Download lecture5 - UMass Astronomy

Origin of Modern Astronomy
Earth's place in the cosmos
The nature of planet motion
How we understand “the truth”
Addressing these three key issues led
to the birth of science .
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Assigned reading:
Chapter 4
When reading a chapter, make sure you study
the Guidepost, the Connections, the Portfolio
inserts and the Summary at the end
Archeoastronomy
• There is evidence that Human kind has paid very closed
attention to the sky, its motions and periodicity.
• Humans always tried to explain them
• Archeoastronomy a blend of superstition, astrology,
religion, but also common sense. Some of this remains this
very day (e.g. 2012 doomsday, astrology, UFO, etc.)
• Greeks were the first to try to understand (logically) the
universe.
• Thales of Miletus: first, true scientific attitude, humans
can understand
– Very different from previous “mysteric” attitude: humans cannot
comprehend mysteries
– Unknown vs. Unknowable
• Pythagoras: universe ruled by geometrical, mathematical
relationship
– This notions still fundamental today
Guidepost
The preceding chapters gave you a modern view of
Earth. You can now imagine how Earth, the moon, and
the sun move through space and how that produces the
sights you see in the sky. But how did humanity first
realize that we live on a planet moving through space?
That required revolutionary overthrow of an ancient and
honored theory of Earth’s place. By the 16th century,
many astronomers were uncomfortable with the ancient
theory that Earth sat at the center of a spherical universe.
In this chapter, you will discover how a Polish
astronomer named Nicolaus Copernicus changed the old
theory, how a German astronomer named Johannes
Kepler discovered the laws of planetary motion, and how
the Italian Galileo Galilei changed what we know about
nature.
The Roots of Astronomy
• Already in the stone and bronze ages, human
cultures realized the cyclic nature of motions in
the sky.
• Monuments dating back to ~ 3000 B.C. show
alignments with astronomical significance.
• Those monuments were probably used as
calendars or even to predict eclipses.
Newgrange, Ireland, built around 3200 B.C.:
Sunlight shining down a passageway into the central chamber
of the mount indicates the day of winter solstice.
Stonehenge
Summer solstice
Heelstone
• Constructed: 3000 – 1800 B.C.
• Alignments with locations of
sunset, sunrise, moonset
and moonrise at summer
and winter solstices
• Probably used as calendar
Other Examples All Around the World
Chaco Canyon,
New Mexico
Slit in the rock formation
produces a sunlit
“dagger” shape,
indicating the day of
summer solstice
Other Examples All Around the World (2)
Mammoth tusk found at Gontzi, Ukraine:
Inscriptions probably describing
astronomical events
Ancient Greek Astronomers (1)
• Unfortunately, there are no written
documents about the significance of
stone and bronze age monuments.
• First preserved written documents
about ancient astronomy are from
ancient Greek philosophy.
• Greeks tried to understand the
motions of the sky and describe
them in terms of mathematical (not
physical!) models.
Ancient Greek Astronomers (2)
Models were generally wrong because they were
based on wrong “first principles”, believed to be
“obvious” and not questioned:
1. Geocentric Universe: Earth at the Center of the
Universe
2. “Perfect Heavens”: Motions of all celestial
bodies described by motions involving objects of
“perfect” shape, i.e., spheres or circles
Greeks assumed the Earth
was not moving because
they did not observe
parallaxes in the sky.
Ancient Greek Astronomers (3)
• Eudoxus (409 – 356 B.C.): Model
of 27 nested spheres
• Aristotle (384 – 322 B.C.), major
authority of philosophy until the
late middle ages:
Universe can be divided in 2 parts:
1. Imperfect, changeable Earth,
2. Perfect Heavens (described by
spheres)
• He expanded Eudoxus’ Model to use 55 spheres.
Eratosthenes (~ 200 B.C.):
Calculation of the Earth’s radius
Angular distance between
Syene and Alexandria:
~ 70
Linear distance between
Syene and Alexandria:
~ 5,000 stadia
 Earth Radius ~ 40,000
stadia (~14 % too large) –
better than any previous
radius estimate
The birth of modern science
• Thales: Universe can be understood
• Pythagoras: Observations show that rules are
mathematical
• Plato: observations imperfect, pure thought can achieve
the truth
• All ingredients there for the methods of modern science:
have a theory and test it against reality
– Science: test theory with observations
– A theory is good only if it (or its consequences) explain the
observations/experiments
• Often, the survival of a (wrong) theory is due to not
sufficiently sensitive observations
• Ultimately, Greek “science” still a blend of scientific
method and “philosophical” believes, however.
• True scientific method had to wait for Galileo
The Old Astronomy:
Geocentric Universe
Aristotle (Greek, 384-322 BC)
Not to scale
Three Basic Assumptions
• The Earth was at the center of the
Universe.
• The only motion in the heavens was uniform
circular motion, because circular is the
“perfect motion”
• The heavens were more perfect than the
Earth, and objects in the heavens were
eternal.
• There was a hierarchy of perfection in
going from Earth to the Moon, the Sun, all
the way up to the stars.
Very different from methods
of modern science
• Build a theory on some hypothesis
• Test the predictions of the theory against
phenomenological reality
• Modify, update, generalize or discard and replace
the theory if *any* of its predictions or
consequences fail to reproduce reality
"Common Sense"
• If the Earth actually spun
on an axis, why didn't
objects fly off the spinning
Earth?
• If the Earth was revolving
around the sun, why didn't
it leave behind the birds
flying in the air?
• If the Earth were actually
on an orbit around the sun,
why wasn't a parallax
effect observed?
Two problems for the
Geocentric model:
(1) Change of
brightness
(2) Retrograde Motion
Ptolemy Solution:
add a special fix:
epicycle
or circle on circle
Brightness changes
because of distance
change
Ptolemic Model
Later refinements (2nd century B.C.)
• Hipparchus: Placing the Earth away from the centers of
the “perfect spheres”
• Ptolemy: Further refinements, including epicycles
Epicycles
Introduced to explain
retrograde (westward)
motion of planets
The Ptolemaic model was considered the
“standard model” of the Universe until the
Copernican Revolution.
The Copernican Revolution:
The Heliocentric System
Nicolai Copernicus (1473-1543).
The Sun, not the Earth, was the
center of the Solar System.
The Earth is just another planet
(the third outward from the Sun),
and the Moon is in orbit around
the Earth, not the Sun.
The stars are distant objects that
do not revolve around the Sun.
Copernicus’ New (and Correct) Explanation
for the Retrograde Motion of the Planets
Retrograde
(westward)
motion of a
planet occurs
when the
Earth passes
the planet.
This made Ptolemy’s epicycles unnecessary.
Retrograde Motion and Varying
Brightness of the Planets
The planets in such a system naturally vary in brightness
because they are not always the same distance from the Earth.
The retrograde motion could be explained in terms of
geometry and a faster motion for planets with smaller orbits.
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Copernicus’ ideas remained rather obscure for about 100
years after his death. Later work of Kepler, Galileo, and
Newton would build on the heliocentric Universe, leading
to the birth of modern astronomy and natural science.
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This sequence is commonly called the Copernican
Revolution.
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Ultimately, however, although revolutionary, Copernicus
model was flawed, because it could not explain the details
of the motions.
•
This had to wait until the first scientific explanation was
offered by Kepler.
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Tycho Brahe (1546 – 1601)
• High precision observations of the
positions of stars and planets
• Measurement of
the nightly motion
of a “new star”
(supernova)
showed no
parallax
• Evidence against
Aristotelian belief of
“perfect”,
unchangeable
heavens
Key Observations of Tycho Brahe
He made the most precise
observations of planetary motion,
particularly that of Mars.
However, Tycho was a firm believer
of the geocentric universe.
Danish nobleman
(1546-1601)
Tycho Brahe’s Legacy
New World model
• Still geocentric (Earth in the center of
the sphere of stars)
• Sun and Moon orbit Earth;
Planets orbit the sun.
Johannes Kepler:
The Laws of Planetary Motion
Unlike Brahe, Kepler believed firmly in
the Copernican system. Based on
Tycho's data on Mars, Kepler
concluded that the orbits of the planets
were not circles, but were instead
ellipses
(1571-1630), German
Kepler’s Laws of Planetary Motion
1
The orbits of the planets are ellipses, with the Sun
at one focus of the ellipse.
2
Planets move proportionally faster in their orbits
when they are nearer the Sun.
3
More distant planets take proportionally longer to
orbit the Sun
Kepler’s Laws of Planetary Motion
1.The orbits of the planets are ellipses with the
sun at one focus.
c
Eccentricity e = c/a
Eccentricities of Ellipses
1)
2)
e = 0.02
3)
e = 0.1
e = 0.2
5)
4)
e = 0.4
e = 0.6
Eccentricities of Planetary Orbits
Orbits of planets are virtually
indistinguishable from circles:
Earth: e = 0.0167
Most extreme example:
Pluto: e = 0.248
Planetary Orbits (2)
2. A line from a planet to the sun sweeps
over equal areas in equal intervals of
time.
Planetary Orbits (3)
3. A planet’s orbital period (P) squared is
proportional to its average distance from
the sun (a) cubed:
Py2 = aAU3
(Py = period in years;
aAU = distance in AU)
Calculations Using Kepler's Third Law
The ratio of the squares of the revolutionary periods
for two planets is equal to the ratio of the cubes of
their semimajor axes.
R(AU)3=P(years)2
As an example, the "radius" of the orbit of Mars
(the length of the semimajor axis of the orbit) is:
R=P2/3=(1.88)2/3=1.52 AU
Galileo Galilei
Galileo discovered that our Moon has
craters, that Jupiter has it's own
moons, that the Sun has spots, that
Venus has phases like our Moon, and
many more discoveries.
These discoveries confirmed the
Copernican hypothesis that the Earth
was just another planet.
The Bible tells us how to go to
Heaven, not how the heavens go
(1564-1642), Italian
The Phases of Venus
Venus went through a complete set of phases, just like the
Moon. This was the first empirical evidence that allowed a
definitive test of the geocentric and heliocentric models.
The phases of Venus
• Galileo explained the phases of Venus
(including “full Venus”) as due to the fact
that Venus orbits the sun, not the Earth!
The Moons of Jupiter
Galileo observed 4 points of light
that changed their positions with
time around the planet Jupiter.
He concluded that these were
objects in orbit around Jupiter.
Therefore, a planet could have
moons circling it that would not
be left behind as the planet
moved around its orbit.
Using the telescope, Galileo was the first to resolve the Milky
Way into individual stars, although he did not understand that the
Milky Way is one galaxy among other galaxies
(nor could have he understood that. Not even Einstein had that
notion, initially. We had to wait 1929, when Huble discovered the
cosmic expansion to understand that)
In summary: the three revolutionaries
Tycho Brahe, Kepler and Galileo Galilei
•Tycho made fundamental contributions
because of the accuracy of his
observations
•He discovered a supernova and
understood that it was a distant star, as
distant as other fixed stars> Starry
sphere no perfect
•Kepler discovered the laws of planetary
motions thanks to Ticho observations,
although he did not understood why
Kepler’s Laws of Planetary Motion
1
The orbits of the planets are ellipses, with the Sun
at one focus of the ellipse.
2
Planets move proportionally faster in their orbits
when they are nearer the Sun.
3
More distant planets take proportionally longer to
orbit the Sun
Kepler’s Three Laws of Orbits
1. The orbit of each planet about the Sun is an
ellipse with the Sun at one focus.
Kepler’s Three Laws of Orbits
2. As a planet moves around it’s orbit, it sweeps
out equal areas in equal times.
1 month
Kepler’s Three Laws of Orbits
3. A planet’s Period (the time it takes to
complete one orbit) is related to its
average distance to the sun.
(orbital period in years)2 = (average distance in AU)3
P2 = a3
Notice that there is nothing stated about the
planet’s or Sun’s mass here!
Galileo: Imperfect and
Changing Universe
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Sun had dark patches on Sun. The motion of such
sunspots indicated that the Sun was rotating on an axis.
The Milky Way was composed of enormous numbers of
stars that had not been seen before.
The planet Saturn had "ears".
The Moon was not smooth, but was covered by
mountains and craters.
The Universe is a physical system to be explored
empirically and described my mathematical models
What is truth to a scientist?
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Scientists explains the universe on terms of models whose
predictions are confirmed by empirical observations.
Truth is simply a theoretical framework capable to explain in
quantitative ways what the empirical investigation finds.
If new observations disagree with the model, the model is either
improved or rejected and replaced with something else.
Religion tells us a different truth that has nothing to do with the
physical word. And tell us to believe it as is told.
Galileo understood that the Universe is a physical system to be
explored empirically and described by mathematical models.
He was tried and found guilty not because he believed in the
Copernicus cosmology, but because he he presented the universe as
something that humans can explore and understand themselves
instead of believing in absolute truths