astronomy notes to accompany the text astronomy today, chaisson, mcmillan jim mims
TRANSCRIPT
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Astronomy
Notes to Accompany the Text Astronomy Today, Chaisson, McMillan
Jim Mims
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Chapter 2
The Copernican Revolution
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Units
Ancient Astronomy
The Geocentric Universe
The Heliocentric Model of the Solar System
The Foundations of the Copernican Revolution
The Birth of Modern Astronomy
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Units, cont.
The Laws of Planetary Motion
Some Properties of Planetary Orbits
The Dimensions of the Solar System
Newton’s Laws
The Moon Is Falling!
Weighing the Sun
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Ancient Astronomy
• Ancient civilizations observed the skies
• Many built structures to mark astronomical events
Summer solstice sunrise at Stonehenge:
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Ancient Astronomy
Spokes of the Big Horn Medicine Wheel are aligned with rising and setting of Sun and other stars:
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Ancient Astronomy
The temple at Caracol has many windows that are aligned with astronomical events
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The Geocentric Universe
Ancient astronomers observed:
Sun
Moon
Stars
Five planets: Mercury, Venus, Mars, Jupiter, Saturn
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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
• have retrograde motion
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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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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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The Geocentric Universe
Earliest models had Earth at center of solar system
Needed many computations to accurately track planetary motions:
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The Heliocentric Model of the Solar System
Only Moon orbits around Earth; planets orbit around Sun
Sun is at center of solar system
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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:
• Venus has phases
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The Birth of Modern Astronomy
Phases of Venus, in particular, cannot be explained by geocentric model
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The Laws of Planetary Motion
Kepler’s laws, derived using observations made by Tycho Brahe:
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The Laws of Planetary Motion
1. Planetary orbits are ellipses, Sun at one focus
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The Laws of Planetary Motion
2. Imaginary line connecting Sun and planet sweeps out equal areas in equal times
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The Dimensions of the Solar System
Astronomical unit: mean distance from Earth to Sun
First measured during transits of Mercury and Venus, using triangulation
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The Dimensions of the Solar System
Now measured using radar:
Ratio of mean radius of Venus’s orbit to that of Earth very well known
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Newton’s Laws
Newton’s laws of motion explain how objects interact with the world and with each other.
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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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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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Newton’s LawsGravity
On the Earth’s surface, acceleration is approximately constant, and directed toward center of Earth:
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Newton’s LawsGravity
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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Newton’s LawsGravity
The constant G is called the gravitational constant; it is measured experimentally and found to be:
G = 6.67 × 10–11 N m2/kg2
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Newton’s Laws
Kepler’s laws are a consequence of Newton’s laws.
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Newton’s Laws
Escape speed: the speed necessary for a projectile to completely escape a planet’s gravitational field
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Summary
• 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
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Summary
• 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