Consumer Research Reports, Science & Technology

How was the Age of the Earth Determined?

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We know the size of the terrestrial globe since the third century BC. AD, the Earth-Sun distance from the second half of the XVII century, but the time of its formation is known only since the 1950s. Why has it taken so long?

In fact, this is only the XVII th and XVII centuries that the Earth’s age has become a scientific question. Previously, scholars interested in the problem were content, in the West at least, to count the generations listed in the Bible between creating the world and the events for which we have historical traces. Thus Johannes Kepler proposed 3993 BC, and Newton, 3998. But the record of accuracy was undoubtedly that of James Usher, an Anglican pastor, who in 1658 dated the instant zero on the evening of October 28, 4004 BC. J.-C.

Gradually, however, the idea emerged to stop referring to a text, even the Bible, and seek objective chronometers in natural phenomena. Once opened, the site ideas were not lacking, even if it took time to find the “right” stopwatch.

Ideas galore

Thus Edmond Halley had the idea that the sea’s salinity was due to the rivers’ contribution, which dissolves salts and minerals of the grounds which they erode. As the water that evaporates from the oceans does not contain salt, it accumulates over the ages. Halley didn’t know how to quantify the pace of this build-up, but the idea was launched. It was taken over by John Joly in 1899, who got a value of about 100 million years – which gave a lower limit to the time of Earth’s formation.

At the end of the XVII century, sedimentary deposits also gave access for a long time. The Comte de Buffon obtained a few million years by measuring the sedimentation speeds in lakes to extrapolate them to oceanic sediments. Again, this was necessarily a lower limit of the age of the Earth.

But the idea that saw the most development was undoubtedly the following. When we go deep into the earth, for example, to dig mines, we see that, on average, the temperature increases at a rate of 1 degree every 30 meters. If we extrapolate this value, we get a thousand degrees at a depth of a few tens of kilometers. Hence, the idea, reinforced by volcanoes’ existence, that the Earth is a globe made up of molten rocks cooling down by its surface. This idea was developed by Buffon by Joseph Fourier in the early nineteenth century and especially by Lord Kelvin in the second half of the XIX century. It gave rise to an exciting conflict between physics, represented by Lord Kelvin, and geology, represented by Charles Darwin.

The Kelvin-Darwin conflict

Kelvin was able to calculate the age of the solar system in two independent ways. The first method gave the age of the Earth; the second gave an estimate of the sun’s age. In the conception proposed by Laplace and Kant of a “primitive nebula” at the origin of the entire solar system, these two ages must have been close.

For the first, he used the theory of the propagation of heat in a rigid medium ( Fourier’s law ) to calculate the time it took for the surface thermal gradient, initially assumed to be steep, to reach the current value of 30 degrees per kilometer.

For the second, by attributing the origin of solar energy by gravity, he could estimate the sun’s age. The idea is as follows: a star is formed by the gravitational collapse of a gas and dust mass initially diluted. By contracting, it heats up, and by heating up, it radiates. As the system can be considered isolated, its energy remains constant. In other words, the radiated power is provided by mechanical energy. However, classical mechanics makes it possible to calculate this mechanical energy as a function of the star’s size and mass. Assuming that the Sun has always radiated as it does today – a rough assumption, but which gives the proper order of magnitude – we get an estimate of the time elapsed from the start of the contraction to its current size.

In both cases, Kelvin was a few tens of millions of years old. Such a coincidence could not be accidental; there had to be something true in these concurring estimates.

For Charles Darwin and the geologists of his day, that was not right. They would have come to terms with an eternal Earth in constant transformation. No trace of the beginning, no prospect of an end, that was their frame of mind, as far removed from the Bible as possible. Eroding mountains, depositing sediments several kilometers thick, causing species to evolve, this amounted to Charles Darwin in hundreds of millions of years – even if he did not have absolute chronometers to calculate these temporal evolutions.

The fascinating thing about the story is that Darwin was right, but without proving it, and that Kelvin was wrong because he was making correct calculations from two false assumptions: that of totally rigid earth and the absence of an internal heat source.

John Perry, a Kelvin student, tried to point out that if the molten rock under the solid crust was animated by convective movements, the observed thermal gradient became compatible with an age of several billion years. But he failed to convince his master.

As for the second hypothesis, Kelvin could not know that the Earth contains radioactive elements, particularly uranium, potassium, and thorium, which bring a significant heat source by disintegrating. Today, geothermal flux (the energy that escapes from the surface per second and per square meter) is estimated to be due for a significant half to the initial internal heat and a small half to radioactivity.

Radioactivity resolves the conflict by providing the correct stopwatch.

Indeed, the transformation of a radioactive nucleus follows a perfectly deterministic law: the time at the end of which a population of unstable nuclei is divided by two is a constant, called the radioactive period of the element. Nature is generous: it provides radioactive nuclei with the full range of possible periods, from a fraction of a second to billion years! For example, the 235 isotope of uranium has 700 million years; isotope 238, a period of 4.5 billion years. They each disintegrate into a particular isotope of the lead after the emission of several helium nuclei.

Fritz Houtermans in 1953 and Clair Paterson in 1956 were two remarkable initiators of this method. Here is their “recipe”: take a meteorite, because it has remained identical to itself since the formation of the solar system ( except perhaps its surface, subjected to cosmic radiation ), measure its concentration of radiogenic lead (that is, that is, which comes from the radioactive transformation of uranium nuclei), and bingo: you determine the age of the meteorite, and suddenly, that of the Earth, the Sun, and all the other members of the family! Repeat on a collection of different meteorites, and see if it converges. And there, it connects!

The age of the Earth, and that of the solar system, is 4.567 billion years, with an uncertainty of a few tens of millions of years. It is now a stabilized knowledge.

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