Download newton`s three laws of motion

The
Copernican
Revolution
Chapter 2
Chapter 2 Learning Objectives
 Know the differences and similarities between the geocentric and
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heliocentric models of the universe proposed by Ptolemy and
Copernicus, respectively.
State Brahe’s contributions to astronomy.
Describe Kepler’s three laws of planetary motion.
Be familiar with Galileo’s contributions to astronomy, especially
those to the heliocentric model.
Know Newton’s Law of Universal Gravitation and how it can be
used to explain an orbiting body around another.
Be able to state the Scientific Method.
Explain what causes stellar parallax.
Define the astronomical unit (AU) and the light year (ly) and state
their size in miles.
Know why planetary retrograde motion is observed.
Distance
 What unit is used to measure depends
on the scale of the object or distance.
 For example:
 Use miles or kilometers to measure
distances between cities.
 Use inches or centimeters to measure
the size of family photographs.
Astronomical Unit
 Astronomical Unit
(AU) -- the average
distance between
the sun and the
earth (93 million
miles ≈ 150 million
km).
 Use the
Astronomical Unit
(AU) to measure
distances to planets
in the solar system.
Light-year
• Light-year (ly)- the distance that light
travels in one year (about 63,000 AU or
about 6x1012 miles).
• Use light-years to measure distances
between stars.
• The nearest star system to the sun
(Alpha Centauri) is about 4.4 ly away.
• The Sun is about 28,000 ly from the
center of the galaxy.
Light-year
About 100,000 ly
Parallax
 The apparent change in the location of an
object due to the difference in location of the
observer is called parallax.
Parsec
• Another way to measure distance is
•
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parallax.
distance (in parsec) = 1/parallax
d = 1/p
1 parsec = 206,265 AU = 3.26 ly.
For Proxima Centauri p =0.76 sec of
arc, d = 1.3 ps = 4.3 ly.
Parsec
1 arcsec
d = 1 ps
1 A.U.
Can only determine distance for “nearby”
stars because AU is “small”.
Scientific Method
 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.
Scientific Method
 Observations
are made.
 Theories and
models are
constructed.
 They are
tested.
 Replaced if
found
inadequate.
Ancient Greeks
 Aristotle(384-322BC), Plato (427-
347BC), Ptolemy(140 AD) …
 Believed that the universe can be
understood.
 The heavens are perfect.
 All celestial motion is uniform and circular.
 Geocentric (Earth-centered) model. The
Earth did not move. Lasted for over 2000
years.
Ptolemy’s Geocentric Model
Retrograde Motion
 The planets don’t always appear to move in
uniform motion with respect to the stars.
They appear to move backwards at times.
Retrograde motion
Retrograde Motion
 Any model of the universe must include planetary
retrograde motion.
 Ptolemy explained this motion by placing the
planets on epicycles which in turn orbited the
Earth.
Copernican
Revolution
 Nicolaus Copernicus (1473 - 1543).
 Heliocentric (Sun-centered) model.
 Model went against the church.
 His work was published after he died.
 Explained retrograde motion.
 Kept stars on a sphere.
 Some inaccuracies--orbits were circular.
Heliocentric
Model
Retrograde Motion
 In the sun-
centered
model, the
retrograde
motion of
Mars is seen
when the
Earth passes
Mars in its
orbit around
the Sun.
Tycho Brahe (1546 - 1601)
 Best known for compiling
careful observations of stellar
and planetary positions.
 In 1572, he saw a new “ star”
that displayed no parallax.
 New “ star” must lie on the
starry sphere of the
geocentric model. A
contradiction to Aristotle’s
perfect heavens.
Tycho’s New “Star”
Question
 Do the planets orbit the Sun at
constant speeds?
 No. 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.
Johannes Kepler (1571 1630)
 Believed in heliocentric
model.
 Used Brahe’s data to
abandon circular orbits.
 Planets orbit the Sun in
elliptical orbits.
 Derived three laws of
planetary motion.
KEPLER’S 1st LAW OF PLANETARY
MOTION
 The orbit of
a planet
around the
Sun is an
ellipse with
the Sun at
one focus.
Elliptical Orbits
 In an elliptical orbit, the distance from a
planet to the Sun varies. The point in a
planet’s orbit closest to the Sun is called
perihelion, and the point farthest from the
Sun is called aphelion.
KEPLER’S 2nd LAW OF PLANETARY
Planet moves
MOTION
slower in its orbit
when farther away
from the Sun.
Planet moves
faster in its orbit
when closer to the
Sun.
 A line
joining the
planet and
the Sun
sweeps out
equal areas
in equal
intervals of
time.
KEPLER’S 3rd LAW OF PLANETARY
MOTION
 The square of a planet’s 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
planet’s 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.
KEPLER’S 3rd LAW OF PLANETARY
MOTION
Galileo Galilei (1564 - 1642)
 First to use the telescope.
 Discovered: the Moon has
mountains and craters, Sun
spots, Sun rotates, moons of
Jupiter, Venus has phases, …
 Phases of Venus disproved
geocentric model over
heliocentric model.
Phases of Venus
 In the
Ptolemaic
(geocentric)
model,
Venus
would be
seen in only
new or
crescent
phases.
Phases of Venus
 However, as Galileo observed, Venus is seen in
all phases, which agrees with the Copernican
model as shown.
Jupiter’s Moons – Galilean Moons
Galileo also discovered
moons in orbit around the
planet Jupiter. This was
further evidence that the
Earth was not the center of
the universe.
Isaac Newton (1642 - 1727)
 Three Laws of Motion.
 Linked falling objects to
the motion of the Moon.
 Both experience Earth’s
force due to gravity.
 Law of Universal
Gravitation.
Question
 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.
NEWTON’S 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.
Gravity
stops it
Goes on
forever
NEWTON’S THREE LAWS OF
MOTION
 LAW #2: The acceleration of an object
is proportional to the force acting on
it.
 Force = (mass)( acceleration)
F
F
m
Easier to move
M
Harder to move
NEWTON’S THREE LAWS OF
MOTION
 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.
I push on you, you push on me.
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.
Orbits
NEWTON’S 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.
Question
 Why was the discovery of Neptune a
major confirmation of Newton’s
universal law of gravitation?
Newton’s laws were applied to other objects in our
solar system.
Using Newton’s methods, Edmund
Halley worked out the details of a
comet’s orbit and predicted its return.
Deviations from
Newton’s Laws in the
orbit of the planet
Uranus led to the
discovery of the eighth
planet, Neptune.
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 Earth’s orbit
around the Sun?
 Elliptical
WHAT DID YOU THINK?
 Do all the planets orbit the Sun at the same
speed?
 No. A planet’s speed depends on its average
distance from the Sun.
 How does an object’s mass differ when
measured on the Earth and on the Moon?
 Its mass remains constant.