Transcript Astro 10: Lecture 4 Why should you believe anything I’ve told you? Is the Earth really round? Does it spin on it’s axis? Does it.

Astro 10: Lecture 4
Why should you believe anything I’ve told
you?
Is the Earth really round?
Does it spin on it’s axis?
Does it really orbit the sun?
Are the stars really far away?
Astro 10: Lecture 4
A brief history of Astronomy
• More than 10,000 years ago
– Phases of the moon as a calendar
– Star maps?
• Neolithic
– Megalithic calendar stones
• Stonehenge
• Smaller calendar circles throughout the world
Calendar circle
N
Sunset
Midsummer
Sunset
Equinox
Sunset
Midwinter
Set points of bright stars
at sunset on important
days
Sunrise
Midsummer
Sunrise
Equinox
Sunrise
Midwinter
Rise points of bright stars
at sunset on important
days
Lecture 4: More history
Mayans ~ 0 C.E.
• Knew about zero
• Calendar based upon cycles of moon and sun.
– They observed and understood the timings
– Didn’t try to understand the cause
• Aztecs
– built cities to align with celestial events.
Lecture 4: Looks like Greek to me
• Greeks in Asia Minor (Turkey)
– 300-100 B.C.E. They started to systematically try to
understand the world. Why?
• Maybe the clash of differing cultures with different
assumptions about the way the world worked led them to
investigate more deeply
• Maybe differing skills combined (“eastern” geometry with
“western” philosophy.
Lecture4: Looks like Greek to me
• 330 B.C.E
– Heraclides develops geocentric model of the universe.
• 270 B.C.E
– Aristarchus develops the heliocentric model of the universe.
• 230 B.C.E.
– Eratosthenese measures the circumference of the earth.
• 170 B.C.E.
– Hipparchus devises magnitude system and catalogues the stars
The geocentric model (Heraclides)
The heliocentric model (Aristarchus)
The well at Syene
(230 B.C.E.)
• Syene is about 800 km south
of Alexandria
• Eratosthenes new on a
certain day of the year
sunlight went directly down
a well at Syene.
• He took a trip to Alexandria
and found that on that day
the sun was 7 degrees from
straight up
• 360/7 ~ 50
• 800km*50 = 40000 km =
circumference of the earth
Magnitudes
170 B.C.E: Hipparchus divides the stars into 5 brightness classes (magnitudes),
with 1st magnitude being the brightest, and 5th magnitude being the dimmest.
Why develop a model solar system?
• Predict events
– (Eclipses, conjunctions, oppositions, festival
dates)
• Predict the future through astrology.
• Build a better calendar.
• Navigation.
The Observations
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•
•
•
•
The sun makes a round trip of the sky every day
The sun moves through the entire zodiac in 1 year
The moon goes through phases over the course of a month
The moon can come between us and the sun.
The planets (in order of speed)
– Mercury, only seen near sunrise and sunset
– Venus, also a morning or evening star
– Mars, Jupiter and Saturn travel the enitre zodiac
• Mars, Jupiter and Saturn reverse their direction for a while
when they are opposite the sun (retrograde motion). The
planets vary in brightness depending upon position
Retrograde Motion
The (ancient greek) laws of nature
(The assumptions)
• Object don’t move unless acted upon by a
mover
• Circular motion (ex. top) can persist
because it is perfect.
• Unsupported things fall
• All things in the heavens are perfect
The geocentric model (Heraclides)
The (ancient greek) laws of nature
(The assumptions)
• Object don’t move unless acted upon by a
mover
• Circular motion (ex. top) can persist
because it is perfect.
• Unsupported things fall
• All things in the heavens are perfect
The heliocentric model (Aristarchus)
Successes and problems of the geocentric model
• Successes:
– Explains phases of the moon
– Does a good job of predicting positions of sun and moon
– Does an OK job of predicting the positions of Mars, Jupiter &
Saturn
• Problems:
– Didn’t explain retrograde motion. Why would perfect circular
motion reverse itself?
– Didn’t explain why Mercury and Venus stay close to the Sun.
– Didn’t explain why planets are brighter when they are opposite the
sun in the sky.
– Keeps earth in the proper “fallen” place.
Successes and problems of the heliocentric model
• Successes:
–
–
–
–
–
Explains phases of the moon
Does a good job of predicting positions of sun and moon
Does an good job of predicting the positions of the planets
Explains why Mercury and Venus stay close to the sun.
Explains why planets are brightest when opposite the sun.
• Problems:
– It is impossible to move without feeling the motion (vibration,
wind, noise).
– Stars would change in brightness and angular position over the
course of the year as the earth got closer or farther. (Don’t forget
parallax).
– Earth is imperfect and cannot be a part of the perfect heavens
– The moon would break the sphere that the earth travels in.
Ptolemy ups the ante
• 200 C.E.
– Ptolemy publishes ‘The Almagest’
• (13 books about many aspects of astronomy,
including history).
• Book 1 proves Earth is motionless.
• Includes MATH!
• Now people can use the geocentric system to make
even better predictions (less than a degree).
The Ptolemaic System
The Ptolemaic System
1300 years later...
• Nikolas Kopernik (Copernicus) reinvents
the heliocentric model.
– Still retains “perfect” circular motion.
– Still requires epicycles to make good preditions
• (Actually needs more epicycles than Ptolemy’s
model and is a little less accurate).
• It the first heliocentric model good enough to use.
– Doesn’t publish until after he’s dead.
• Publisher’s Preface: “It’s only a model, not reality”
• It does get noticed in Italy
The Copernican System
The Copernican System
Concept Test
• True/False: Both the Ptolemaic (geocentric)
and the Coppernican (heliocentric) models
can explain retrograde motion, so this
cannot be used to choose between them.
Bruno & Galileo
• Bruno: burned at the stake, in part for
advocacy of heliocentric theory
• Galileo: Builds a telescope
– Craters, mountains and “seas” on the moon: Not a prefect circle, a
world like earth
– Milky way is made of stars.
– Sunspots: The sun is not perfect
– Venus has phases: Supports heliocentrism.
– Jupiter has moons: Mini solar system.
Phases of Venus
Tycho & Kepler
• Tycho makes good observations, but
remains a geocentrist.
• Kepler takes Tycho’s observations and
figures out where Copernicus went wrong
1. Paths of the planets are ellipses with the sun at one focus
2. Orbits sweep out equal are in equal time (closer=faster)
3. Farther orbits take longer to complete. P2=a3
Click here
But Kepler doesn’t figure out WHY his laws work
Newton’s Laws
1. A body at rest or in uniform motion
continues unless acted upon by a force.
DEMO
2. Force = mass * acceleration
DEMO
3. Equal and opposite forces
DEMO
What does this have to do with orbits?
Universal Gravitation: Everything sucks
• Every object in the universe attracts every
other with a force:
– F=Gm1m2/r2
– proportional to mass.
• 2x mass : 2x force
– inversely proportional to distance:
• 2x distance : 1/4 force
• This little formula predicts all of Kepler’s Laws
• Newton invented Calculus to prove this. You won’t have to.
Concept Test
• Your weight is caused by the gravitational force between
you and the Earth. If you weigh 140 lbs, how much force
does the Earth feel due to the gravitational attraction of
your body?
–
–
–
–
A.
B.
C.
D.
An unmeasureably small amount.
70 lbs.
140 lbs.
Exactly zero.
– Click here
Weight and mass.
• Why are astronauts weightless?
– No gravity?
– What holds the moon in orbit?
• What does it mean to be weightless?
“weigthless” = falling
“falling” = not being held up
Weight and Mass
• Mass causes gravity, weight is the force of
gravity
– If your mass doubled, your weight would
double
– If the earth’s mass doubled with no radius
change, your weight would double.
– If the earth’s radius quadrupled with no mass
change, your weight would go to 1/4 its current
value
Yet another concept test
• If the Earth were in the same size orbit
around a star with twice the mass of the sun:
–
–
–
–
A.
B.
C.
D.
A year would be the same length.
A year would be longer
A year would be shorter
The Earth would collide with the sun.
Orbit concepts
• Circular velocity: velocity required to
maintain a circular orbit.
– Slower: object falls into an elliptical orbit
– Faster: the object rises into an elliptical orbit
• Newtons version of Kepler’s 3rd law.
– P2 = 4p2a3/(G(m1+m2))
– (m1+m2) P2 =a3
• for m in solar masses, P in years, a in astronomical
units
Orbits
More physics
• Energy is conserved.
– What is energy?
– For an orbit
• Kinetic energy: KE=mv2/2
• Potential energy: PE=-G m1 m2/r
• KE+PE=constant. If r decreases, v increases.
– Other energy: light energy, sound energy,
electrical energy, binding energy
More physics
• Conservation of momentum
– momentum=m*v
– In a collision momentum can be transferred, but
the total momentum stays the same.
– This is really the same as F=m*a.
• Rocket (low mass exaust at high velocity=high
mass rocket at lower velocity)
Tides
• Due to the sun and moon.
– The inverse square law of gravity says the
moon attracts the close side of the earth more
then the far side. Same with the sun, but less
magnitude due to 1/r2
– Rotation of the earth is being slowed by the
moon and sun.
– Conservation of energy and momentum mean the moon is
also getting farther away.
– Evidence from marine fossils confirms this.
Tides
Tides boost the moon and slow the rotation of
the Earth