IMPROVING OBSERVATIONS LEADS TO HIGHER ACCURACY

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IMPROVING OBSERVATIONS LEADS TO HIGHER ACCURACY
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Chapter 2 The Copernican Revolution The Birth
of Modern Science

• Ancient Astronomy
• Models of the Solar System
• Laws of Planetary Motion
• Newtons Laws
• Laws of Motion
• Law of Gravitation

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ARAB SCHOLARS STUDYING ASTRONOMY
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THE PTOLEMAIC SYSTEM
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STONEHENGE A STONE AGE COMPUTER
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APPARENT ORBITS (EPICYCLE)
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THE DEFINING PROBLEM
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EXPLAINING THE EPICYCLE OF MARS
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TYCHO BRAHE, THE DANE, IN HIS LABORATORY
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GALILEO APPLIED THE TELESCOPE TO ASTRONOMY
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COPERNICUSLAWS OF PLANETS
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CONSTRUCTING AND ELLIPSE
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ELLIPSE GEOMETRY
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VENUS PHASES (COPERNICUS)
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VENUS PHASES (PTOLEMY)
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SORTING EVIDENCE BY OBSERVATION OF PHASES
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Ancient Astronomy
Stonehenge on the summer solstice. As seen from
the center of the stone circle, the Sun rises
directly over the "heel stone" on the longest day
of the year.
The Big Horn Medicine Wheel in Wyoming, built by
the Plains Indians. Its spokes and rock piles
are aligned with the rising and setting of the
Sun and other stars.
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Astronomy in Early Americas
Maya Indians developed written language and
number system. Recorded motions of Sun, Moon, and
planets -- especially Venus. Fragments of
astronomical observations recorded in picture
books made of tree bark show that Mayans had
learned to predict solar and lunar eclipses and
the path of Venus. One Mayan calendar more
accurate than those of Spanish.
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• Ancient Contributions to Astronomy
• Egyptians
• recorded interval of floods on Nile every 365
  days
• noted Sirius rose with Sun when floods due
• invented sundials to measure time of day from
  movement of the Sun.
• Babylonians
• first people to make detailed records of
  movements of Mercury, Venus, Mars, Jupiter,
  Saturn
• only planets visible until telescope

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Greek Astronomy Probably based on knowledge from
Babylonians. Around 550 B.C., Pythagoras noted
that the Evening Star and Morning Star were
really the same body (actually planet
Venus). Some Greek astronomers thought the Earth
might be in the shape of a ball and that
moonlight was really reflected sunlight.
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Conservation of Angular Momentum
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Angular momentum before Angular momentum
after
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Newtons Laws of Motion

• 1st Inertia
• A body in uniform motion stays in motion unless
  acted upon by a net external force.
• penny/cup/paper
• 2nd Fma
• A net external force, F, acting on a body of
  mass, m, will result in a change in the motion of
  the body described by its acceleration, a.
  chair/empty/person
• 3rd Action-Reaction
• To every action force there is an equal and
  opposite reaction force.
• hand-to-hand

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Newton and Gravitation

• Newtons three laws of motion enable calculation
  of the acceleration of a body
  and its motion, BUT must first
  calculate the forces.
• Celestial bodies do not touch ------ do not
  exert forces on each other directly.
• Newton proposed that celestial bodies exert an
  attractive force on each other at a distance,
  across empty space.
• He called this force gravitation.

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Newtons Law of Gravitation

• Sir Isaac Newtons conceptual leap in
  understandingof the effects of gravity largely
  involved his realizationthat the same force
  governs the motion of a falling objecton Earth
  (for example, an apple)
• and the motion of the Moon in its orbit around
  the Earth.

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• Isaac Newton discovered that two bodies share a
  gravitational attraction, where the force of
  attraction depends on both their masses

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• Both bodies feel the same force,
  but in opposite directions.

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This is worth thinking about - for example, drop
a pen to the floor. Newtons laws say that the
force with which the pen is attracting the Earth
is equal and opposite to the force with which
the Earth is attracting the pen, even though the
pen is much lighter than the Earth!
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• Newton also worked out that if you keep the
  masses of the two bodies constant, the force of
  gravitational attraction depends on the distance
  between their centers

mutual force of attraction
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Universal Law of Gravitation

• Every mass attracts every other mass through a
  force called gravity.
• The force of attraction between any two objects
  is directly proportional to the product of their
  masses.
• Doubling the mass of one object doubles the force
  of gravity between the two objects.
• The force of attraction between two objects
  decreases with the square of the distance between
  their centers.
• Doubling distance between two objects weakens
  force of gravity by a factor of 22 (or 4).

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• For any two particular masses, the gravitational
  force between them depends on their separation
  as

as the separation between the masses is
increased, the gravitational force of
attractionbetween them decreases quickly.
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• Gravity is
• a universal force
• (every mass attracts every other mass)
• always an attractive force
• The force due to gravity
• is always directed along the line
  connecting two masses
• depends on the product of the two masses
• depends on the distance between
  the two masses squared
• (obeys the inverse square rule)
• Today, physicists describe gravity in
  terms of a gravitational field
  produced by the presence of matter.

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Gravity and Weight

• The weight of an object is a measure of the
  gravitational force the object feels in the
  presence of another object.
• For example on Earth, two objects with different
  masses will have different weights.
• Fg m(GmEarth/rEarth2) mg
• What is the weight of the Earth on us?

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Mass and Weight

• Mass A measure of the total
  amount of matter contained within an object
  a measure of an objects
  inertia.
• Weight The force due to gravity
  on an object.
• Weight and mass are proportional.
• Fg mg where m
  mass of the object and g
  acceleration of gravity acting on
  the object

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Free Fall

• If the only force acting on an object is force of
  gravity (weight), object is said to be in a state
  of free fall.
• A heavier body is attracted to the Earth with
  more force than a light body.
• Does the heavier object free fall faster?
• NO, the acceleration of the body depends on both
• the force applied to it and
• the mass of the object, resisting the motion.
• g Fgravity/m Fgravity/m

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Newtons Law of Gravitation

• We call the force which keeps the Moon in its
  orbit around the Earth gravity.

Sir Isaac Newtons conceptual leap in
understandingof the effects of gravity largely
involved his realizationthat the same force
governs the motion of a falling objecton Earth -
for example, an apple - and the motion of the
Moon in its orbit around the Earth.
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Planets, Apples, and the Moon

• Some type of force must act on planet otherwise
  it would move in a straight line.
• Newton analyzed Keplers 2nd Law and saw that the
  Sun was the source of this force.
• From Keplers 3rd Law, Newton deduced that the
  force varied as 1/r2.
• The force must act through a distance, and
  Newton knew of such a force - the one that
  makes an apple accelerate downward from the tree
  to the Earth as the apple falls.
• Could this force extend all the way to the Moon?

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• Your pen dropping to the floor and a satellite in
  orbit around the Earth have something in common -
  they are
  both in freefall.

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To see this, lets review Newtons thought
experiment Is it possible to throw an object
into orbit around the Earth?
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On all these trajectories,the projectile is in
free fall under gravity.(If it were not, it
would travel in a straight line - thats
NewtonsFirst Law of Motion.)
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If the ball is not given enough sideways
velocity, its trajectory intercepts the Earth
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that is, it falls to Earth eventually.
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On the trajectories which make complete orbits,
the projectile is travelling sideways fast
enough ...
On all these trajectories, the projectile is in
free fall.
On all these trajectories, the projectile is in
free fall.
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that as it falls, the Earth curves away
underneathit, and the projectile completes
entire orbits without ever hitting the Earth.
On all these trajectories, the projectile is in
free fall.
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Gravity and Orbits

• The Suns inward pull of gravity on the planet
  competes with the planets tendency to continue
  moving in a straight line.

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The Why of Keplers Laws

• Newton solved the law of universal gravitation
  together with the laws of motion for the problem
  of orbital motion.
• The solution requires use of calculus.
• One possible solution is elliptical orbits with
  varying speeds
• As described by Keplers 1st and 2nd Laws.

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Newtons Form of Keplers 3rd Law

• Newton generalized Keplers 3rd Law to include
  sum of masses of the two objects in orbit about
  each other (in terms of the mass of the Sun).
• (M1 M2) P2 a3
• Observe orbital period and separation of a
  planets satellite, can compute the mass of the
  planet.
• Observe size of a double stars orbit and its
  orbital period, deduce the masses of stars in
  binary system.
• Planet and Sun orbit the common center of mass of
  the two bodies.
• The Sun is not in precise center of orbit.

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Orbital Motion

• The distance between any two objects is measured
  NOT between their surfaces,
  
  but between
  their CENTERS.
• A small object does not orbit the large
  object. They both orbit about the common CENTER
  of MASS.
• For example, the Moon does NOT orbit the Earth.
  The Earth and Moon
  orbit their common center of mass.

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Escaping Gravity

• For an object to escape from a massive object,
  the escaping object must achieve
  sufficient velocity to overcome the force of
  gravity.
• Applies to spacecraft leaving Earth
  particles
  blasted from stars.

Escape Speed speed needed by an object to leave
the gravitational pull of another body Types
of Orbits Bound The orbit is bound, or
confined,
to follow the same curvilinear
path. Unbound The orbit is not bound, or
confined, and will continue charting a new path
through time.
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Navigating in Space

• According to Newton's laws of motion and
  gravitation, if an object moves fast enough, its
  path will match the curvature of the Earth, and
  it will never hit the ground -- it goes into
  orbit.
• Circular orbital velocity for a low Earth orbit
  is 5 miles/sec.
• If object's velocity is gt 5 miles/sec, but lt 7
  miles/sec its orbit will be an ellipse.
• Velocities gt7 miles/sec reach escape velocity,
  and the object moves in a curved path that does
  not return to Earth.

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The effect of launch speed on the trajectory of a
satellite.

• Required launch speed for Earth satellites is
• 8 km/s (17,500 mph) for circular orbit
  just above atmosphere,
• 11 km/s (25,000 mph) to escape from
  Earth.

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Navigating in Space Transfer Orbits

• To send a spacecraft to another planet, it is
  launched into a transfer orbit around the Sun
  that touches both the Earth's orbit and the orbit
  of the planet.
• Once the spacecraft is in the transfer orbit, it
  coasts to the planet. The gravitational force of
  the Sun takes over and this part of the ride is
  free.
• But transfer orbits put constraints on space
  travel.
• The launch must occur when the planet and the
  Earth are in the correct relative positions in
  their orbits.
• This span of time is called a launch opportunity.
  
• During each launch opportunity, which can be a
  few weeks in duration, the spacecraft must be
  launched during a specific time of the day -
  launch window.
• If the spacecraft is headed for an inner planet
  (Mercury or Venus), the launch window occurs in
  the morning.
• For outer planets (Mars and beyond), the launch
  window occurs in the early evening.

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Navigating in Space Gravity Assist

• Another technique used by space navigators is
  called gravity assist.
• When a spacecraft passes very close to a planet,
  it can use the strong gravitational field of the
  planet to gain speed and change its direction of
  motion.
• According to Newton's laws of motion, the planet
  looses and equal amount of energy in the process,
  but because the mass of the planet is so much
  greater than the mass of the spacecraft, only the
  spacecraft is noticeably affected.