Astronomy 100Tuesday, Thursday 2:30 - 3:45 pm

Tom Burbinetburbine@mtholyoke.edu

Class

• I was very impressed by the zodiac assignments people turned in

Test Next Tuesday

• What you should do:• Read the book• Go over the lecture notes• I will talk about it a lot more on Thursday since I

am making it up tonight• If you try to take the test without studying and if

you haven’t been to class, I am pretty sure you will flunk it

Hint

If I have talked about it in class, I consider it important

Homework #4• Its on OWL.• The first homework assignment has 10 questions. For

each question, you will get two attempts to answer it correctly.

• After your last attempt, the correct answer will be shown.• If you get all 10 questions correct, you will get one

homework point. • If you get less than 10 questions correct, I will divide the

number of questions you get correct by 10 to determine the fraction of a homework point that you will receive.

• This is due by Thursday evening (2/10) at 11:59 pm

PRS question #1

• What class is this?– A) Psychology 100– B) Astronomy 100– C) Geology 100– D) Physics 100

Models

• When you have a model of how something works, you should be able to predict what will happen

• If observations do not fit the model, either the observations or the model is wrong

• The ancient astronomers wanted to predict the positions of planets in the sky

What did the ancients think

• That the Earth was the center of the universe

• That the celestial sphere was rotating around the Earth

• However, there was two observations that caused problems with this idea– apparent retrograde motion– Inability to detect stellar parallax

Greek model

Apparent Retrograde Motion = “backward” motion

Retrograde Motion

Stellar Parallax

• Stellar Parallax – The apparent shift in the position of a nearby star (relative to distant objects) that occurs as we view the star from different positions in the Earth’s orbit of the Sun each year

The distance the star moves is greatly exaggerated in this figure.Stellar parallax can only be seen by a telescope.

Ancient astronomers could not detect stellar parallax

• If Earth orbited the Sun, ancient astronomers believed that they would see differences in angular separation of stars as the Earth rotated around the Sun

• Since they saw no changes in angular separation of the stars, they assumed the Earth was the center of the universe

• They could not fathom that stars are so far away that stellar parallax is undetectable by the human eye

Ptolemy’s (100-170 AD) Model of the Universe

Nicholas Copernicus (1473-1543)

• Copernicus came up with a model that the Earth revolves around the Sun

• Similar to what Aristarchus (310 – 230 BC) thought 2000 years before

• However, Copernicus’ models did not match observations since he wanted everything to arouind in perfect circles

Tycho Brahe (1546-1601)

• Tycho Brahe was the greatest naked eye observer of all time

• He lived before the invention of the telescope• His observations of the alignment of Jupiter and

Saturn occurred two days later than when predicted by Copernicus

• Tycho came up with a model where the planets orbit the Sun but the Sun orbits Earth

Johannes Kepler (1571-1630)

• Tried to match circular orbits to Tycho’s data

• Couldn’t do it

• Because Tycho’s observations were so good, Kepler had to come up with a new model

Kepler was trying to match an orbit to Tycho’s observations of Mars

• “If I 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 8 minutes pointed to the road to a complete reformation in astronomy.”

• Kepler came up with his 3 laws of planetary motion

Kepler’s 1st Law

• The orbit of each planet about the Sun is an ellipse with the Sun at one focus (there is nothing at the other focus)

Differences between ellipses and circles

Show Video

Definitions

• Perihelion – planet closest to the Sun

• Aphelion – planet farthest from the sun

• Semimajor axis – the average of a planet’s perihelion and aphelion distances

Kepler’s 2nd law

• As a planet moves around its orbit, it sweeps out equal areas in equal times.

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

Show Video

Show Video

Kepler’s 3rd Law

• More distant planets orbit the Sun at slower average speeds, obeying the precise mathematical relationship

p2 = a3

where p is a planet’s orbital period in years and a is the average distance from the Sun in

astronomical units.

Calculations

• The period for the Earth to go around the Sun is 1 year

• The distance of the Earth to the Sun is 1 Astronomical Unit

How long does it take Jupiter to go around the Sun

• If Jupiter is 5.2 Astronomical Units from the Sun, how long does it take Jupiter to go orbit the Sun once

• p2 = a3 = 5.23 = 140.6

• p = √140.6 = 11.9 years

PRS question #2

• Mercury is 0.4 Astronomical Units from the Sun.

• How long does it take Mercury to orbit the sun once?– A) 1 year– B) 3 months– C) 9 months– D) 5 years

The calculation

• p2 = a3 = 0.43 = 0.064

• p = √0.064 = 0.25 years

You can calculate a planet’s orbital speed

• Since you know a planet’s orbital distance

• And you know its orbital time

• You can calculate a planet’s average orbital speed

Arguments against the Sun being the center of the solar system

• 1) If the Earth was moving, objects such as birds and clouds would be left behind as the Earth moved

• 2) The heavens must be perfect and unchanging. Noncircular orbits do not fit this model

• 3) Stellar parallax would be observable

Galileo Galilei (1564-1642)

• He was able to figure out answers to these arguments

• 1) Things in motion tend to remain in motion.

• 2) He used a telescope to see sunspots on the Sun and features on the Moon.

• 3) Galileo found that stars were more numerous and more distant than imagined

He also

• He discovered the moons of Jupiter and saw that they were orbiting Jupiter

• Proving that bodies could orbit other bodies besides the Earth

Galileo also found that Venus orbited the Sun

However

• Galileo was brought to a church inquisition in Rome and made to recant his views

• He did it to save his life

• Supposedly said Epper si muove “And yet it moves” under his breath while getting up from his knees.

So why did observations that the Earth was not the center of the

universe fall out of favor

So why did observations that the Earth was not the center of the universe fall out

of favor

• Because models based on this did not accurately predict observations

Questions?