Models of the Solar System

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Models of the Solar System

• Positions of planets change, whereas stars
  appear relatively fixed
• Greeks held on to the Geocentric model because
  they could not observe stars to change their
  positions, and therefore thought that the earth
  must be stationary
• Ptolemy, Aristotle and others refined the
  geocentric model
• But there were problems.such as the path
  reversal by Mars ? Retrograde motion

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Retrograde motion of Mars(path reversal seen in
the Sky)
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Epicycles Ptolemic Geocentric Model
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How do we know the Earth is spherical ?

• The ancient Greeks had deduced not only that the
  Earth is spherical but also measured its
  circumference !
• What kind of an object always has a round shadow
  ?

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Earth Shadow during Lunar Eclipse
Multiple Exposure Photograph
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Cyrene
Syene
Tropic of Cancer
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Eratostheness method to measure the
circumference of the earth
7º
At noon on summer solstice day the Sun is
directly overhead at Syene, but at an angle of 7o
at Alexandria

• Distance (Alexandria - Syene)
• -- ---------------------------------------
• 360 Circumference of the Earth

Sunlight
Alexandria
Answer 40,000 stadia 25,000 mi !
Syene
Earth
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Earth-Moon-Sun GeometryAristarchuss
determination of distances(Closer the S-E-M
angle to 90, the farther the Sun)
If we replace the moon with a planet, then can
determine relative distances, as done by
Copernicus
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Copernicus
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Copernican ModelInferior and Superior
Planets(orbits inside or outside the Earths
orbit)

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Configurations of Inferior Planets, Earth, and
the Sun
Earth
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Configurations of Superior Planets, Earth, and
the Sun
Opposition
Conjunction
Earth
Synodic (apparent) period one conjunction to
next (or one opposition to next)
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Synodic and Sidereal Orbital Periods

• Inferior planets are never at opposition
  superior planets can not be at inferior
  conjunction
• Copernican model of orbital periods
• Synodic period is the apparent orbital period of
  a planet, viewed from the earth, when the
  earth-planet-sun are in successive conjunction or
  opposition
• Sidereal (with respect to stars) period is the
  real orbital period around the Sun
• Synodic periods of outer planets (except Mars)
  are just over one year

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Apparent (Synodic) and true (Sidereal with
respect to stars) orbital periods of planets
differ due to Earths relative motion
Synodic periods of all outer planets (except
mars) are just over 1 year because their Sidereal
periods are very long and they are in opposition
again soon after an earth-year
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Earth-Venus-Sun
Inferior planets appear farthest away from the
Sun at greatest elongation
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Measurements of Distances to Planets
Angle of max elongation
P-E-S
P
90 deg
Earth
P-E-S
E
S
Sin (P-E-S) PS / ES ES 1 AU
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Copernicus first determined the relative
distances of planets
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Copernican Heliocentric Model(Retrograde motion
of Mars seen when Earth overtakes Mars
periodically)
Earth is closer to the Sun, therefore moves
faster than Mars
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Tycho The most accurate pre-telescopic observer
Tycho charted very accurately the movement of
Mars in the Sky, but still believed In the
Geocentric Universe
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Kepler Tychos assistant(used Tychos data to
derive Keplers Laws)
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Planetary Orbits

• The Copernican heliocentric model is essentially
  correct
• But it consisted of circular orbits which did not
  exactly fit observations of planetary positions
• Kepler realized, based on Tychos data of the
  orbit of Mars, that orbits are elliptical ?
  Keplers First Law
• However, the difference for Mars is tiny, to
  within the accuracy of drawing a circle with a
  thick pen !

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Keplers First LawAll planetary orbits are
elliptical, with the Sun at one focus
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Eccentricity ee distance between foci/major
axis AB / ab
a
A
B
b
A circle has e 0, and a straight line has e
1.0
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Keplers Second LawPlanetary radius sweeps
equal area triangles in equal time
It follows that the velocity of the planet must
vary according to distance from the Sun --
fastest at Perihelion and slowest at Aphelion
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Keplers Third Law P2 a3P Orbital Period, a
semi-major axis
What is the size a of the orbit of a comet with
the period P of 8 years?
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Keplers Laws

• Empirically derived from observational data
  largely from Tycho (e.g. observations of the
  positions of Mars in its orbit around the Sun)
• Theoretical explanation had to await Newtons
  discovery of the Law of Gravitation
• Universally valid for all gravitationally
  orbiting objects (e.g. stars around black holes
  before falling in)

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Galileo
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Galileos Discoveries With Telescope

• Phases of Venus
• - Venus displays phases like the Moon as it
  revolves around the Sun
• Mountains and seas on the Moon
• - Other objects in the sky are like the
  Earth (not therefore special)
• Milky Way is made of stars like the Sun
• Sunspots
• - Imperfections or blemishes in
  otherwise perfect heavenly objects
• 4 Galilean satellites of Jupiter
• - Objects in the sky revolve around other
  objects, not the Earth (i.e. other moons)
• All of these supported the Copernican System
• Galileo also conducted experiments on
  gravity
• Regardless of mass or weight objects fall at
  the same rate

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Phases of Venus
Venus is never too far from the Sun, therefore
can not be in opposition like the Moon. Changing
phases of Venus demonstrate that it orbits the
Sun like the Earth.
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Orbits and Motions

• Orbits can not be circular since objects do NOT
  revolve around each other, but around their
  common center-of-mass
• The Earth and the Moon both revolve around each
  other
• This motion is in addition to Earths Rotation,
  Revolution, Precession

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The Earth-Moon Barycenter

• The earth and the moon both revolve around a
  common center of mass called the Barycenter
• The barycenter of Sun-planet systems lies inside
  the Sun
• As the earth is much more massive, the barycenter
  lies 1700 Km inside the earth
• Calculate its position O from
• M(E) x EO M (M) x MO

M
E
O
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Gravity

• Galileos observations on gravity led to Newtons
  Law of Gravitation and the three Laws of Motion
• Objects fall at the same rate regardless of mass
  because more massive objects have more inertia or
  resistance to motion
• Fgrav G (m1 x m2) / r2
• Force of gravity between two masses is
  proportional to the product of masses divided by
  distance squared ? inverse square law