### Mass Distribution of the Earth - Fan-Chi Lin`s

```Mass Distribution of the Earth
GEO-3010
University of Utah
Fan-Chi Lin
Announcement
– Chapter 1-3 of the textbook
• Lecture Note for week 1
– http://noise.earth.utah.edu/GEO3010/
What do we know about the mass
distribution of the Earth?
Earth Total Mass?
Earth Mass
GMm
F= 2
r
Equation of
Gravity
Earth Mass
GMm
F= 2
r
GM
g= 2
r
Equation of
Gravity
Gravitational
acceleration
How can we estimate Gravitational
constant?
Gravitational Constant
Earth Mass
GMm
F= 2
r
GM
g= 2
r
Equation of
Gravity
Gravitational
acceleration
g=9.8 m s-2
G=6.67384 × 10-11 m3 kg-1 s-2
r=6,371 km
Earth Mass
GMm
F= 2
r
GM
g= 2
r
M≈5.96× 1024 kg
Equation of
Gravity
Gravitational
acceleration
Any other way to estimate earth mass?
Any other way to estimate earth mass?
Earth Mass
GMm
F= 2
r
2
mv
F=
r
Equation of
Gravity
Centrifugal
Force
Earth Mass
GMm
F= 2
r 2
mv
F=
r
GM
2
=v
r
Equation of
Gravity
Centrifugal
Force
Earth Mass
GMm Equation of
F= 2
Gravity
r 2
mv
Centrifugal
F=
Force
r
GM
2p r 2
2
=v =(
)
r
T
Earth Mass
GMm
F= 2
r 2
mv
F=
r
2 3
4p r
M=
2
GT
Equation of
Gravity
Centrifugal
Force
Earth Mass
GMm Equation of
F= 2
Gravity
r 2
mv
Centrifugal
F=
Force
r
2 3
4p r G=6.67384 × 10 m kg s
M=
2 r=385,000 km
GT
-11
3
-1 -2
Earth Mass
GMm Equation of
F= 2
Gravity
r 2
mv
Centrifugal
F=
Force
r
2 3
4p r G=6.67384 × 10 m kg s
M=
2 r=385,000 km
GT T= 27.3 days
-11
3
-1 -2
Earth Mass
GMm Equation of
F= 2
Gravity
r 2
mv
Centrifugal
F=
Force
r
2 3
4p r G=6.67384 × 10 m kg s
M=
2 r=385,000 km
GT T= 27.3 days
-11
3
-1 -2
Earth Mass
GMm Equation of
F= 2
Gravity
r 2
mv
Centrifugal
F=
Force
r
2 3
4p r
24
M≈6
×
10
kg
M=
2
GT
Mass Distribution
Rock Density
Mass Distribution
Volume of a sphere:
4 3
Volume = p R
3
R=385,000 km
Mass Distribution
Volume of a sphere:
4 3
Volume = p R
3
R=385,000 km
Volume =1.08´10 m
21
M≈5.96× 1024 kg
3
Density increases with depth!
What Control Density?
H2O
H2O
What Control Density?
• Composition
• Pressure
• Temperature
Phase Transition
Constraining Mass Distribution using
Moment of Inertia
Constraining Mass Distribution using
Moment of Inertia
Moment of Inertia of the Earth
Precession
Latsis foundation (2001)
Normal Model
String Mode
What is normal mode?
What is normal mode?
What is normal mode?
What is normal mode?
2004 Sumatra earthquake (Park et al., 2005,
Science)
Spheroidal and toroidal modes
(Breathing mode, 20.5 min)
(44 min)
1D earth model
```