# 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: $5.974 \times 10^{24}~\mathrm{kg}$
• 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.

• 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 $$\tau_{\mathrm{cool}} = \frac{E_{\mathrm{therm}}} {(L_{\mathrm{geo}}-L_{\mathrm{decay}})} \approx 1.4 \times 10^{10}~\mathrm{yr}$$

• 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 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.