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Mass Distribution of the Earth GEO-3010 University of Utah Fan-Chi Lin

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Reading – Chapter 1-3 of the textbook Lecture Note for week 1 – Announcement

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What do we know about the mass distribution of the Earth?

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Earth Total Mass?

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Earth Mass Equation of Gravity

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Earth Mass Equation of Gravity Gravitational acceleration

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How can we estimate Gravitational constant?

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Gravitational Constant

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Earth Mass G= × m 3 kg -1 s -2 r=6,371 km g=9.8 m s -2 Equation of Gravity Gravitational acceleration

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Earth Mass M≈5.96× kg Equation of Gravity Gravitational acceleration

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Any other way to estimate earth mass?

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Earth Mass Equation of Gravity Centrifugal Force

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Earth Mass Equation of Gravity Centrifugal Force

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Earth Mass Equation of Gravity Centrifugal Force

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Earth Mass Equation of Gravity Centrifugal Force

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Earth Mass Equation of Gravity Centrifugal Force G= × m 3 kg -1 s -2 r=385,000 km

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Earth Mass Equation of Gravity Centrifugal Force G= × m 3 kg -1 s -2 r=385,000 km T= 27.3 days

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Earth Mass Equation of Gravity Centrifugal Force G= × m 3 kg -1 s -2 r=385,000 km T= 27.3 days

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Earth Mass Equation of Gravity Centrifugal Force M≈6 × kg

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Mass Distribution

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Rock Density

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Mass Distribution Volume of a sphere: R=385,000 km Earth radius:

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Mass Distribution Volume of a sphere: R=385,000 km Earth radius: M≈5.96× kg

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Density increases with depth!

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What Control Density?

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H2OH2O

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H2OH2O

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Composition Pressure Temperature

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Phase Transition

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Constraining Mass Distribution using Moment of Inertia

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Moment of Inertia of the Earth

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Precession

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Latsis foundation (2001)

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Normal Model

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String Mode

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What is normal mode?

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2004 Sumatra earthquake (Park et al., 2005, Science)

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Spheroidal and toroidal modes (Breathing mode, 20.5 min) (44 min)

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1D earth model

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