Mass Extinction, an Old Explanation

Apparent Periodicity of Mass Extinctions

The Earth orbits around the Sun, once every year.   It follows an orbit that is very slightly elliptic, currently described as being 0.016.   That means that when the Earth is farthest from the sun (in early July) it is about 1.6% farther than its average distance from the Sun, and when it is nearest to the Sun (in early January) it is around 1.6% closer than average.

The Earth's orbit is considered rather circular, with this value of eccentricity being small.   But still, in January, we are around 3.2% or almost 3,000,000 miles closer to the Sun than in July.

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The amount of energy we receive from the Sun depends on our distance from the Sun, in what is called the inverse-square law (of Newton). This 3.2% difference in our distance (1.032) from the Sun in January and July therefore represents about 6.5% difference (1.0322 or 1.065) in the amount of heat we receive from the Sun.   (Interestingly, more in Winter in the Northern Hemisphere!)   The Earth has to stay close to a thermodynamic equilibrium over any period of time.   This means that the Earth must warm up so that it can radiate off into space the same average amount of heat it receives.   Otherwise, the entire Earth would heat up or cool off!   But over countless centuries, the Earth has gotten to the equilibrium of having an average temperature of around 59°F or 15°C.   It is possible to figure out how much radiation is sent out into space using the Stefan-Boltzmann law:   Radiation given off is equal to σ * area * temp4.   σ is the Stefan-Boltzmann constant, 5.67 * 10-8 watts/m2/K4.   The temp given above is 288°K.   The total area of the Earth is about 1.3 * 1014 m2.   This gives about 5 * 1016 watts/second as the (average) total amount of radiation the Earth gives off to space.   This value is in basic agreement with the amount of energy the Earth receives from the Sun.   The Earth actually intercepts about 1.8 * 1017 watts/second of the Sun's energy, around 3 times as much, but some of that energy from the Sun is immediately reflected back out into space and is therefore never in the Earth's energy accounting.

We can then easily see how much the average temperature of the Earth would need to change regarding maintaining a difference of 3.2% different distance (as we now experience between Jan 3 and July 3).   We know from above that we receive about 6.5% different total amounts of energy from the Sun, so we must account for that (by a different average Earth temperature).   The fourth-power effect is used to show fairly easily that the temp must be different by a factor of the fourth-root of 1.065. This (1.0651/4 = 1.016) results in an average Earth temp being about 4.6°C or 8.2°F higher on January 3 than on July 3.   (1.016 * 288°K = 292.6°K, a difference of 4.6°K or 4.6°C.)

It turns out that the Earth is so large and massive, and heat does not flow through its materials very fast, so in just 6 months, the entire Earth does not change in average temperature by that much.   But an interesting observation is that living in the Northern Hemisphere quite possibly has less annual temperature variations as compared an identical location in the Southern hemisphere.   Down there, the winter (July) is colder because of the tilt of the Earth's axis, but also because we are then farther from the Sun, which might easily represent another few degrees of annual difference!

It might seem like a reasonable assumption that the eccentricity of the Earth's orbit would stay constant.   It does not!

There is a very powerful method of mathematical analysis called a Fourier Analysis. When a lot of accurate data has been collected for ANY measurement which might vary over time, a Fourier Analysis is done to that mass of data. The result of a Fourier Analysis is a series of mathematical terms called harmonic terms. They each have either a sine or a cosine as part of the value of that term.

Each resulting term also has an "amplitude" which describes how large the effect is of that term.

Say that there was a Fourier Term that had the cosine term being of a period that was around 780 days, in an analysis of the long-term eccentricity of the Earth's orbit. An astronomer would consult a book and notice that Mars has a "synodic period" (the period from when it seems to be in the same position in the sky when compared to the position of the Sun, as seen from Earth. That Fourier Term would therefore be judged to be due to the effect of Mars, whether the details were known about how that might occur or not.

Many Fourier Terms are of relatively short periods, and of small amplitude, and they are generally quickly identified and associated with some causing planet or satellite or even asteroid.

However, there are also some very long-term Fourier Terms in such an eccentricity analysis. Some rather obvious ones are where the orbital eccentricity, which is currently 0.016, will reduce for around another 24,000 years, at which time it will be around 0.003, extremely circular. After that, the eccentricity will increase for around another 40,000 years, where it will again eventually approach its absolute maximum of 0.070.

Here is a graph that was generated based on a Fourier Analysis of data regarding the Earth in its orbit. Note that the Eccentricity of the Earth's orbit changes a lot and in somewhat complicated ways! Today is at the left hand side of this graph, with "KYR BP" (thousands of years Before the Present) going to the right.

A Milankovitch graph of Eccentricity of the Earth's orbit The Fourier Analysis is so powerful that, as long as there is enough data and it is accurate enough, we can know such things will certainly occur! And, that they have occurred in the past. If we extrapolate back toward the past, we find that around 960,000 years ago, the Earth's orbit had a very high eccentricity, roughly that 0.070.

Well, do you really care? You might! Consider 960,000 years ago. The Earth was then about 15% closer to the Sun at one time of the year as compared to the opposite. The Sun's radiation (and heat) goes as an inverse square law, which means that there was around a 32% difference in sunlight heating between summer and winter. That is huge! (Distance varies from 0.93 AU to 1.07 AU, which is a change of 15.1%. Energy from the Sun goes as the square of the distance, so we must square 1.151, and get 1.32, a 32% difference in received radiation. With the Earth then receiving 32% different, it must heat or cool such that it can radiate approximately that new amount into space, to maintain a (meta-)equilibrium. We know from above that the Stefan-Boltzmann Law indicates that the Earth's average temperature must differ by the fourth-root of that difference of radiation. So we need the fourth root of 1.32, which is 1.073. We then multiply this by the (approximate) temperature in Kelvin (288°K) and get 308.9°K. This tells us that there would be a 20.9°K difference in the Earth's average temperature if the Earth had long enough to get to equilibrium [308.9 - 288 = 20.9]. A temp difference of 20.9°K is the same as 20.9°C or 37.7°F.)

Following the procedure described above (fourth-root), we have found that the perihelion equilibrium Earth average temp would be 20.9°C or 37.7°F higher than at aphelion six months later! That is an enormous difference, and it would have tremendous effects on all living creatures.

There are some complicated issues related to the earth's Precession (like a gyroscope), but the summer and winter associated with the Earth's tilted axis (and seasons) could sometimes match up with the huge eccentricity change and sometimes oppose it (depending on which hemisphere you happened to be in!). The AVERAGE DAILY temperature difference between summer and winter in mid-latitudes (like where the USA is now), in the BAD hemisphere, might have been well over 100°F (maybe 65°F difference as we might now experience it due to the tilt of our axis, and another 38°F difference due to the perihelion-aphelion difference due to the large eccentricity. A summer day might average 105°F (instead of the current 85°F) and sometimes get up to 150°F. Six months later, a winter day might average -0°F (instead of the current 20°F) and dropped down to -50°F at night.

Would that qualify as a tough life? Wow! It is pretty understandable that virtually all of really ancient human artifacts seem to be fairly close to the Equator in Africa. Only in relatively recent times were areas like Europe, Asia and North America even reliably survivable in either summer or winter!

It is interesting to note that being in the opposite hemisphere from what we have just discussed would be far better! Instead of the current 85°F average for a summer day, it might be around 65°F. Instead of the current 20°F average for a winter day, it might be around 40°F. Survival might easily depend on which hemisphere a creature happened to be in (unless it was near the Equator where there is less normal seasonal difference.)

This discussion has not actually been about any mass extinction. But it has also only been about a brief moment in the Earth's history, 960,000 years or so. Looking at the graph above, we can see that there were similar period around 100 Kyr, 200 Kyr, 300 Kyr, 600 Kyr, etc periods in the Earth's recent past. The accuracy and quantity of the collected data regarding the Earth's orbital eccentricity limit us from knowing accurately any terms that might involve millions of years, but they might equally have even larger amplitude values, so that the eccentricity over millions of years could conceivably vary by even more than we know about in these time periods described.

The kinds of temperature ranges suggested above would be tough on the survival of almost any animal or plant. Worse, if an animal found the cold too unbearable, or the hot too unbearable, it might have tried to migrate to a more temperate region, only to have found it even worse.

As more and more accurate orbital data is measured, the possibility for generating more and more accurate Fourier Analyses will come along. We may some day see very, very long term perturbations such as these, which have amplitudes enough to cause true mass extinctions.

Note: all of the other orbital parameters of the Earth also continuously vary, and Analyses are done on them, too. We have not included them in this discussion because those other orbital elements do not drastically alter the overall world climatic conditions like the eccentricity does. They certainly affect localized climates.

A man named Milankovitch had thought of the basics of this around seventy years ago. His ideas were based on even earlier ideas along the same lines. Much of this subject is now referred to as the Milankovitch Theory.

There could also a very new explanation for repetitive mass extinctions. Please see Mass Extinction, a New Explanation A New Explanation for Apparent Periodicity of Mass Extinctions.

First Presented on the Internet, August, 2003.

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C Johnson, Theoretical Physicist, Physics Degree from Univ of Chicago