Homework #2Homework #2 Due Wednesday, September 9, 6PM

Covers Chapters 1, 2, and 3

Estimated time to complete: 1 hour 10 minutes (so don’t wait until the last minute!) – can stop and start as you wish

Read chapters, review notes before starting

Some questions have multiple parts – do not skip them

For some of the drag-and-drop ordering questions, two or more of the answers might be in the same location (i.e., two objects might have the exact same age if you are sorting by age). In this case, place the two answers on top of each other.

Note: Incorrect guesses will count against you.

Due Wednesday, September 9, 6PM

Covers Chapters 1, 2, and 3

Estimated time to complete: 1 hour 10 minutes (so don’t wait until the last minute!) – can stop and start as you wish

Read chapters, review notes before starting

Some questions have multiple parts – do not skip them

For some of the drag-and-drop ordering questions, two or more of the answers might be in the same location (i.e., two objects might have the exact same age if you are sorting by age). In this case, place the two answers on top of each other.

Note: Incorrect guesses will count against you.

This Week in AstronomyThis Week in AstronomyZipping By Pluto!Zipping By Pluto!

Best image with Hubble Space Telescope

What’s next for New Horizons?

Planned fly-by of Kuiper Belt object 2014 MU69 in early January 2019.

2014 MU69 is only 30-45 kilometers in size at a distance of 43 AU.

• Greeks were the first people known to make models of nature.

• They tried to explain patterns in nature without resorting to myth or the supernatural.

Greek geocentric model (c. 400 B.C.)

Why does modern science trace its roots to the Greeks?

Underpinnings of the Greek geocentric model:

How did the Greeks explain planetary motion?

• Earth at the center of the universe (since no detected parallax)• Heavens must be “perfect”: Objects move on perfect spheres or in perfect circles.

AristotlePlato

The most sophisticated geocentric (Earth-centered) model was that of Ptolemy (A.D. 100-170) — the Ptolemaic model:

• Sufficiently accurate to remain in use for 1,500 years. • Arabic translation of Ptolemy’s work named Almagest (“the greatest compilation”)

PtolemyExtremely contrived…..

But this model made it difficult to explain apparent retrograde motion

of planets…

But this model made it difficult to explain apparent retrograde motion

of planets…

Review: Over a period of 10 weeks, Mars appears to stop, back up, then go forward again.

So how does the Ptolemaic model explain retrograde motion?Planets really do go backward in this (wrong) model…

Epicycles (circles upon circles)

This system predicts the orbits reasonably well if you add enough epicycles to the system….

Mercury eventually required 11 epicycles in Ptolemaic model to remain sufficiently accurate!

Needed to mimic retrograde motion

Extremely contrived!

Ptolemy’s Geocentric Model

Ptolemy’s Geocentric Model

• Earth is at center• Sun orbits Earth• Planets orbit on small circles (epicycles) whose centers orbit the Earth on larger circles

• This view of the Solar System held for 1500 years….

Which of the following was not a feature of the Ptolemaic model?Which of the following was not a feature of the Ptolemaic model?

A) Epicycles were used to explain planetary retrograde motion.

B) The Earth was at the center of the Solar System.

C) The Earth orbited the Sun.D) The orbits of planets were perfect circles.

Which of the following was not a feature of the Ptolemaic model?Which of the following was not a feature of the Ptolemaic model?

A) Epicycles were used to explain planetary retrograde motion.

B) The Earth was at the center of the Solar System.

C) The Earth orbited the Sun.D) The orbits of planets were perfect circles.

Greeks thought the Earth did not move because they could not measure stellar parallax.

How was Greek knowledge preserved through history?

• The Muslim world preserved and enhanced the knowledge they received from the Greeks.

• Al-Mamun’s House of Wisdom in Baghdad was a great center of learning around A.D. 800.

• With the fall of Constantinople (Istanbul) in 1453, Eastern scholars headed west to Europe, carrying knowledge that helped ignite the European Renaissance.

How did Copernicus, Tycho, and Kepler challenge the Earth-centered model?

Copernicus (1473-1543)

• Nicolas Copernicus proposed a Sun-centered model (published 1543)

• Used model to determine layout of solar system (planetary distances in AU)

But . . .

• The model was no more accurate and not any simpler than the Ptolemaic model in predicting planetary positions,

because it still assumed perfectly circular orbits (and therefore still

had to use epicycles).

Tycho Brahe (1546-1601)

• Compiled the most accurate (one arcminute) naked eye measurements ever made of planetary positions. • Still could not detect stellar parallax, and thus still thought Earth must be at center of solar system (but recognized that other planets go around Sun).

• Hired Johannes Kepler, who used Tycho’s observations to discover the truth about planetary motion.

Tycho Brahe

• Kepler first tried to match Tycho’s observations with circular orbits -- no success

• An 8-arcminute discrepancy led him eventually to use ellipses rather than circles

“If I had believed that we could ignore these eight minutes [of arc], I would have patched up my hypothesis accordingly. But, since it was not permissible to ignore, those eight minutes pointed the road to a complete reformation in astronomy.”

Johannes Kepler(1571-1630)

Good scientist!

Johannes Kepler

An ellipse is the locus of points where the sum of distances from two specified points is the same.

Ellipses

Kepler’s First Law: The orbit of each planet around the Sun is an ellipse with the Sun at one focus.

What are Kepler’s three laws of planetary motion?

Kepler’s First Law: The orbit of each planet around the Sun is an ellipse with the Sun at one focus.

What are Kepler’s three laws of planetary motion?

You will NEVER find an orbit that looks like this!

Remember This!!

Sun

Kepler’s Second Law: As a planet moves around its orbit, it sweeps out equal areas in equal times.

This means that a planet travels faster when it is nearer to the Sun and slower when it is farther from the Sun.

More distant planets orbit the Sun at slower average speeds, obeying the relationship p2 = a3

p = orbital period in years a = avg. distance from Sun in astronomical units (AUs) – this is the semi-major axis

For Earth, P = 1 year, a = 1 AU it works!

Kepler’s Third Law

Kepler’s Law’s were purely empirical in nature – he had no idea why the planets followed these laws – it was simply what he observed.

It was later shown by Isaac Newton (Chapter 4) that these laws are a natural consequence of gravity.

Kepler’s Laws

A) Less than one yearB) One yearC) More than one yearD) We need to know the size of the

asteroid

Imagine a hypothetical near-Earth asteroid that has a semi-major axis (average distance from Sun) that is the same as that of the Earth. What is its period around the Sun?

A) Less than one yearB) One yearC) More than one yearD) We need to know the size of the

asteroid

Imagine a hypothetical near-Earth asteroid that has a semi-major axis (average distance from Sun) that is the same as that of the Earth. What is its period around the Sun?

Since p2 = a3, and a for this object is about the same as for Earth, its period around the Sun must also be the same as Earth’s.

How did Galileo solidify the Copernican revolution?

How did Galileo solidify the Copernican revolution?

Galileo overcame major objections to the Copernican view. Three key objections rooted in Aristotelian view were:

1. Earth could not be moving because objects in air would be left behind (“Great Wind”).

2. Non-circular orbits are not “perfect” as heavens should be.

3. If Earth were really orbiting Sun, we’d detect stellar parallax.

Galileo’s experiments showed that objects in air would stay with Earth as it moves.

Overcoming the first objection (nature of motion):

• Aristotle thought that all objects naturally come to rest.

• Galileo showed that objects will stay in motion unlessa force acts to slow them down

Earth’s atmosphere moves with Earth, so no Great Wind

Overcoming the second objection (heavenly perfection):

Using his telescope, Galileo saw: • Sunspots on Sun (“imperfections”)

• Mountains and valleys on the Moon (proving it is not a perfect sphere)

• Showed that Venus exhibited non-crescent phases (e.g., gibbous)

Galileo’s 2-inch diameter telescope

• Tycho thought he had measured stellar distances, so lack of parallax seemed to rule out an orbiting Earth.

• Galileo showed stars must be much farther than Tycho thought — in part by using his telescope to see the Milky Way is countless individual stars.

• Planets resolved into disks while stars were still point sources

If stars were much farther away, then lack of detectable parallax was no longer so troubling.

Overcoming the third objection (parallax):

Galileo also saw four moons orbiting Jupiter, proving that not all objects orbit Earth.

However, he angered the Catholic church by insulting the Pope (Sun–centered models were not accepted by the Church at the time), leading to him spending the rest of his life under house arrest.

Despite Sun-centered models being outlawed, the undeniable evidence collected by Galileo eventually convinced everyone of a Sun-centered Solar System

Summary of Renaissance Cast of Characters

Copernicus – suggested a Sun-centered solar system - still insisted on circular orbits, epicycles

Tycho Brahe – best astronomy observer of his day - lost his nose, had a drunk moose

Kepler – proposed elliptical orbits Bingo! - used Brahe’s excellent data - developed 3 laws of planetary motion

Galileo – pointed newly-invented telescope at the night sky - final nail in the coffin of Earth-centered models with his telescopic observations of Moon, Sun, Venus, Jupiter