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Transcript
CHAPTER 2:
Gravitation
and the
Waltz of the
Planets
Geocentric Model
•
•
•
•
Earth centered
Aristotle (384 - 322 B.C.)
Heavens are fixed
Circular orbits
Problem with Geocentric Model
• Did not explain
retrograde motion,
• Planets usually move
from west to east
along ecliptic.
Occasionally they
would stop and move
from east to west
Problem “solved” with Ptolemy
140 A.D.
• Planets move around
earth on epicycles.
• Epicycles move around
earth on deferents.
• Seemed to solve problem
of backward motion of
planets.
• Unchallenged for 1300
years even though it was
not perfect
Heliocentric Model
• Sun in in the center
• First proposed by
Aristarchus in (310230 B.C)
• Not taken seriously
until 1500 with
Copernicus
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.
Many people disagreed with
the Copernican Theory,
However, the works of
Brahe, Kepler,
Galileo, and Newton
proved that
Copernicus’s
heliocentric theory
was correct
Tycho Brahe
• Accurate records of
the stars and planets
• Observed a supernova
with a small parallax
angle so is was far
away
• Inspired Kepler to
develop his laws
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.
KEPLER’S THREE LAWS OF PLANETARY MOTION
LAW #1. The orbit of a planet around the Sun is an ellipse
with the Sun at one focus.
The amount of elongation in a planet’s 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 planet’s orbit closest to the
Sun is called perihelion, and the point farthest from the
Sun is called aphelion.
KEPLER’S 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.
KEPLER’S THREE LAWS OF PLANETARY MOTION
LAW #3: 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.
Galileo Galilei
• Observed celestial
motion with telescope
• Evidence to support
Heliocentric model
• Opposed the church’s
view of a geocentric
model
Galileo also discovered
moons in orbit around the
planet Jupiter. This was
further evidence that the
Earth was not the center of
the universe.
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.
Newton
• Identified gravity and
gave the reason why
Kepler’s Laws
worked.
• Gravity is everwhere!
• Sun keeps planets in
orbit around it.
Isaac Newton formulated three laws to
describe the fundamental properties of
physical reality.
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.
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.
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.
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.
With his laws, Newton
was able to derive
Kepler’s three laws, as
well as predict other
possible orbits.
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.