Astronomy 217

 
 

Prof. Andrew W. Steiner

 
 
Oct. 28, 2021
 
 

TA James Ternullo

Last Time

  • Origin of the Solar System

Today

  • The Structure of Earth

Earth Facts

  • Mass: \( 5.974 \times 10^{24}~\mathrm{kg} \)
  • Radius: 6371 km
  • Escape velocity 11.2 km/s
  • Density \(5515~\mathrm{kg}~\mathrm{m}^{-3} \)
  • Orbital semi-major axis: \( 1.496 \times 10^8~\mathrm{km} \)
  • Eccentricity: 0.0167
  • Mean surface temperature: 287 K
  • Albedo: 0.367, 29% of surface is land

Earth's Structure

  • Understanding the structure of the Earth provides a template for understanding the structure of other terrestrial planets, both in our Solar system and beyond.
  • Chemically, the Earth is differentiated into
    • Inner and outer core
    • Mantle
    • Thin crust
    • Hydrosphere
    • Atmosphere
    • Magnetosphere

Seismic Waves

  • While light is unable to penetrate the Earth’s surface, seismic waves pass through.
  • Earthquakes produce both pressure and shear waves.
  • Pressure (sound) waves are longitudinal and travel through both liquids and solids.
  • Shear waves are transverse and do not travel through liquid, as liquids do not resist shear forces.
  • Wave speed depends on the density of the material.

Seismology

  • The waves from a single earthquake will travel throughout the Earth revealing information about the layers traversed. Studying a series of earthquakes reveals the interior structure of Earth.
  • The travel time reveals the sound speed.
  • Absence of S-waves and direct P-waves from \( 103^{\circ} \) to \( 142^{\circ} \), reveals liquid core.
  • P-waves near \( 180^{\circ} \) arrive earlier than expected, revealing solid inner core.

Earth's Interior

  • Core is metallic, largely iron and nickel. It is 16% of Earth’s volume, but 32% of mass.
  • Outer core is liquid; inner core is solid, due to pressure.
  • Mantle is rocky, much less dense than core.
  • Volcanic lava comes from mantle, allowing analysis of its composition (O 44%, Si 22%, Mg 23%, Fe 6%).
  • Crust is only \( 0.5%~\mathrm{M}_{\oplus} \), made of O (47%), Si (28%), Al (8%), Fe (5%)

Interior History

  • The Earth as it formed by coalescence was a homogeneous conglomeration of planetesimals.
  • Accretion of planetesimals, short- lived radioactivity and contraction heated the Earth, forming a molten surface layer.
  • Heavier materials sank to the center, producing additional energy by differentiation.
  • With the clearing of the orbit and the completion of differentiation, a solid surface formed.

Radioactive Heating

  • Though the exhaustion of short-lived radioactive species have reduced the rate of nuclear energy generation, radioactive decay continues to be a significant source of heat in the Earth’s interior.
  • Total heat flow from the Earth’s core is determined from temperature gradients near the surface. $$ F_{\mathrm{geo}} \approx 0.09~\mathrm{W}~\mathrm{m}^{-2} $$ $$ \begin{eqnarray} L_{\mathrm{geo}} &=& 4 \pi R_{\oplus}^2 F_{\mathrm{geo}} \\ &\approx& 4.6 (\pm 3) \times 10^{13}~\mathrm{W} \end{eqnarray} $$
  • The KamLAND & Borexino neutrino detectors measured geoneutrinos from uranium and thorium decay, implying \( L_{\mathrm{decay}} = 23.3^{+8.8}_{-8.6}~\mathrm{TW} \)

Molten Core

  • The flow of energy from the Earth’s core represents a potential cooling of the core, which could one day affect the molten iron core, if not balanced by radioactive decay, etc. $$ L_{\mathrm{geo}} - L_{\mathrm{decay}} \approx 23 TW $$
  • An estimate of the total thermal energy of the Earth is $$ E_{\mathrm{therm}} = \frac{3 k T}{40 m_p} M_{\oplus} \approx 1.1 \times 10^{32}~\mathrm{J} $$ where \( 40 m_p \) is the average atomic mass
  • The cooling timescale is thus $$ \tau_{\mathrm{cool}} = \frac{E_{\mathrm{therm}}} {(L_{\mathrm{geo}}-L_{\mathrm{decay}})} \approx 1.4 \times 10^{10}~\mathrm{yr} $$

Radioactive Families

  • The radioactive species in the Earth decay by fission, releasing alpha-particles, neutrons and electrons. Each radioactive nucleus has a unique decay chain.

Decay Chain

  • A decay chain is a series of reactions linking the parent to daughter.

Radioactive Dating

  • Radioactive dating requires determining the ratio of the current abundance of the radioactive species and its original abundance
  • The abundance of the daughter nucleus allows us to determine theoriginal radioactive abundance.
  • This works best for chemically selected samples where the original abundance of the daughter nucleus was small.

Moving Crust

  • The crust is divided into plates, which move atop the mantle. Most of the Earth’s surface features are the result of these plate movements; collisions and the like.

Tectonic History

  • Plate movements change the face of the planet over time.
  • If we follow continental drift backward 200 million years, the continents merge to form Pangaea.

Earthquakes and Mountains

  • Plates sliding along or over each other create faults, where tension builds. Earthquakes mark the release of this tension.
  • Colliding plates can raise or sink mountains. The subduction of the Indian plate under the Eurasian plate creates a thrust fault, lifting and folding the crust into the Himalayan mountains.

Lithosphere

  • The plates are part of the lithosphere, the solid surface of the Earth, consisting of the crust plus the solid upper mantle
  • Plates move atop the partly molten asthenosphere.
  • A subduction zone occurs where one plate slides below another, with material from the crust reaching the molten layers.

Rifts

  • When crustal plates move away from each other, either mid- continent or under the ocean, rising material from the mantle fills the void, creating rift valleys or undersea ridges. Collectively these are called rifts.

Driving the Crust

  • The driving force for plate tectonics is convection in the upper mantle.
  • Crustal plates ride the upper surface of convective cells in the mantle. These cells provide the energy to collide and deform the plates.