chapter 2 the copernican revolution...2.4 the birth of modern astronomy phases of venus cannot be...

© 2011 Pearson Education, Inc.

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)


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


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



•  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)


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.



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.



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)


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)



•  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



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



Earliest models had Earth at center of solar system

Needed lots of complications to accurately track planetary motions


2.3 The Heliocentric Model of the Solar System

This figure shows retrograde motion of Mars.

Sun is at center of solar system. Only Moon orbits around Earth; planets orbit around Sun.

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.


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.



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)



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)


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)



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.



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.



3. Square of period of planet’s orbital motion is proportional to cube of semimajor axis


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


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)


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.


2.7 Newton’s Laws

Newton’s laws of motion explain how objects interact with the world and with each other.


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.


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.


2.7 Newton’s Laws Gravity

On the Earth’s surface, acceleration of gravity is approximately constant, and directed toward the center of Earth



For two massive objects, gravitational force is proportional to the product of their masses divided by the square of the distance between them



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



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.


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 (!)



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.


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


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

chapter 2 the copernican revolution...2.4 the birth of modern astronomy phases of venus cannot be...

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