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Chapter 2The Copernican Revolution
Units of Chapter 2
• 2.1 Ancient Astronomy
• 2.2 The Geocentric Universe
• 2.3 The Heliocentric Model of the Solar System
• 2.4 The Laws of Planetary Motion
• Brahe’s Complex Data
• Kepler’s Simple Laws
Units of Chapter 2 (continued)
• 2.5 The Birth of Modern Astronomy
• Galileo’s Historic Observations
• The Ascendancy of the Copernican View
• 2.6 The Dimensions of the Solar System
• 2.7 Newton’s Laws
2.1 Ancient Astronomy• Many cultures around
the world built large, elaborate structures to mark astronomical events
• Stonehenge: stones pointed in the direction of the summer solstice
2.1 Ancient Astronomy
• Spokes of the Big Horn Medicine Wheel in Wyoming (built by the Plains Indians) are aligned with the rising and setting sun and other stars
2.1 Ancient Astronomy
• Caracol Temple- Mayans built many windows that aligned with astronomical events.
• The structure was also used for sacrifices when Venus appeared in the sky
2.1 Ancient Astronomy
• Other Astronomers:
• Chinese- “omens”- comets and guest stars- astronomers still look at chinese data to fill in gaps from the dark ages
• Arabic- Math techniques involved in trigonometry were developed by muslim astronomers. Founded the Zenith, Azimuth and Vega
2.2 The Geocentric Universe
• Cosmology- the study of the workings of the universe on the very largest scales
• Today: galaxies are mere points
• Greeks: solar system (Earth, Moon, Sun, stars are fixed, 5 planets)
2.2 The Geocentric Universe
• Sun, Moon, and stars all have simple movements in the sky
• Planets:
• Vary in apparent brightness
• Don’t maintain fixed positions
• Change speed
• Undergo retrograde motion
2.2 The Geocentric Universe• Early Observations:
• Inferior planets (Mercury and Venus) are never too far from the sun
• Superior planets (Mars, Jupiter, Saturn) are not tied to the sun; exhibit retrograde motion
2.2 The Geocentric Universe
• The Geocentric Model- developed Aristotle- Earth centered universe
• Needed lots of complications to accurately track planetary motions
• Epicycles- each planet moves in small circles, circling bigger circles (deferent) around the Earth
2.2 The Geocentric Universe• Ptolemy (140 A.D.)- ptolemaic
model- 80 circles- accepted for thousands of years
2.2 The Geocentric Universe
• Errors:
• Geocentric center
• Uniformed circular motion (philosophical)
2.2 The Geocentric Universe
• Arictarchus of Samos- (310-230 B.C.)- “all planets revolve are the sun- Earth rotates on an axis”
• Not accepted because Aristotle had too much influence and support
2.3 The Heliocentric Model of the Solar System
• Sun is at the center of the solar system. Only the moon orbits the Earth; planets orbit the sun.
• This figure shows the retrograde motion of Mars
2.3 The Heliocentric Model of the Solar System
• Copernican Revolution- realization that the Earth is not the center of the universe
• Violated religious teachings and previous thinking- Earth is non-central, non-distinguishable
• Book was in Latin- Galileo made the ideas popular- the church banned him and put the book in the Index of Prohibited Books (1616)
2.3 The Heliocentric Model of the Solar System
• Earth is not at the center of everything.
• Center of earth is the center of moon’s orbit.
• All planets revolve around the Sun.
• The stars are much farther away than the Sun.
• The apparent movement of the stars around the Earth is due to the Earth’s rotation.
• The apparent movement of the Sun around the Earth is due to the Earth’s rotation.
• Retrograde motion of planets is due to Earth’s motion (faster) around the Sun
2.4 The Laws of Planetary Motion
• Johannes Kepler- used others’ observations
• Galileo Galilei- used emerging technology- telescope
2.4 The Laws of Planetary Motion
• Brahe’s Complex Data
• Kepler’s work was based on the work of Tycho Brahe
• When Brahe died, Kepler inherited all his data- which was accurate to 1 arc second
• With Brahe’s data, Kepler abandoned the Copernicus Model and created the Laws of Planetary Motion
2.4 The Laws of Planetary Motion
• Kepler’s Simple Laws:
• 1st Law:
• The orbital paths of the planets are eliptical, with the sun at one focus
• semi-major axis- 1/2 the length of the long axis
• eccentricity- ratio of the distance between the foci to the length of the major 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
2.4 The Laws of Planetary Motion
• 2nd Law:
• An imaginary line connecting the sun to any planet sweeps out equal areas of the ellipse in equal intervals of time
• Explains the variation in planetary brightness
2.4 The Laws of Planetary Motion
• 3rd Law:
• The square of the planet’s orbital period is proportional to the cube of its semi-major axis
• Period- time needed for the planet to complete one orbit around the sun
• Astronomical Unit: (AU) one is equal to the average distance between the earth and the sun
p2 = a3
p: sidereal orbital period
a: length of semi-major axis
*A planet’s “year” (p), increases more rapidly
than the size of the orbit (a)
2.5 The Birth of Modern Astronomy
• Galileo’s Historic Observations
• heard of the telescope and built his own (1609)
• discovered the moon had mountains, valleys, and craters
• sun had imperfections (sunspots)- which changed- inferring that it rotates perpendicular to the elliptic plane
• discovered Jupiter’s moons
• noticed that Venus showed phases
2.5 The Birth of Modern Astronomy
• Phases of Venus cannot be explained by the geocentric model
2.6 The Dimensions of the Solar System
• Kepler’s laws allow for relative sizes of planetary orbits because his triangulation all used a portion of Earth’s orbit as a baseline
• Measurements were made as Mercury and Venus went in front of the Sun (transits)
2.6 The Dimensions of the Solar System
• Radar- modern way to derive an absolute scale
2.7 Newton’s Laws• Laws of Motion-
• 1st Law:
• a moving object will move forever unless some external force (push or pull) changes its direction
• inertia- tendency of an object to keep moving at the same speed/direction unless acted upon
2.7 Newton’s Laws• 2nd Law:
• When a force is exerted on an object, its acceleration is inversely proportional to its mass:
• a = F/m
• 3rd 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
2.7 Newton’s Laws
For two massive objects, gravitational force is proportional to the product of their masses divided by the square of the distance between them- Inverse Square Law
2.7 Newton’s Laws
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
MORE PRECISELY 2-2: THE MOON IS FALLING!
Newton’s insight: same force causes apple to fall and keeps Moon in orbit; decreases as square of distance, as does centripetal acceleration: a = v2/r
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 (!)
2.7 Newton’s LawsEscape 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 (continued)
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.
