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A blog devoted to science and reason
Written after a glass or two of Pinot Noir.

Saturday, July 6, 2013

Getting Crankier

Mr. Anonymous, who may or not be John Stojanowski, left two comments on my recent post, Feeling Cranky. To recap, Mr. Stojanowski has a hypothesis that the dinosaurs became extinct because the gravitational field of the Earth increased and that increase was caused by movement of the Earth's core accompanied by the shifting of the planet's crust.

The first comment:

Notice how he slyly calls into question my credentials, but I'll let that go. I do know how angular momentum works, and I seriously question Mr. Anonymous's understanding, not just of angular momentum, but of the meaning of the word latitudinally.

Watch this animation of the spreading of Pangaea.

There seems to some movement of the underlying tectonic plates northward and southward (latitudinal motion), but the greatest change in seen longitudinally; that is eastward and westward.

Be that as it may, let's examine our understanding of angular momentum which is conventionally denoted not by AM but by
Angular momentum is conserved, that is, it stays the same, when there are no unbalanced torques acting on the object. Mathematically it can expressed thusly,
Here's an excellent example of this principle. 

Here when the figure skater starts her spin she is spinning relatively slowly.  Then as she pulls her arms and leg in, she spins much faster. The Greek letter omega in the equation above represents the spin rate. The I in the equation is called the moment of inertia and describes how the mass is distributed around the rotation axis.  When the skater pulls her arm in, she is distributing her mass closer to the spin axis, and her rotation rate increases. There's no "compensating action." 

I can show with a simple model how the spreading of Pangaea could affect the length of the day. First, let's suppose the entire supercontinent is located at the equator. Second, let me suppose that the continental crust is now uniformly distributed across the globe. [Note: those simplifications are not necessary; they just make the work relatively easy to follow and make the calculations possible to do in a minute or two.]

Now here's the data (1):
Now we can plug in all the numbers and calculate what the Earth's the rotation rate should have been 250 million years ago.

You can see that the rotation rate is less than it is today by a factor of 0.995.  We conclude then that that day should have been 1.005 times longer than now - about 7 1/2 minutes.

Oops.  We know that 350 million years ago, one day lasted less than 23 hours.(2) Mr. Stojanowski's angular momentum hypothesis disastrously gives the wrong direction of change.

By the way, Mr. Anonymous, I am not a geologist, so can you explain what effect your oscillating core would have on the convection currents in the mantle, and what effect those changing currents would have had on driving plate tectonics?

The second comment:

Again with questioning my credentials. Oh well. Rotational dynamics is usually covered in an undergraduate third year classical mechanics course. All physicists learn early in their career how to do physics in a rotating reference frame.  Here's what we derive, essentially Newton's 2nd law in a rotating reference frame.(3)
One consequence of this is that the Earth is not spherical, but it bulges outward at the equator, and we drop something it drops straight down, perpendicular to the Earth's Surface.  However, straight down is not the same as pointing to the center of the Earth.  

Mr. Anonymous is curiously unaware of the size of the Earth's rotation rate.  He appears to say that the Earth has a high spin rate. As I can show from Newton's 2nd Law, the rotation of the Earth has about a 0.05% effect. The gravitational field is about 0.05% larger at the poles than it is at the equator.

If Mr. Anonymous cares to respond again, perhaps he would be so kind as to provide some mathematical and physical details. I think I'm qualified enough to handle them.

1. The numerical data can be found in any physics, astronomy, or geology book with the exception of the continental mass.  That estimate comes from Mass and Composition of the Continental Crust Estimated Using the CRUST2.0 Model Peterson, B. T.Depaolo, D. J., American Geophysical Union, Fall Meeting 2007, abstract #V33A-1161.  Any introductory physics text will have a chapter or two on rotational dynamics at this level.
2. See for example, this article at Scientific American.
3. For those you have completed an introductory calculus-based physics sequence, as well as a differential equations course, see a standard classical mechanics textbook such as Symon's Mechanics, or Thorton and Marion's Classical Dynamics of Particles and Systems. Graduate level students can consult Goldstein's Classical Mechanics.


  1. Noticed a typo,
    "... at the equator, and we we drop something ..."

  2. I will give Mr. Priest credit for responding to criticism of his earlier posts.

    The Scotese animation of Pangea’s breakup and dispersal is interesting and Mr. Priest’s statement that the greatest change is longitudinal and not latitudinal is correct, but is not germane to the discussion. Only the latitudinal movement is relevant to angular momentum (which I will refer to as “AM”).
    Note that the latitudinal movement during the breakup of Pangea was considerable. India was a subcontinent at the southern tip of Africa which rapidly moved to its current location. Australia moved northeast. South America rotated counterclockwise away from Africa and moved northward until it was positioned beneath the equator. Africa moved north colliding with southern Eurasia forming the mountain chains found there.

    But again, the latitudinal movement of Pangea, and its remnants, during the past 350 myrs is what is important, not just the dispersal movement after its breakup.

    The latitudinal movement of Pangea, during its consolidated state and afterward as discrete, separated continents has been documented in a recent research paper entitled “Plate tectonics may control geomagnetic reversal frequency.” Charts within this paper clearly illustrate how the center of mass of Pangea, and of the subsequent discrete continents, moved substantially below and above the equator during the last ~350myrs. I will refer to this paper as the CNRS study.

    The question originally asked was what would compensate for the major latitudinal movement of Pangea in order to conserve the Earth’s angular momentum.

    Regarding the skater, by pulling her arms in, moves mass closer to the spin axis, as Mr. Priest states. There is a “compensating action”; it is her increase in angular velocity which compensates for the mass movement toward the axis of rotation in order to conserve AM.
    When Pangea’s center of mass moved north and south of the equator, per the CNRS study, mass also moved closer to the Earth’s axis of rotation. However the “compensating action” was not a change in the angular velocity of the Earth (i.e., a shorter day), as it is for the skater; it was the displacement of the core elements, an action which would increase the Earth’s AM to balance the reduction of AM from Pangea’s center of mass moving closer to the spin axis as it moved to a higher latitude.

    If the Earth’s interior were “rock solid”, incapable of any deformation, then the Earth’s angular velocity would have to increase as Pangea moved to higher latitudes. Since the CNRS study indicates that Pangea, and its remnants after breakup moved several times to high latitudes during the last 350 myrs, and there is no evidence that the Earth’s length of a day corresponded to those movements, it is safe to assume that something other than angular velocity was the “compensating action.”
    Note that the length of a day has been gradually increasing over the last 350 myrs due to the movement of the moon, which is moving away from the Earth, stealing AM. This is not related to the current discussion.

    Continued in next post

  3. Mr. Priest attempts to calculate the purported change in angular velocity of the Earth due to the breakup and dispersal of Pangea. His assumptions in his calculation are:
    1. Pangea’s center of mass was located on the equator 250 myr.
    2. Today, the continental crust is distributed uniformly across the globe.

    Based on the above assumptions, in both cases, the center of mass of continental crust is on the equator. Therefore, the moment of inertia in both cases must be the same, meaning the angular velocity must also be the same to conserve AM.

    I am not a geologist either but the effects of oscillating core elements is apparent in geological history. All major flood basalt volcanic eruptions (e.g., Emeishan Traps, Siberian Traps, Deccan Traps, CAMP and others) occurred when Pangea’s center of mass moved toward the equator (per the CNRS study), and therefore, according to the theory, the core elements moved back toward Earth centricity. Vincent Courtillot, in his book ‘Evolutionary Catastrophes’, points out that a major extinction coincides with just about all massive flood basalt volcanic eruptions. The theory being discussed posits a pulse of increasing surface gravity is the primary cause of those extinctions resulting from the core elements moving toward Earth-centricity.

    Regarding the response to the Second Comment, I’m confused. Yes, surface gravity at the poles is less than at the equator based on difference in distance to the Earth’s center of mass. This is evident from the inverse square law (relative to distance) postulated by Newton. It’s exactly why surface gravity on Pangea changed when the Earth’s core elements moved off-center and away from Pangea, moving the Earth’s center of mass further away from Pangea.

    1. Here you go. http://oenobareus.blogspot.com/2013/07/getting-crankier-part-2.html

  4. So, the reason dinosaurs are were so giant was because of the gravitational pull of the earth was different 250 years ago than today?

  5. At times, surface gravity was lower on Pangea. But specifically, at 250 Myr, surface gravity rapidly increased to near current values as Pangea's center of mass crossed the equator (see CNRS study mentioned earlier).

    When Pangea's center of mass crossed the equator, the Earth's core elements would have returned close to Earth-centricity, near where they are today. The theory we are discussing attributes the primary cause of the mass extinction 250 Myr (The Permian-Triassic Extinction) to this increase in surface gravitation.