Gravitation

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CHAPTER 2 Gravitation and the Waltz of the
Planets
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WHAT DO YOU THINK?

• What makes a theory scientific?
• What is the shape of the Earths orbit around the
  Sun?
• Do the planets orbit the Sun at constant speeds?
• Do all the planets orbit the Sun at the same
  speed?
• How much force does it take to keep an object
  moving in a straight line at a constant speed?
• How does an objects mass differ when measured on
  the Earth and on the Moon?

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You will discover

• what makes a theory scientific
• clues suggesting that Earth is not the center of
  the universe
• the scientific revolution that dethroned Earth
  from its location at the center of the universe
• Copernicuss argument that the planets orbit the
  Sun
• why the direction of motion of the planets on the
  celestial sphere sometimes appears to change
• that Keplers determination of the shapes of
  planetary orbits depended on the careful
  observations of his mentor, Tycho Brahe
• how Isaac Newton formulated an equation to
  describe the force of gravity
• how Isaac Newton explained why the planets and
  moons remain in orbit

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The scientific method is used to develop new
scientific theories. Scientific theories are
accepted when they make testable predictions that
can be verified using new observations and
experiments.
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Early models of the universe attempted to explain
the motion of the five visible planets against
the background of fixed stars. The main
problem was that the planets do not move
uniformly against the background of stars, but
instead appear to stop, move backward, then move
forward again. This backward motion is referred
to as retrograde motion.
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Ptolemy explained this motion using a geocentric
(Earth-centered) model of the solar system in
which the planets orbited the Earth indirectly,
by moving on epicycles which in turn orbited the
Earth.
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Nicolaus Copernicus developed the first
heliocentric (sun-centered) model of the solar
system. In this model, the retrograde motion of
Mars is seen when the Earth passes Mars in its
orbit around the Sun.
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We define special positions of the planets in
their orbits depending where they appear in our
sky. For example, while at a conjunction, a
planet will appear in the same part of the sky as
the Sun, while at opposition, a planet will
appear opposite the Sun in our sky.
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However, the cycle of these positions (a synodic
period) is different from the actual orbital
period of the planet around the Sun (a sidereal
period) because both the Earth and the planet
orbit around the Sun.
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When a new star appeared in the sky during the
16th century, a Danish astronomer named Tycho
Brahe reasoned that the distance of the object
may be determined by measuring the amount of
parallax.
The apparent change in the location of an object
due to the difference in location of the observer
is called parallax.
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Because the parallax of the star was too small
to measure, Tycho knew that it had to be among
the other stars, thus disproving the ancient
belief that the heavens were fixed and
unchangeable.
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After Tycho Brahes death, Johannes Kepler
(pictured here with Tycho in the background) used
Tychos observations to deduce the three laws of
planetary motion.
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KEPLERS THREE LAWS OF PLANETARY MOTION LAW 1.
The orbit of a planet around the Sun is an
ellipse with the Sun at one focus.
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The amount of elongation in a planets orbit is
defined as its orbital eccentricity. An orbital
eccentricity of 0 is a perfect circle while an
eccentricity close to 1.0 is nearly a straight
line.
In an elliptical orbit, the distance from a
planet to the Sun varies. The point in a
planets orbit closest to the Sun is called
perihelion, and the point farthest from the Sun
is called aphelion.
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KEPLERS THREE LAWS OF PLANETARY MOTION LAW 2
A line joining the planet and the Sun sweeps out
equal areas in equal intervals of time.
Planet moves slower in its orbit when farther
away from the Sun.
Planet moves faster in its orbit when closer to
the Sun.
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KEPLERS THREE LAWS OF PLANETARY MOTION LAW 3
The square of a planets sidereal period around
the Sun is directly proportional to the cube of
its semi-major axis.
This law relates the amount of time for the
planet to complete one orbit around the Sun to
the planets average distance from the Sun. If
we measure the orbital periods (P) in years and
distances (a) in astronomical units, then the law
mathematically can be written as P2 a3.
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Galileo was the first to use a telescope to
examine celestial objects. His discoveries
supported a heliocentric model of the solar
system.
Galileo discovered that Venus, like the Moon,
undergoes a series of phases as seen from Earth.
In the Ptolemaic (geocentric) model, Venus would
be seen in only new or crescent phases. However,
as Galileo observed, Venus is seen in all phases,
which agrees with the Copernican model as shown.
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Galileo also discovered moons in orbit around the
planet Jupiter. This was further evidence that
the Earth was not the center of the universe.
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Isaac Newton formulated three laws to describe
the fundamental properties of physical reality.
NEWTONS THREE LAWS OF MOTION LAW 1 A body
remains at rest or moves in a straight line at
constant speed unless acted upon by a net outside
force. LAW 2 The acceleration of an object is
proportional to the force acting on it. LAW 3
Whenever one body exerts a force on a second
body, the second body exerts an equal and
opposite force on the first body.
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Newton also discovered that gravity, the force
that causes objects to fall to the ground on
Earth, is the same force that keeps the Moon in
its orbit around the Earth.
NEWTONS LAW OF UNIVERSAL GRAVITATION Two objects
attract each other with a force that is directly
proportional to the product of their masses and
inversely proportional to the square of the
distance between them.
With his laws, Newton was able to derive Keplers
three laws, as well as predict other possible
orbits.
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Newtons laws were applied to other objects in
our solar system.
Using Newtons methods, Edmund Halley worked out
the details of a comets orbit and predicted its
return.
Deviations from Newtons Laws in the orbit of
the planet Uranus led to the discovery of the
eighth planet, Neptune.
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WHAT DID YOU THINK?

• What makes a theory scientific?
• If it makes predictions that can be objectively
  tested and potentially disproved.
• What is the shape of the Earths orbit around the
  Sun?
• Elliptical
• Do the planets orbit the Sun at constant speeds?
• The closer a planet is to the Sun in its orbit,
  the faster it is moving. It moves fastest at
  perihelion and slowest at aphelion.

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WHAT DID YOU THINK?

• Do all the planets orbit the Sun at the same
  speed?
• No. A planets speed depends on its average
  distance from the Sun.
• How much force does it take to keep an object
  moving in a straight line at a constant speed?
• Unless an object is subject to an outside force,
  it takes no force at all to keep it moving in a
  straight line at a constant speed.
• How does an objects mass differ when measured on
  the Earth and on the Moon?
• Its mass remains constant.

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Key Terms
acceleration angular momentum aphelion astronomica
l unit configuration (of a planet) conjunction con
servation of angular momentum cosmology ellips
e elongation focus (of an ellipse) force Galilean
moons (satellites) gravity heliocentric cosmology
hyperbola inferior conjunction Keplers
laws kinetic energy law of equal areas law of
inertia light-year mass model momentum Newtons
laws of motion Occams razor opposition parabola p
arallax parsec
perihelion physics potential energy retrograde
motion scientific method scientific
theory semimajor axis (of an ellipse) sidereal
period superior conjunction synodic
period universal constant of gravitation universal
law of gravitation velocity weight work