Chapter 1: The Scientific Method

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Chapter 1 The Scientific Method

• Alyssa Jean-Mary
• Source The Physical Universe by Konrad B.
  Krauskopf and Arthur Beiser

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The Scientific Method

• The scientific method is a general scheme for
  looking at the universe, whether a direct
  approach or an indirect approach is used
• The scientific method is not a mathematical
  process, but a human one, that requires creative
  thinking in all four steps
• Examining the natural world is at the heart of
  the scientific method observations and
  experiment of the natural world are the
  foundations on which ideas are built as well as
  what is used to test these ideas

• Step 1 Formulating a problem either choose a
  field to work in or a specific idea to
  investigate in nature
• Step 2 Observation and Experiment testing the
  problem proposed accurate and objective data is
  collected
• Step 3 Interpretation the data collected is
  analyzed to form a law (a general rule) or a
  theory (a more ambitious attempt to explain the
  data) initially a scientific interpretation is
  called a hypothesis
• Step 4 Testing the Interpretation make new
  observations and experiment to test whether the
  interpretation is correct and can predict results

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The Scientific Method
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The Laws of Nature

• The laws of nature are different than the laws of
  a country the laws of a country can change and
  can vary from country to country, but the laws of
  nature are the same throughout the entire
  universe
• A regularity is a law of nature only if it holds
  everywhere at all times
• The laws of nature are important for 2 reasons
• 1. They can be used to predict phenomena not yet
  discovered
• For instance, the law of gravity was used to
  discover the planet Neptune
• 2. They can give an idea of what goes on in
  places that cannot be examined directly
• For instance, we cannot visit the center of the
  sun

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Theory vs. Law

• A law deals with what
• A theory deals with why it explains why
  certain events take place, and it can explain how
  a law originates in broader considerations
• For instance, Albert Einsteins general theory of
  relativity says that gravity is a distortion in
  the properties of space and time around a body of
  matter and it accounts for Newtons law of
  gravity, going one step further to say that the
  law of gravity also applies to light

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A Model

• A model is a simplified version of reality that
  can be used to understand some part of nature
• For instance, when Newton was developing his law
  of gravity, he treated the earth to be a perfect
  sphere and the orbit of the earth around the sun
  to be an ellipse. In reality, the earth is
  somewhat squashed and its orbit around the sun
  has irregularities in it. After he made the law
  of gravity, he then used it to explain why the
  earth is somewhat squashed (due to the spinning
  of the earth) and why the earths orbit around
  the sun is not a perfect ellipse (due to
  attractions to other planets).

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Why Science is Successful

• Science is a powerful tool for investigating
  nature because its ideas are constantly tested
  and retested i.e. it is a living body of
  information, correcting itself when needed,
  searching for a better understanding of the
  natural world
• The laws and theories of science are only valid
  until no contrary evidence is found
• If contrary evidence to a law or theory is found,
  then the law or theory has to be modified or even
  discarded
• What counts in science is definite measurements
  and clear reasoning a scientists experiments
  can be followed by another scientist in order to
  double check the law or theory behind the
  experiments
• Science is also all around us in our daily lives
  in the cars we drive, the clothe we wear, the
  way we communicate, etc.
• Curiosity and imagination are a key part of the
  scientific process
• Nothing is taken for granted in science
  everything can be tested and changed if need be

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Religion and Science

• Many scientists have been punished for the
  interpretations they have made from the data they
  collected because it does not follow the
  universal beliefs
• The essence of science is that its results are
  open to change if new information is discovered,
  which is different from the essence of
  creationism, which is a fixed doctrine with no
  basis for observation
• Religious beliefs are not a part of science
  because they are based on faith, to be
  unquestioned. Science on the other hand has
  skepticism at its heart.
• The great thing about the world is that it is a
  free marketplace of ideas, whether it be
  religious or scientific

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The Solar System Polaris

• Polaris is the north star
• It is used as a guide by travelers because
  Polaris seems to barely move at all
• Stars near Polaris appear to move around Polaris
  in circles
• Those stars above Polaris move from east to west
• Those stars below Polaris move from west to east
• As you get farther from Polaris, the circles the
  stars move in get bigger, until they eventually
  dip below the horizon

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Why does Polaris seem to be at the center?

• Polaris appears to be at the center because it
  lies almost directly above the north pole, where
  the earth circles about its axis
• Everything else seems to be moving in a circle
  around Polaris, but their positions with respect
  to each other are fixed
• For instance, the Big Dipper always has the shape
  of the Big Dipper, but it is not always in the
  same position in regards to Polaris

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Constellations

• Constellations are easily recognized groups of
  stars, like the Big Dipper
• Polaris is located on the end of the handle of
  the constellation, the Little Dipper
• Cepheus and Cassiopeia are constellations located
  opposite to the Big Dipper, around Polaris
• These two constellations are named for an ancient
  kind and queen of Ethiopia
• Draco is the constellation next to Cepheus
• Draco means dragon
• There are many constellations besides these, and
  most of them require a lot of imagination to see

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The Solar System The Sun and The Moon

• As they do their daily crossing of the sky from
  east to west, the sun and the moon move slightly
  eastward when compared to the constellations due
  to their slow movement
• The moon takes four weeks to drift eastward
  enough to return to its starting position in the
  sky
• The sun moves more slowly east than the moon
  does, so slowly that its day to day movement is
  barely noticeable the constellations appear to
  rise only 4 minutes early each night the sun
  takes one year to drift eastward enough to return
  to its starting position in the sky

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The Solar System Planets

• The are five planets (Greek for wanderer) that,
  like the sun and the moon, also shift their
  positions in the sky with respect to the stars
• These five planets are Mercury, Venus, Mars,
  Jupiter, and Saturn
• They shift so slowly that the day to day shift is
  hard to notice
• The paths of the planets are quite complex,
  unlike the path of the sun or the moon the
  planets do slowly drift eastward, but they do so
  at different speeds and even sometimes they
  reverse direction and head westward, thus the
  path of a planet appears as a loop

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The Ptolemaic System

• In this model, the earth is the center of the
  universe
• The earth is motionless, and everything else in
  the universe moves around the earth
• The celestial objects that move around the earth
  do so in circles or combinations of circles
• The sun moves around the earth exactly once a day
• The moon is in an orbit that is closer to the
  earth, and it moves around the earth more slowly
  than the sun and in an orbit that is smaller than
  the suns orbit
• The planets Venus and Mercury are located in
  orbits that are between the moons orbit and the
  suns orbit, with Venus orbit closer to the
  earth
• The other planets are located in orbits that are
  larger than the sun, and are thus further away
  from the earth than the sun
• The irregularities in the motions of the planets
  were dealt with by saying that the planets move
  in small circles around a point and then move
  around the earth in a large circle thus, the
  planets move in a series of loops

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Testing the Ptolemaic System

• The Ptolemaic System was tested using
  observations collected both by Ptolemy and by
  others
• The observations were used to calculate the speed
  of each celestial object, which allowed him to
  figure out the location of each celestial object
  in the sky at any time (past and future)
• The calculated positions of the celestial objects
  were close, but not exact, to the positions
  recorded centuries earlier and to the positions
  recorded in future years
• Thus, the Ptolemaic System fulfilled all the
  requirements of a scientific theory
• It was based on observations
• It took into account all known data
• It predicted data that could be tested in the
  future

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Errors with the Ptolemaic System

• In the sixteenth century, scientists began to
  notice that planets were not in the positions in
  the sky that the Ptolemaic System predicted they
  would be in
• The errors with the model could be correct in two
  ways
• 1. The Ptolemaic System could be made more
  complicated
• 2. The Ptolemaic System could be replaced by a
  different model of the universe

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The Copernican System

• In this model, the sun is the center of the
  universe, and all planets, including the planet
  earth, rotate around the sun in a circle
• The earth is a sphere that rotates around its
  axis once a day
• The moon circles the earth, much like the earth
  circles the sun
• The stars are very far away

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Objections to The Copernican System

• Protestant and Catholic religious leaders argued
  against the Copernican System because they did
  not want the earth be taken from its place as the
  center of the universe
• For example, on the issue of the earth making a
  complete turn about its axis every day, each side
  said
• Supporters of the Ptolemy System They stated
  that the speed needed for the earth to accomplish
  this would be so great that everything that was
  lose on the earth would be flung into space, and
  that a great wind would be created that would
  blow down buildings and trees.
• Supporters of the Copernican System They stated
  that the speed at which the earth turns is
  balanced by another force that holds us and
  everything else lose on the earth to the ground.
  Also, they stated that, if the supporters of the
  Ptolemy System thought that the earth was moving
  at such tremendous speeds, then what of the
  speeds that the sun and the other planets were
  moving at to complete their rotations about their
  axis once a day.

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Tycho Brahe and Johannes Kepler

• Tycho Brahe built an observatory with quite
  precise instruments
• He made thousands of measurements using these
  instruments and his exceptional eyesight
• Even without a telescope (since they had not yet
  been invented), Tycho determined celestial angles
  to better than 1/100 of a degree
• Johannes Kepler was Tychos assistant, and upon
  Tychos death in 1601, began to work on the data
  that Tycho collected
• Kepler set out to prove that the Copernican
  System was correct, but ended up finding out that
  none of the proposed models of the universe (i.e.
  the Ptolemaic System or the Copernican System)
  fit the data that Tycho collected, and thus, had
  to discard all proposed models and create a new
  model that fit Tychos collected data
• Kepler created three laws that explained the
  universe using the data that Tycho collected

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Keplers First Law

• Kepler formed the First Law after he determined,
  though calculations, that the proposed circular
  obits did not match the data
• Since circles didnt match the data, he examined
  other geometrical figures to see if they match,
  until he found that if the orbits were
  elliptical, they would fit Tychos data
• Keplers First Law states The paths of the
  planets around the sun are ellipses with the sun
  at one focus.

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Keplers Second Law

• Kepler formed the Second Law in order to relate
  the speeds of the planets to their positions in
  their orbits
• Keplers Second Law A planet moves so that its
  radius vector sweeps out equal areas in equal
  times.
• The radius vector of a planet is the imaginary
  line between it and the sun
• A conclusion from Keplers Second Law is that a
  planet travels faster when it is near the sun and
  slower when it is away from the sun
• For instance, the earth travels 30 km/s when it
  is near the sun, and 29 km/s when it is away from
  the sun, a 3 difference

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Keplers Third Law

• Kepler formed the Third Law by making further
  calculations in order to put more order in his
  model of the universe
• Keplers Third Law The ratio between the square
  of the time needed by a planet to make a
  revolution around the sun and the cube of its
  average distance from the sun is the same for all
  the planets.
• This law states the following (period of a
  planet)2/ (average orbit radius)3 is the same
  value for every planet
• The period of a planet is the amount of time it
  needs to go once around the sun
• The average orbit radius is the average
  distance the planet is away from the sun

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Keplers Model of the Universe

• Keplers model explains that the universe moves
  in simple motions
• The positions his model predicts for celestial
  objects agrees with Tychos data as well as with
  data collected thousands of years earlier
• His predictions for future positions of celestial
  objects is accurate
• Keplers model also explains that the speed of a
  planet is different depending on where it is in
  its orbit and that the speed of a planet is
  related to the size of its orbit

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Evidence The Copernican System vs. The Ptolemaic
System

• The Copernican System is a much more simple model
  of the universe than the Ptolemaic System
• Once the Copernican System was modified by
  Kepler, it became much more accurate than the
  Ptolemaic System
• However the Ptolemaic System could have been
  modified by Kepler to be just as accurate as the
  Ptolemaic System the only way to prove this
  model wrong is by observations
• The Copernican System is seen as correct today
  because there is direct evidence for many kinds
  of motions of the planets around the sun and for
  the rotation of the earth
• For example, starts that are near to the earth
  shift slightly when compared to the positions of
  stars that are far away.

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Gravity

• Since you need a force to keep an object on a
  curve path, Newton theorized that there must be a
  force holding the planets in orbit around the sun
• Newton thought that what was holding the planets
  in their orbits was a gravitational force between
  the planets and the sun, a force much like the
  force that holds us to the earth
• He also thought that the moon was held in an
  orbit around the earth by the same type of
  attraction
• If there was no gravitational attraction between
  the earth and the moon, the moon would just fly
  off into space
• Newtons discovery of the Law of Gravity depended
  on using the Copernican System for the model of
  the universe
• Gravity is a fundamental force i.e. it is a
  force that cannot be explained in terms of any
  other force
• There are four types of fundamental forces
• 1. gravitational forces these are forces that
  act between all bodies everywhere i.e. they
  hold bodies together
• 2. electromagnetic forces these are forces that
  act between electrically charged particles and
  are forces that have an unlimited range
• 3. strong forces these are forces that act
  inside atomic nuclei and are forces that have
  very short ranges
• 4. weak forces these are forces that have the
  same properties as strong forces in terms of that
  they act inside atomic nuclei and that they are
  forces that have very short ranges

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Evidence for the Law of Gravity outside our Solar
System

• There is evidence for the Law of Gravitys
  accuracy outside our solar system
• For instance, there is something known as double
  stars. Double stars are two stars that are
  rotating around each other. Since they are
  rotating around each other, there must be some
  force (i.e. gravity) that is holding them
  together.
• The reason for applying the Law of Gravity to the
  rest of the universe is that there is evidence
  that shows that the universe is made up of the
  same matter that makes up the earth
• In order to believe that the Law of Gravity is
  not the same throughout the universe, there has
  to be evidence to support this, which there isnt

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Why the Earth is Round

• The earth is round because gravity squeezes the
  earth into this shape
• For instance, if a part of the earth is sticking
  out, the gravitational attraction of the rest of
  the earth would pull on it until it is level or
  nearly level with the rest of the earth
• The same holds true for the reverse if a part of
  the earth is quite deep, the gravitational
  attraction of the rest of the earth would push on
  it until it is level or nearly level with the
  rest of the earth
• Irregularities on the earths surface (i.e.
  mountains and ocean basins) are very small
  compared to the size of the earth the distance
  between the lowest point (in the depths of the
  Pacific Ocean) and the highest point (the summit
  of Mount Everest) of the earth is less than 20
  km, compared to the earths RADIUS, which is 6400
  km

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The Shape of the Earth

• The earth is not a perfect sphere it bulges
  slightly at the equator and is slightly flattened
  at the north and south poles
• The distortion of the earth is not that much
  the width of the earth is only 43 km more than
  the height of the earth
• The distortion of other planets from a perfect
  sphere
• Venus has almost no distortion because it moves
  so slowly around its axis
• Saturn is almost 10 not as round because it
  moves so rapidly around its axis

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The Tides

• The level of the ocean rises and falls twice a
  day
• Usually the daily change of height in the ocean
  is not more than a few meters, but in some
  places, the height of the ocean can change daily
  by more than 20 meters
• This difference in the daily change of the height
  in the ocean is due to the fact that the
  gravitational attraction of the moon is more in
  some places than in others
• The moon attracts places on the earth that are
  closer to it more strongly that places that are
  far from it
• The sun also affects the height of the ocean
  since it too has a gravitational attraction to
  the earth
• Even though the sun has a greater gravitational
  attraction to the earth than the moon does, the
  affect the sun has on the height of the ocean is
  much less than the moon since the sun is farther
  away from the earth than the moon. This is
  because the tides depend on the difference
  between attractions on the side of the earth near
  the object (i.e. the moon or the sun) and on the
  side of the earth far from the object (i.e. the
  moon or the sun).
• When the sun, moon, and earth line up in a
  straight line, solar tides increase the lunar
  tides, and thus creates especially high and low
  tides. These especially high and low tides are
  called spring tides and happen about twice a
  month
• There are also neap tides, which are tides that
  are smaller than average high and low tides.
  These tides occur when the line between the moon
  and earth is perpendicular to the line between
  the sun and the earth

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The Tides
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The Discovery of Neptune

• Neptune was discovered from calculations done on
  Uranus
• Uranus, the seventh planet, was discovered in
  1781
• Calculations were done on Uranus to predict its
  orbit and its future positions in the sky
• These calculations were done using the
  attractions of the sun and the nearby planets on
  Uranus
• These predictions were correct for 40 years,
  which is about half the time Uranus needs to make
  one complete revolution around the sun, and then
  Uranus began to move differently than the
  predictions
• Two possibilities could account for this
• 1. The law of gravity was incorrect since the
  calculations were based on this
• 2. There was another unknown body acting on
  Uranus, pulling it away from the predicted path,
  that was not taken into account in the
  calculations
• Two scientists, Urbain Leverrier and John Couch
  Adams, set out to prove the second possibility
  since the law of gravity was firmly established
• Both scientists finished their calculations, and
  then sent them to an astronomer to find the
  object that their calculations predicted existed.
  Although Adams finished first, Leverriers
  calculations were verified by an astronomer
  first.
• The verification of their calculations reinforced
  the law of gravity, thus continuing the
  scientific method

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Measurement The SI System

• Units are standard quantities that are used to
  compare a given value to
• For example, if a distance is said to be 456
  miles, what is really being said is that the
  value is 456 when compared to the standard
  quantity, a mile
• The SI System (International System) is the most
  widely used system of units today
• In the SI System, the common units are
• meter (m) for length
• second (s) for time
• kilogram (kg) for mass
• Joule (J) for energy
• Watt (W) for power
• The SI System is used in most countries
  throughout the world, while the British System of
  units (i.e. foot (ft) for length and pound (lb)
  for mass) is used in only a few countries
• The SI System has the advantage that the units
  are broken into subdivisions that are multiples
  of 10
• For instance, 1 meter (m) 100 centimeters (cm)
• The British System doesnt have this same
  advantage its units arent broken into equal
  subdivisions
• For instance, 1 foot (ft) 12 inches (in)

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The Subdivisions of the SI System and Conversions
between the SI System and the British System

• Table 1.1 represents the subdivisions of the SI
  System
• Each subdivision is a factor of 10
• Table 1.2 represents the conversion of lengths
  between the SI System and the British System

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Example Calculations of Conversions between the
SI System and the British System

• Example 1 How many feet are in 45 meters?
• Answer 45.0 meters x (3.28 feet/1 meter) 148
  feet

• Example 2 How many centimeters are in 2.6
  inches?
• Answer 2.6 inches x (2.54 centimeters/1 inch)
  6.6 centimeters

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Significant Figures

• Significant Figures show how accurate a
  measurement is i.e. how sure we are of the
  measurement
• If a measurement is 65 meters, it is accurate to
  2 significant figures
• A measurement can never be more accurate than it
  originally was i.e. if it has 2 significant
  figures, it cant have any more or less than two
  significant figures
• When you multiply or divide two figures together,
  the answer has the amount of significant figures
  in the figure that has the least amount of
  significant figures
• For example, if you multiply 65.2 by 3.285, the
  answer is 214, with three significant figures
  because 65.2 has the least amount of significant
  figures (3 instead of the 4 in 3.285)
• When you are performing a series of calculations,
  keep an extra digit in intermediate steps only
  round to the correct significant figures for the
  final answer