#### Transcript Models of the Solar System

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Title your notes: Models of the Solar System
Models of the Solar System
What is the Center of the Solar System?
• The early scientists, in their attempt to answer this
fundamental question created various models of
the solar system.
• Models, which placed Earth at the center, are
called Earth-centered, or geocentric, models.
Models of the Solar System
The Geocentric Model
• The early philosopher and
astronomer believed that
everything in the universe
is “perfect”; and that the
planets are perfect spheres
circling in perfect circular
orbits.
• They believed the Earth
was the most important
object in space and
therefore assumed it to be
the center of the universe.
Models of the Solar System
The Geocentric Model
• Aristotle, a Greek philosopher reasoned that if
Earth circled around the sun, then the relative
positions of the stars would change as Earth
moves.
• This apparent change in the position of an
object when viewed from different angles or
locations on Earth is known as parallax.
• What Aristotle did not take into account is the fact
that stars are very far away. At such great
distance parallax cannot be observed
without a telescope.
What is Parallax?
 nearby star appears to move back and
forth compared to more distant stars
 parallax depends on distance  use it
to measure distance
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Trigonometry
 Use basic trigonometric
relations.
 Used by modern
surveyors to measure
great distances (also
called surveyor's
method).
d : distance
b
d
b : baseline
tan p p : angle
b
p
d
February 14, 2006
Astronomy 2010
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Parallax  Distance
 measure angular shift p
 know baseline distance (1 AU)
 trigonometry  star distance d
February 14, 2006
Astronomy 2010
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Parsecs
 Distances to the stars in units of astronomical
units are huge, a more convenient unit of
distance called a parsec is used
 abbreviated “pc”.
 parsec = distance of a star that has a parallax of
one arc second using a baseline of 1
astronomical unit.
 1 parsec = 206,265 AU = 3.26LY.
 Nearest star (Alpha Centuri) is ~1.3 parsecs
from the Sun.
 The astronomical unit (AU) is roughly the
distance from the Earth to the Sun. However,
that distance varies as the Earth orbits the Sun,
from a maximum (aphelion) to a minimum
(perihelion) and back again once a year.
Originally conceived as the average of Earth's
aphelion and perihelion, it is now defined as
million kilometers, or 93 million miles).
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Models of the Solar System
The Geocentric Model
• The geocentric model of the solar system became
a very important part of ancient Greek
Astronomy beginning in the sixth century
B.C.E.
• The Greek philosopher Aristotle (384–322 B.C.E.)
was among the first scholars to put forward an
Earth-centered model of the Solar System.
• His model positioned the moon, sun, planets, and
stars on a series of circles that moved around
Earth.
Models of the Solar System
The Geocentric Model
• Aristarchus, a Greek astronomer and
mathematician, is believed to have proposed a
sun-centered model of the solar system.
• Ptolemy an astronomer, geographer, and
mathematician, exploited Aristotle’s Earthcentered view and developed a complex
geocentric model that was used by
astronomers over the next thousand years.
Historical Models of the Solar System
The Geocentric Model
• According
to
Ptolemy’s
model, the
planets
moved on
small
circles that
in turn
moved on
larger
circles.
Historical Models of the Solar System
The Geocentric Model
• Ptolemy’s “wheels-on-wheels” model seemed to
make sense since it very well illustrated
observations made at the time going back
hundreds of years.
• Scientist for many centuries used Ptolemy’s model
to make predictions of the motions of planets
years into the future.
Historical Models of the Solar System
The Heliocentric Model
(Sun-Centered)
Models of the Solar System
The Heliocentric Model
• The model which placed the sun at the center is
called the heliocentric or sun-centered model.
• The Polish astronomer Nicolaus Copernicus
adopted Ptolemy’s idea that planets’ orbits are
perfect circles, he however developed
Aristarchus’s primitive sun-centered model into a
well thought out heliocentric model.
• Copernicus’s model is known as the most
influential of modern astronomy.
of planetary motion.
Tycho Brahe (1546-1601):
Danish astronomer
Tycho’s contributions to astronomy
Tycho discovered ‘new
star’, or ‘nova’,
upsetting ancient
notion of perfect,
unchanging heavens.
measurements of
planetary positions.
Johannes Kepler (1571-1630): German
Was Tycho’s assistant.
Used Tycho’s data to
discover
Three Laws of
Planetary Motion.
Kepler’s First Law of planetary
motion
The orbits of planets around the Sun are
ellipses with the Sun at one focus.
Ellipse = an oval built around two points,
called focuses (or foci).
SIZE of ellipse:
Major axis = longest
diameter of ellipse.
Semimajor axis = half
the major axis.
SHAPE of ellipse:
Eccentricity = distance between foci divided by major axis.
Foci close together: ellipse nearly circular, eccentricity close to zero.
Foci far apart: ellipse very flattened, eccentricity close to one.
Example: Mars
Semimajor axis =
1.524 A.U.
Eccentricity = 0.093
(much smaller
than one)
(3) Kepler’s
Second Law of planetary motion
A line
to a planet
from the Sun
sweeps out equal
areas in equal time intervals.
Consequences of Kepler’s Second Law:
Planets move fastest when closest to the Sun.
Example: Mars
Perihelion: 206,600,000 km (1.381 A.U.)
Max. Orbital Speed: 26.5 km/s
Aphelion: 249,200,000 km (1.666 A.U.)
Min. Orbital Speed: 22.0 km/s
Kepler’s Third Law of planetary motion
The square of a planet’s orbital period is
proportional to the cube of its average
distance from the Sun*:
P
2

a
3
*A planet’s average distance from the Sun is equal to the
semimajor axis of its orbit.
Kepler’s Third Law in mathematical form:
P
2

a
3
P = orbital period (in years)
a = semimajor axis (in A.U.)
Example: The orbit of Mars
P  1.881 yr
P  3.54
a  1.524 A.U.
a 3  3.54
2
the heliocentric model.
Galileo Galilei (15641642): Italian
Galileo was among the
first to observe the
sky with a telescope
(1609).
Models of the Solar System
The Heliocentric Model
• Galileo Galilei was a scientist who conducted his
experiments in the manner of moderns scientists.
He actually used a very systematic approach very
similar to the scientific methods.
• Galileo’s observations showed that they are
other celestial objects beside Earth with
orbiting satellites.
Models of the Solar System
The Heliocentric Model
• His discovery best fit the heliocentric model.
• Galileo also observed that Venus went
through phases similar to the phases of
Earth’s moon.
• The observation of these phases was more in line
with the idea that planets revolve around the sun
rather than the Earth.
Phases of Venus in the
geocentric model of Ptolemy.
Only new and
crescent
phases.
The Phases of Venus
Phases of Venus in the
heliocentric model.
All phases; smaller angular size
when full than when new.
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