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

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Sunrise Midsummer

Sunrise Midwinter

Sunrise Equinox

Sunset Equinox

Sunset Midsummer

Sunset Midwinter

Rise points of bright stars at sunset on important days

Set 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

• 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 wrong1. 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 Laws1. 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. An unmeasureably small amount.

– B. 70 lbs.

– C. 140 lbs.

– D. 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. A year would be the same length.– B. A year would be longer– C. A year would be shorter– D. 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 = 42a3/(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