for a lowering of the surface gravity of Pangea.
The shift of the core would act to maintain the center of mass of the Earth at its axis. … A rough estimate of the change in the gravitational force can be made using Newton’s Universal Gravity Law: W=GMm/r2 … Using a core-shift of 1000km would result in a ratio of about .75 (i.e. the weight of an object with the core-shift would be 75% of that without it at the equator) ignoring other factors. Again, this is only a crude estimate because the assumption being made is that the Earth’s mass is all concentrated at a single point.
Where does he get his value for the core-shift from? It appears that he pulls it out of thin air, simply choosing a value that allows his argument to work. But if you want to use a core-shift as an explanation for why the dinosaurs went extinct, you can’t simply assume it happened. You need to have a reason for why it happened. What would cause this core-shift, and what would the magnitude of the core-shift be?
John does answer the first question. The core-shift, according to him, is to counter the concentration of Pangaea’s mass, such that the center of mass remains at its axis. From his wording, we can ignore the effect of the mantle and assume that the radius of the Earth remains constant. What John is arguing, therefor, is that the core and Pangaea will form a barycenter where the center of the equatorial circle at sea level is. This is actually a fairly reasonable assumption.
If we know the masses, we can calculate the new distance between Pangaea and the core. Let’s call that distance ‘a’ and the distances from Pangaea and the core to the barycenter rp and rc, respectively. Using the same subscripts for the masses, we get the following relationships:
a = rp + rc
a = rp * (1 + (mp/mc)
Note that the ratio of radii about the barycenter is inversely proportional to the mass. We can plug in real numbers for the masses (Note: mass for Pangaea taken from previous thread and is about 12 times more massive than all of the modern continents combined):
mp = 4.05 x 10
mc = 1.16 x 10
mc = 1.83 x 10
a = rp * (1 + 0.035) OR rp * (1 + 0.0022)
In other words, if just the inner core shifts, the distance from the core to the barycenter is just 3.5% that of the distance from Pangaea to the barycenter (and only 0.22% if the entire core shifts). If the radius of the Earth remains the same (leading to a core-shift of 224 km), without taking into account any other effects, this would mean the gravity at Pangaea’s surface would be reduced by at most 6.6%. Even coupled with the most favorable calculations from the previous thread, the maximum reduction would be about 7.5%, much less than what John requires for his argument. To get that total increase in distance of 1000 km, the radius of the Earth would need to increase by 741 km – more than 11%. Obviously, this would have to create a bulge on one side, rather than an overall increase in diameter. Such a large bulge is physically impossible in an object of that size. It would shatter the Earth.
When you start adding in other effects, such as the mantle (which would shift to fill the void left by the core), the reduction in gravity gets lessened significantly. For instance, the inner core makes up less than 2% of the mass of the Earth. That means that the effect on gravity would remain unchanged – or rather it would shift slightly towards Pangaea, tending to increase gravity. The net effect would still be a lessening of gravity, but one slightly less than 2% of what you would calculate from the core and Pangaea alone. Or a decrease of about 0.07% (this number is the same for the entire core, due to the geometry).
The core problem with all of John’s arguments is that he fails to understand how puny Pangaea is compared to the Earth. It simply is not large enough to have any effect much larger than 1%, even under assumptions bordering on absurdity.