Astronomy 171
Solar System Astronomy
Prof. Paul Martini

Lecture 26: 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 the rock solidified; Old rocks, moon rocks, meteorites
The Earth is 4.6 +/- 0.1 Billion years old: Determined from radioactive isotope dating

The Concept of Time

For "The Age of the Earth" to make sense, you must conceive of a beginning for the Earth.
Two ways people have conceived of time:: Cyclical Time: Earth has no beginning or end
Linear Time: past beginning and a future end

Time's Cycle

On human scales, time seems cyclical: Cycle of day and night; Monthly cycle of moon phases; Yearly cycle of the seasons; Generational cycle of birth, life, and death
Examples:: Hinduism and Buddhism posit cyclical time; Plato's 72,000 year cycle: 36,000 year Golden Age followed by a 36,000 year age of disorder and chaos.

Time's Arrow

Linear History posits a beginning in the past and an end in the future.
Judaism provides an example of linear time:: Past divine creation of the Earth (Genesis); Promised end of time
Christianity and Islam adopted this idea: See history as fulfillment, not growth; No change in the world, except decay from past perfection (fall from perfection/grace)

Historical Ages of the Earth

Eusebius of Caesarea (AD 260-340):: 3184 BC, based on biblical chronology
Kepler:: 3993 BC, combining biblical and other sources
Hevelius:: October 24, 3963 BC at 6pm
Newton:: 3998 BC, including the voyage of the Argonauts as a historical event

The Central Assumption

All of these dates are based upon the same assumption:: Human history can be equated with the physical history of the Earth
Why do they all get 4000 BC?: It roughly corresponds with the invention of writing, and thus the earliest historical records.

Is this central assumption correct?

Edmund Halley

Physical Estimate: Rivers wash salts into the oceans; Oceans get more salty over time
Time required for an initially fresh-water ocean to achieve its current salinity:: If a few 1000 years, the oceans would be fresh; If infinite, the oceans would be saturated with salts like the Dead Sea
John Joly (1890s) estimated 80-90 Myrs.

George-Louis Leclerc

Comte de Buffon (1707-1788): Naturalist and Geologist
Age based on cooling:: Estimated the time needed for a molten Earth to cool down; Experimented with hot iron spheres and scaled up to an Earth-sized mass; Got an age of ~75,000 years
Kelvin (1897) revised this to 20-40 Myr

James Hutton (1726-1797)

Theory of the Earth (1795): Founder of medern geology
Described repeated cycles of uplift and erosion in the geology of the land: Introduced "repair" into geological history; Previous idea was decay from an initial creation
Concluded earth was millions of years old: But, he also asserted that the cycle of decay and repair erased much of this history

Charles Lyell (1797-1875)

Principles of Geology: 11 editions between 1830 and 1872
Doctrine of Uniformitarianism:: Earth undergoes perpetual, uniform change, not just change in response to catastrophe; Stratographic Ages: Rock strata separate ages of gelogical history; Changes in fossils found in strata can fix their relative ages
Friend of Charles Darwin, who thought even 400 Myr was not old enough for natural selection

Role of Radioactivity

Radioactivity was discovered by Becquerel in 1896
Marie and Pierre Curie and Albert Laborde showed that radioactivity produces heat
George Darwin and John Joly realized (1903) that this heat would increase age estimates based on cooling of an initially molten Earth
Subsequent work also showed that radioactive decay could be used as an accurate chronometer for rocks

Radioactive Isotope Dating

Consider a rock that solidified containing two Uraniam (element U) isotopes: ²³⁸U and ²³⁵U:: ²³⁸U turns into ²⁰⁶Pb with a half life of 4.51 Gyr; ²³⁵U turns into ²⁰⁷Pb with a half life of 710 Myr; Both lead (element Pb) isotopes are stable.
Over time the rock will have:: Less ²³⁸U and even less ²³⁵U; More lead, but in different isotopic proportions
Careful measurements can yield accurate ages

Radiochronometry

Use radioactive isotopes to age-date rocks:
Some of the radioactive isotopes used are:: ²³⁸U turns into ²⁰⁶Pb with a half life of 4.51 Gyr; ²³⁵U turns into ²⁰⁷Pb with a half life of 710 Myr; ⁸⁷Rb turns into ⁸⁷Sr with a half life of 50 Gyr; ⁴⁰K turns into ⁴⁰Ar with a half life of 1.30 Gyr
Measure detailed isotope ratios in crystalline inclusions, exploit chemical differences, etc.

Time Since Solidification

Once you make a rock,: Its elements are locked in; Other elements are locked out; The decay products of locked-in radioactive isotopes also stay locked in.
Once you melt it,: Everything gets mixed up ("resets the clock")

Radioactive dating measures the time since the rock solidified

Radioactive Dating of the Earth

The Problem: the Earth is geologically active.: Surface rocks are being melted and reprocessed (Rocky Mountains are only ~60 Myr old); Most of the crust is less than 100 Myr old
The Solution: Find the oldest rocks: Continental shields in Australia (4.3 Gyr) and Canada (3.96 Gyr); Moon rocks; Meteorites

Age of the Earth

Oldest surface rocks known are 4.3 Gyr old (Australian Shield)
Moon Rocks and Meteorites:: Ages of 4.6 Gyr with spread of about 100 Myr; Implies rapid formation of planetary material
The best estimate of the age of the Earth is 4.6 +/- 0.1 Gyr

See A Note about Graphics to learn why some of the graphics shown in the lectures are not reproduced with these notes.