Download Chapter 2 The Copernican Revolution

Chapter 2
The Copernican Revolution
This collage, clockwise from upper le4, shows four outstanding astronomers of the 20th century: Harlow Shapley (1885–1972) discovered our place in the “suburbs” of the Milky Way. Annie Cannon (1863–1941) classified nearly a million stars over the course of a 50-­‐year career. Karl Jansky (1905–1950) first detected radiaTon at radio wavelengths coming from the Milky Way. And Edwin Hubble (1889–1953) principally discovered the expansion of the universe. (Harvard Observatory; NRAO; Caltech) © 2011 Pearson Education, Inc.
Units of Chapter 2
2.1 Ancient Astronomy
2.2 The Geocentric Universe
2.3 The Heliocentric Model of the Solar System
The Foundations of the Copernican Revolution
2.4 The Birth of Modern Astronomy
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Units of Chapter 2, continued
2.5 The Laws of Planetary Motion
Some Properties of Planetary Orbits
2.6 The Dimensions of the Solar System
2.7 Newton’s Laws
2.8 Newtonian Mechanics
Weighing the Sun
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2.1 Ancient Astronomy
•  Ancient civilizations observed the skies
•  Many built structures to mark astronomical
events
Summer solstice sunrise at
Stonehenge:Figure 2-­‐1. Cap/on: Stonehenge. This remarkable site in the south of England was probably constructed as a primi/ve calendar or almanac. The inset shows sunrise at Stonehenge at the summer sols/ce. As seen from the center of the stone circle, the Sun rose directly over the “heel stone” on the longest day of the year. (English Heritage) © 2011 Pearson Education, Inc.
2.1 Ancient Astronomy
Spokes of the Big Horn Medicine Wheel are
aligned with the rising and setting of the Sun
and other stars
Figure 2-­‐2a. Cap/on: Observatories in the Americas. (a) The Big Horn Medicine Wheel in Wyoming, built by the Plains Indians, has spokes and other features that roughly align with risings and seMngs of the Sun and other stars. © 2011 Pearson Education, Inc.
2.1 Ancient Astronomy
This temple at
Caracol, in Mexico,
has many windows
that are aligned with
astronomical events
Figure 2-­‐2b. Cap/on: Observatories in the Americas. (b) The Caracol temple in Mexico, built by the Mayan civiliza/on, has some windows that seem to align with astronomical events, sugges/ng that at least part of Caracol’s func/on may have been to keep track of the seasons and the heavens. © 2011 Pearson Education, Inc.
2.2 The Geocentric Universe
Ancient astronomers
observed:
Sun
Moon
Stars
Five planets: Mercury, Venus,
Mars, Jupiter, Saturn
Figure 2-­‐3. Cap/on: Turkish Astronomers at Work. During the Dark Ages, much scien/fic informa/on was preserved and new discoveries were made by astronomers in the Islamic world, as depicted in this illustra/on from a 16th-­‐century manuscript. (The Granger CollecTon) © 2011 Pearson Education, Inc.
2.2 The Geocentric Universe
Sun, Moon, and stars all have simple movements in the sky
Planets:
•  Move with respect to fixed
stars
•  Change in brightness
•  Change speed
•  Undergo retrograde motion
Figure 2-­‐4. Cap/on: Planetary Mo<on. Most of the /me, planets move from west to east rela/ve to the background stars. Occasionally
—roughly once per year—however, they change direc/on and temporarily undergo retrograde mo/on (east to west) before looping back. The main illustra/on shows an actual retrograde loop in the mo/on of the planet Mars. The inset depicts the movements of several planets over the course of several years, as reproduced on the inside dome of a planetarium. The mo/on of the planets rela/ve to the stars (represented as unmoving points) produces con/nuous streaks on the planetarium “sky.” (Boston Museum of Science) © 2011 Pearson Education, Inc.
2.2 The Geocentric Universe
•  Inferior planets: Mercury, Venus
•  Superior planets: Mars, Jupiter, Saturn
Now know:
Inferior planets have
orbits closer to Sun
than Earth’s
Superior planets’
orbits are farther
away
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2.2 The Geocentric Universe
Early observations:
•  Inferior planets never too far from Sun
•  Superior planets not tied to Sun; exhibit
retrograde motion
•  Superior planets brightest at opposition
•  Inferior planets brightest near inferior
conjunction
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2.2 The Geocentric Universe
Earliest models had Earth at center of solar
system
Needed lots of
complications to
accurately track
planetary motions
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2.3 The Heliocentric Model of the
Solar System
Sun is at center of solar system. Only Moon orbits around Earth; planets
orbit around Sun.
This figure shows
retrograde motion of
Mars.
Figure 2-­‐9. Cap/on: Retrograde Mo<on. The Copernican model of the solar system explains both the varying brightnesses of the planets and the phenomenon of retrograde mo/on. Here, for example, when Earth and Mars are rela/vely close to one another in their respec/ve orbits (as at posi/on 6), Mars seems brighter. When they are farther apart (as at posi/on 1), Mars seems dimmer. Also, because the (light blue) line of sight from Earth to Mars changes as the two planets orbit the Sun, Mars appears to loop back and forth in retrograde mo/on. Follow the lines in numerical order, and note how the line of sight moves backward rela/ve to the stars between loca/ons 5 and 7. The line of sight changes because Earth, on the inside track, moves faster in its orbit than does Mars. The actual planetary orbits are shown as white curves. The apparent mo/on of Mars, as seen from Earth, is indicated by the red curve. © 2011 Pearson Education, Inc.
Discovery 2-1: The Foundations of
the Copernican Revolution
1.  Earth is not at the center of everything.
2.  Center of Earth is the center of Moon’s orbit.
3.  All planets revolve around the Sun.
4.  The stars are very much farther away than the
Sun.
5.  The apparent movement of the stars around the
Earth is due to the Earth’s rotation.
6.  The apparent movement of the Sun around the
Earth is due to the Earth’s rotation.
7.  Retrograde motion of planets is due to Earth’s
motion around the Sun.
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2.4 The Birth of Modern Astronomy
Telescope invented around 1600
Galileo built his own, made observations:
•  Moon has mountains and valleys
•  Sun has sunspots, and rotates
•  Jupiter has moons (shown)
•  Venus has phases
Figure 2-­‐11. Cap/on: Galilean Moons. The four Galilean moons of Jupiter, as sketched by Galileo in his notebook. The sketches show what Galileo saw on seven nights between January 7 and 15, 1610. The orbits of the moons (sketched here as asterisks, and now called Io, Europa, Ganymede, and Callisto) around the planet (open circle) can clearly be seen. More of Galileo’s remarkable sketches of Saturn, star clusters, and the Orion constella/on can be seen in the opener to Part 1 on page 1. (From Sidereus Nuncius) © 2011 Pearson Education, Inc.
2.4 The Birth of Modern Astronomy
Phases of
Venus cannot
be explained by
geocentric
model
Figure 2-­‐12. Cap/on: Venus Phases. Both the Ptolemaic and the Copernican models of the solar system predict that Venus should show phases as it moves in its orbit. (a) In the Copernican picture, when Venus is directly between Earth and the Sun, its unlit side faces us and the planet is invisible to us. As Venus moves in its orbit (at a faster speed than Earth moves in its orbit), progressively more of its illuminated face is visible from Earth. Note the connec/on between the orbital phase and the apparent size of the planet: Venus seems much larger in its crescent phase than when it is full because it is much closer to us during its crescent phase. This is the behavior actually observed. (The insets at bo_om le` and right are actual photographs of Venus taken at two of its crescent phases.) (b) The Ptolemaic model (see also Figure 2.7) is unable to account for these observa/ons. In par/cular, the full phase of the planet cannot be explained. Seen from Earth, Venus reaches only a “fat crescent” phase, then begins to wane as it nears the Sun. (Both these views are from a sideways perspec/ve; from overhead, both orbits are very nearly circular, as shown in Figure 2.18.) (Images from New Mexico State University) © 2011 Pearson Education, Inc.
2.5 The Laws of Planetary Motion
Kepler’s laws were
derived using
observations made by
Tycho Brahe
Figure 2-­‐14. Cap/on: Tycho Brahe. The astronomer in his observatory Uraniborg, on the island of Hveen in Denmark. Brahe’s observa/ons of the posi/ons of stars and planets on the sky were the most accurate and complete set of naked-­‐eye measurements ever made. (Royal Ontario Museum) © 2011 Pearson Education, Inc.
2.5 The Laws of Planetary Motion
1. Planetary orbits are ellipses, Sun at one focus
Figure 2-­‐15. Cap/on: Ellipse. An ellipse can be drawn with the aid of a string, a pencil, and two thumbtacks. The wider the separa/on of the foci, the more elongated, or eccentric, is the ellipse. In the special case where the two foci are at the same place, the curve drawn is a circle. © 2011 Pearson Education, Inc.
2.5 The Laws of Planetary Motion
2. Imaginary line connecting Sun and planet
sweeps out equal areas in equal times
Figure 2-­‐16. Cap/on: Kepler’s Second Law. A line joining a planet to the Sun sweeps out equal areas in equal intervals of /me. The three shaded areas A, B, and C are equal. Any object traveling along the ellip/cal path would take the same amount of /me to cover the distance indicated by the three red arrows. Therefore, planets move faster when closer to the Sun. © 2011 Pearson Education, Inc.
2.5 The Laws of Planetary Motion
3. Square of period of planet’s orbital motion
is proportional to cube of semimajor axis
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More Precisely 2-1: Some
Properties of Planetary Orbits
Semimajor axis and eccentricity of orbit
completely describe it
Perihelion: closest approach to Sun
Aphelion: farthest
distance from Sun
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2.6 The Dimensions of the Solar System
Astronomical unit: mean distance from
Earth to Sun
First measured during transits of Mercury
and Venus, using triangulation
Figure 2-­‐17. Cap/on: Solar Transit. The transit of Mercury across the face of the Sun. Such transits happen only about once per decade because Mercury’s orbit does not quite coincide with the plane of the eclip/c. Transits of Venus are even rarer, occurring only about twice per century. The most recent took place in June 2004. (AURA) © 2011 Pearson Education, Inc.
2.6 The Dimensions of the Solar System
Now measured using radar:
Ratio of mean
radius of Venus’s
orbit to that of
Earth is very well
known
Figure 2-­‐18. Cap/on: Astronomical Unit. Simplified geometry of the orbits of Earth and Venus as they move around the Sun. The wavy blue lines represent the paths along which radar signals are transmi_ed toward Venus and received back at Earth at the par/cular moment (chosen for simplicity) when Venus is at its minimum distance from Earth. Because the radius of Earth’s orbit is 1 AU and that of Venus is about 0.7 AU, we know that this distance is 0.3 AU. Thus, radar measurements allow us to determine the astronomical unit in kilometers. © 2011 Pearson Education, Inc.
2.7 Newton’s Laws
Newton’s laws of
motion explain how
objects interact with
the world and with
each other.
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2.7 Newton’s Laws
Newton’s first law:
An object at rest will remain at rest, and an object
moving in a straight line at constant speed will
not change its motion, unless an external force
acts on it.
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2.7 Newton’s Laws
Newton’s second law:
When a force is exerted on an object, its
acceleration is inversely proportional to its mass:
a = F/m
Newton’s third law:
When object A exerts a force on object B, object
B exerts an equal and opposite force on object A.
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2.7 Newton’s Laws
Gravity
On the Earth’s
surface, acceleration
of gravity is
approximately
constant, and
directed toward the
center of Earth
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2.7 Newton’s Laws
Gravity
For two massive
objects, gravitational
force is proportional to
the product of their
masses divided by the
square of the distance
between them
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2.7 Newton’s Laws
Gravity
The constant G is called the gravitational
constant; it is measured experimentally and
found to be
G = 6.67 x 10-11 N m2/kg2
© 2011 Pearson Education, Inc.
2.8 Newtonian Mechanics
Kepler’s laws are
a consequence of
Newton’s laws;
first law needs to
be modified: The
orbit of a planet
around the Sun is
an ellipse, with the
center of mass of
the planet–Sun
system at one
focus.
© 2011 Pearson Education, Inc.
More Precisely 2-3: Weighing the Sun
Newtonian mechanics tells us that the force
keeping the planets in orbit around the Sun is the
gravitational force due to the masses of the
planet and Sun.
This allows us to calculate the mass of the Sun,
knowing the orbit of the Earth:
M = rv2/G
The result is M = 2.0 x 1030 kg (!)
© 2011 Pearson Education, Inc.
2.8 Newtonian Mechanics
Escape speed: the
speed necessary for
a projectile to
completely escape a
planet’s
gravitational field.
With a lesser speed,
the projectile either
returns to the planet
or stays in orbit.
© 2011 Pearson Education, Inc.
Summary of Chapter 2
•  First models of solar system were
geocentric but couldn't easily explain
retrograde motion
•  Heliocentric model does; also explains
brightness variations
•  Galileo's observations supported
heliocentric model
•  Kepler found three empirical laws of
planetary motion from observations
© 2011 Pearson Education, Inc.
Summary of Chapter 2 (cont.)
•  Laws of Newtonian mechanics explained
Kepler’s observations
•  Gravitational force between two masses is
proportional to the product of the masses,
divided by the square of the distance
between them
© 2011 Pearson Education, Inc.