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Astronomy 161
An Introduction to Solar System Astronomy
Prof. Scott Gaudi

Lecture 27:
The Age of the Earth

Key Ideas:

The Earth is 4.5 ± 0.1 Billion Years old, determined from radioactive dating of meteorites.

Different Age Determinations

Radioactive Isotope Dating


The Idea of Time

For "the age of the Earth" to make any sense, you have to conceive of a beginning for the Earth.

There are two ways that people have conceived of time:


Cyclic Time

On human scales, time can appear to be cyclical: Examples of Cyclic Time:

Linear Time

Linear History posits a beginning in the past, and an end in the future.

Judaism provides an early example of linear time in a religious context:

Christianity & Islam adopted this idea:

Historical Ages of the Earth

The traditional Jewish calendar starts from 3760 BC, which is taken to be a date for the creation of the Earth.

A belief in a unique event of creation makes it meaningful to talk about the "age of the Earth" in this context.

In Christianity & Islam, scholars took up the effort to fix the date of the Creation described in Genesis, and so fix the age of the Earth.


James Ussher (1581-1656)

Protestant Archbishop of Armagh (Anglican Primate of All Ireland). His date for the Creation, from volume 4 of his Annals of the World (1650), was:
The evening of Sunday, October 23, 4004 BC (Julian)

The is the first Sunday after the Autumnal Equinox in 4004 BC by the Julian Calendar (recall that Britain did not adopt the Gregorian Calendar until 1752).


The Central Assumption

All of these dates are based upon the central assumption that human history may be equated with the physical history of the Earth.

Why do they all get a date of around 4000BC? One possible explanation is that this date is within a millennium of the invention of writing, and thus within a millennium of the earliest historical records.

Is this central assumption correct?


Edmund Halley

Among his many studies, Halley argued for a way to make a physical estimate of the Earth's age. He reasoned as follows:

What Halley's work accomplished was to make the idea of the Earth having a physical history that was older than human history (but not infinitely old) philosophically acceptable.


George-Louis Leclerc, Comte de Buffon (1707-1788)

Naturalist and Geologist who was convinced of the Earth's antiquity from his geological studies (Epochs of Nature 1774).

What makes Buffon's estimate stand out is that he not only posited a physical process that required a finite time to occur (the time for the Earth to cool from a hot molten state), but performed experiments designed to help him make the best possible estimates. This is solid scientific practice.

The British physicist Lord Kelvin refined Buffon's calculation in 1862 (On the Secular Cooling of the Earth), deriving the time for a molten Earth to cool of 98 Million years, which he revised downward to 20-40 Million years in 1897. Both are gross underestimates because they do not take into account natural radioactivity in rocks (which Kelvin did not know about) that makes the Earth warmer that it would be in the absence of any other sources of heat.


James Hutton (1726-1797)

Author of the Theory of the Earth (1788), a textbook which was one of the foundations of modern geology. The Earth was thus millions of years old, but Hutton concluded (incorrectly) that the repeated cycles of decay & repair have effectively erased this history from the geologic record. In Hutton's memorable words "The result, therefore, of our present enquiry is, that we find no vestige of a beginning - no prospect of an end."

Thus, while Hutton is credited with having introduced the idea of deep time, an age for the Earth far older than human history, he was also to deny that one could read that history in the Earth!


Charles Lyell (1797-1875)

Lyell is the most famous of Hutton's students. He wrote the Principles of Geology, which went through 11 editions between 1830 & 1872.

Lyell introduced the idea of Stratigraphic Ages for geological formations still in use (in modified form) today. This provided a way out of Hutton's dilemma, but it is still somewhat limited in its utility for measuring the ultimate age of the Earth, even if it does give an idea of the geologic ages of particular parts of the Earth.

A better way is to look at the rocks themselves.


Radioactive Isotope Dating

Method first suggested by Ernest Rutherford in 1905.

When the mineral Zircon crystalizes, it can chemically trap isotopes of Uranium within it. The two most abundant isotops of Uranium are 238U and 235U.

Both are radioactive:

Both of these lead (Pb) isotopes are stable.

But, while Uranium can be trapped in Zircon at formation, Lead is strictly excluded chemically.

Thus, if you find Lead isotops inside Zircon, the only way it could get there is as the daughter product of Uranium decay.

The Zircon will thus start out with no Lead of any form, but small amount of 238U and 235U.

Over time, inside the Zircon you will find:

Example
A zircon forms 4.5Gyr ago with equal proportions of 238U and 235U, but no Lead.

When we analyze the zircon 4.5Gyr later...

This lets you use the radioactive decay of trapped radioactive elements as the the basis of a geological clock.


Radiometric Dating

Radiometric Dating is the use of radioactive isotopes to measures the ages of rocks (or, more specifically, of minerals in the rocks).

A number of different isotope combinations are used to seek a consistent answer, since all have their own sublties and difficulties that must be intercompared to give a meaningful answer.

Some of the radioactive isotopes used for radiochronology are:

One measures the detailed isotope ratios in crystalline inclusions, exploits chemical differences to distinguish original elemental content from radioactive decay products, etc. to form the basis of dating the time since the rock solidified. This is far too invovled to go into in detail here, but it is a well-defined, if exacting technique that gives good results.


Time Since Solidification

Once you make a mineral,

Once you melt and re-solidify the mineral, however, the daughter isotopes are released and then chemically rejected from the re-solidified mineral

Radioactive dating therefore gives you the time that has elapsed since the rock solidified.


Radioactive Dating of the Earth

The problem is this: the Earth is geologically active, so that surface rocks are being melted & re-processed all the time. We need to find the oldest rocks in order to date the Earth: The latter two are remnants from the formation of the Solar System, and we expect the Earth to be of the same age (i.e., it formed at the same time as the other planets).

Deep Time

The Oldest Earth rocks known are about 4.4 Gyr old zircons.

Moon Rocks & Meteorites:

The best estimate of the age of the Earth is:

4.5 ± 0.1 Gyr

Since the Earth formed at the same time as the rest of the planets, this number will also serve as the age of the Solar System in general.

This is a somewhat conservative estimate, the current best estimate has greater precision, 4.55±0.02 Gyr, from work by Clair Patterson and F.G. Houtermans, but for our purposes the more conservative value will suffice.


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