1 Today Kepler`s Laws Question Kepler`s 2nd Law of Planetary Motion

GSC307
Introduction to Global Geophysics
GSC307
Introduction to Global Geophysics
Today
Kepler’s Laws
In
•  Lecture:
–  Earth as a Planet
–  Plate Tectonics
17th
century, Kepler created 3 empirical laws of
planetary motion
–  = based on observations alone
1.  orbit of each planet is ellipse with Sun at one focus
V
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4/7/2015
Cal Poly Pomona
4/7/2015
Cal Poly Pomona
GSC307
Introduction to Global Geophysics
GSC307
Introduction to Global Geophysics
Kepler’s 2nd Law of Planetary Motion
Question
2.  The orbital radius of a planet sweeps out equal areas in
equal time
Which trajectories are
possible stable
orbital paths (of a
planet around a
single star)?
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4/7/2015
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GSC307
Introduction to Global Geophysics
GSC307
Introduction to Global Geophysics
Kepler’s 2nd
Law
Kepler’s 3rd Law
p2 = a3
=> Planet travels faster
when it is nearer to
Sun and slower when
farther
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=> The square of each
planet’s orbital period (in
years) is equal to the
cube of its average
distance from the Sun (in
AU).
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GSC307
Introduction to Global Geophysics
GSC307
Introduction to Global Geophysics
Kepler’s Third Law
•  Valid for all closed
planetary systems and
motion of satellite about
parent body
•  “Complete” version of 3rd
law:
!PHELION
4π 2
GM = 2 a 3
T
€
T: orbital period of satellite
G: gravitational constant
M: mass of parent body
a: semi-major axis of orbit of
satellite
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0g
Kepler’s Laws
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1
!
0 R 0ERIHELION
1.  Orbit of each planet
is an ellipse
2.  Sweeping out equal
areas in equal times
3.  T2 = a3
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GSC307
Introduction to Global Geophysics
GSC307
Introduction to Global Geophysics
Example
Application:
Dwarf
Planet Eris
2
GM =
4π 3
a
T2
•  By measuring orbit (a) and period (T) of Eris’ moon
Dysnomia, Eris’ mass was determined to be 27% greater than
that of Pluto & thus its density substantially
higher (consistent
€
with composition of rocky materials)
Planetary Lay-out
Planets fall into two main categories:
•  Terrestrial (i.e. Earth-like)
–  inner
–  Mars, Venus, Mercury, Earth
•  Jovian (i.e. Jupiter-like)
–  outer
–  Saturn, Jupiter, Uranus, Neptune
http://www.mikebrownsplanets.com/2011/10/and-answer-is.html
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GSC307
Introduction to Global Geophysics
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GSC307
Introduction to Global Geophysics
Jovian Planets
What are the
characteristics
of the two main
categories of
planets?
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GSC307
Introduction to Global Geophysics
GSC307
Introduction to Global Geophysics
/BSERVEDDISTANCEFROM3UN!5
Solar System
Bode’s Law
0LUTO
.EPTUNE
•  Empirical formula for
approximate distances
of planets from Sun
•  Series of numbers
created by:
5RANUS
3ATURN
*UPITER
!STEROIDBELTMEAN
-ARS
%ARTH
6ENUS
-ERCURY
$ISTANCEFROM3UN!5
PREDICTEDBY"ODEgSLAW
dn = 0.4 for n = 1
–  first number is 0
–  second is 0.3
–  rest is double previous
number
–  add 0.4 to all in series
•  dwarf planets
•  asteroid belt
•  comets (Kuiper belt and Oort cloud)
dn = 0.4 + 0.3 × 2 n -2 for n ≥ 2
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4/7/2015
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€
GSC307
Introduction to Global Geophysics
GSC307
Introduction to Global Geophysics
Dwarf
Planet
Dwarf planet is celestial body that:
•  is in direct orbit around Sun
•  has sufficient mass so that it assumes nearly round shape
•  has NOT "cleared neighborhood" around its orbit
Five dwarf planets currently recognized—Ceres, Pluto, Haumea, Makemake,
and Eris.
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Mercury
• 
• 
• 
• 
• 
Most extreme range of surface temperatures (100 - 700 K)
Geologically dead
Relatively high density: large iron core
Weak magnetic field
Has shrunk significantly
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GSC307
Introduction to Global Geophysics
GSC307
Introduction to Global Geophysics
Mars
Venus
• 
• 
• 
• 
Most easily observable
Retrograde spin
Similar in size to Earth
Very dense atmosphere
(mainly carbon dioxide)
and strong greenhouse
effect
•  Volcanic features
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GSC307
Introduction to Global Geophysics
•  Dramatic topography:
mountains, volcanoes and
canyons
•  Possible evidence of
recent(?) presence of liquid
water on surface
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GSC307
Introduction to Global Geophysics
Earth is Special Because:
Asteroids
•  Millions of small, rocky
bodies
•  Includes one dwarf
planet: Ceres
•  Most reside in the
asteroid belt between
Mars and Jupiter
•  May consist of material
that was never able to
consolidate into a
planet
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4/7/2015
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GSC307
Introduction to Global Geophysics
GSC307
Introduction to Global Geophysics
Trans-Neptunian Objects
Jovian Moons
•  Composition is
mainly ice
•  Much larger and
more numerous
than asteroids
•  Several are dwarf
planets (may be
more?)
•  Some of outer solar system moons are similar in size to
terrestrial planets and prime targets for exploration
•  Io: active volcanism
•  Europa: may have liquid water ocean below icy crust
•  Titan: only moon with dense atmosphere
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4/7/2015
GSC307
Introduction to Global Geophysics
Cal Poly Pomona
GSC307
Introduction to Global Geophysics
Nebular Hypothesis
Any successful
hypothesis for this
origin of the solar
system must account for
observed characteristics:
• 
– 
– 
– 
• 
What are some of
the properties of
our solar system?
• 
• 
• 
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Large cloud of gas and dust
cools and contracts
4/7/2015
Speeds up
Forms a flat disk
Sun forms at center
Material cools and condenses
in small grains
High boiling point material
(metals and rocks) condenses
everywhere, ices could form
only farther away from Sun
Grains coalesce and form
planetesimals, then planets
Biggest planets attract gases
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Introduction to Global Geophysics
Planetary Formation Simulation
Plate Tectonics
Computer simulations demonstrate that gas disk around young
star can produce giant gas planets. This proto planet has
properties similar to observed extra-solar planets.
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GSC307
Introduction to Global Geophysics
4/7/2015
GSC307
Introduction to Global Geophysics
Dynamic Earth
Continental Drift
•  Earth is constantly changing
due to internal (endogenic)
processes, as well as
exogenic (external)
processes, at fast as well as
slow rates
– 
– 
– 
– 
Alfred Wegener
(1912) proposed that:
volcanism
tectonics
erosion
deposition
Continents are slowly drifting
across the globe
based on many different lines of evidence.
•  What is the underlying
mechanism responsible?
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GSC307
Introduction to Global Geophysics
GSC307
Introduction to Global Geophysics
Break up of Pangaea
Continental
Drift
Wegener proposed
one large super
continent, Pangaea,
started to break up
into individual
continents about
225 million years
ago.
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