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

Lecture 27:
The Age of the Earth

Key Ideas:

Different Age Determinations

• Ages based on Human History
• Pre-20th century Physical ages.

Radioactive Isotope Dating

• Measures the time since a rock solidified
• Old rocks, Moon rocks, & meteorites

The Idea of Time

There are two ways that people have conceived of time:

• Cyclical Time: Earth has no beginning or end

• Linear Time: Past beginning & a future end.

Cyclic Time

• Cycle of day & night
• Monthly cycle of Moon phases
• Yearly cycle of the seasons
• Generational cycle of birth, life, and death...

• Hinduism & Buddhism posit cyclical time and cyclical lives.
• Plato's 72,000 year cycle: 36,000 year Golden Age followed by a 36,000 year age of disorder & chaos.

Linear Time

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

• Past divine creation of the Earth (cf. Genesis)
• Promised end of the world.

• Both see history as a fulfillment of a divine plan, not as a process of growth or development.
• There is no process of renewal in the Earth, it was formed in whole at the Creation and has only grown old and decayed over time.

Historical Ages 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)

• Classical & biblical scholar.
• Sought a careful and critical chronology of human history, including the date of the Creation.
• Sources were biblical and middle-eastern and Mediterranean history.

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

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

• Rivers are continually washing small amounts of dissolved salts into the oceans, so over time the oceans should get more salty.
• He then asked how much time it would take for an initially fresh-water ocean to achieve its current level of salinity.
• He argued that the Earth cannot be very young (few thousand years) because otherwise the oceans would still be mostly fresh water.
• Similarly, the Earth could not be infinitely old, otherwise the the oceans would be thoroughly saturated with salt, like the Dead Sea.

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)

• Estimated the time it would take for a molten Earth to cool to its present state.
• Experimented with heating irons spheres and scaling their cooling to an Earth-sized mass
• Got an age of about 75,000 years.

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)

• Found repeated cycles of uplift & erosion in the geology of the land.
• Introduced the idea of "repair" into geological history.
• Previous idea was decay from initial creation.

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)

• Used strata of different rocks to separate the ages of previous geological history
• Noted change in fossils in strata as ways to fix relative ages.
• Old rock are like young rocks, but life shows great variation with time.

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

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:

• ²³⁸U decays into ²⁰⁶Pb with a half-life of 4.47 Gyr
• ²³⁵U decays into ²⁰⁷Pb with a half-life of 704 Myr

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:

• Less ²³⁸U and even less ²³⁵U (it decays faster).
• Increasing amounts of ²⁰⁶Pb and ²⁰⁷Pb.
• Because of the different radioactive decay rates of the parent Uranium isotopes, the relative isotopic ratios of Lead will change with time as well.

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...

• Only half the ²³⁸U remains, the rest having become ²⁰⁶Pb (1 half life).
• Only 1.2% of the ²³⁵U remains, the rest having become ²⁰⁷Pb (~6.4 half lives).

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

Radiometric Dating

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:

• ²³⁸U -> ²⁰⁶Pb: Half-life = 4.51 Gyr
• ²³⁵U -> ²⁰⁷Pb: Half-life = 710 Myr
• ⁸⁷Rb -> ⁸⁷Sr: Half-life = 50 Gyr
• ⁴⁰K -> ⁴⁰Ar: Half-life = 1.30 Gyr

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

• Allowed elements are locked in
• Rejected elements are locked out.
• The daughter products created later by locked-in radioactive parent isotopes stay locked in.

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

• This resets the clock.

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

Radioactive Dating of the Earth

• Most of the crust is less than 100 Myr old

• Jack Hills of Australia (4.4 Gyr)
• Acasta Gniess in Canada (4.03 Gyr)
• Isua Greenstone Belt in Greenland (3.8Gyr)
• Moon Rocks
• Meteorites

Deep Time

Moon Rocks & Meteorites:

• Ages of 4.5 Gyr with spread of about 100 Myr.
• Implies rapid formation of planetary material.

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.