class06

ASTRO 101

Principles of Astronomy

Instructor: Jerome A. Orosz (rhymes with “boris”)Contact:• Telephone: 594-7118

• E-mail: [email protected]

• WWW: http://mintaka.sdsu.edu/faculty/orosz/web/

• Office: Physics 241, hours T TH 3:30-5:00

mailto:[email protected]

http://mintaka.sdsu.edu/faculty/orosz/web/

Homework

• Homework due February 5: Question 11 from Chapter 2 (In what ways did the astronomical observations of Galileo support a heliocentric cosmology?)

• Write down the answer on a sheet of paper and hand it in before the end of class on Febuary 5.

Dispatches from the Deparment of Anal Retention

• The Earth’s axis is tilted…

• What is the tilt relative to?

• The Northern Hemisphere is more exposed to the Sun…

• Why is it warmer in the summer than in the winter?

Homework• Go to a planetarium show in PA 209:• Tuesday, January 29 1:00 -- 2:00 PM

• Wednesday, January 30 2:00 -- 3:00 PM

• Friday, February 1 1:00 -- 2:00 PM

• Monday, February 4 11:00 AM -- 12:00 PM

• Tuesday, February 5 5:30 PM -- 6:30 PM

• Wednesday, February 6 2:00 -- 3:00 PM

• Thursday, February 7 5:30 -- 6:30 PM

• Friday, February 8 2:30 -- 3:30 PM

• Get 10 points extra credit for homework part of grade.• Sign up for a session outside PA 209.• Hand in a sheet of paper with your name and the date and time of

the session.

Watch Your Head!

• http://www.cnn.com/2013/02/05/world/space-asteroid/index.html?hpt=hp_c4

http://www.cnn.com/2013/02/05/world/space-asteroid/index.html?hpt=hp_c4

http://www.cnn.com/2013/02/05/world/space-asteroid/index.html?hpt=hp_c4

A Brief History of Astronomy


• An early view of the skies: The Sun: it rises and sets, rises and sets… The Moon: it has a monthly cycle of phases. The “fixed stars”: the patterns stay fixed, and

the appearance of different constellations marks the different seasons.

• Keep in mind there were no telescopes, no cameras, no computers, etc.


• But then there were the 5 “planets”: These are star-like objects that move through the

constellations. Mercury: the “fastest” planet, always near the Sun. Venus: the brightest planet, always near the Sun. Mars: the red planet, “slower” than Venus. Jupiter: the second brightest planet, “slower” than

Mars. Saturn: the “slowest” planet.


• By the time of the ancient Greeks (around 500 B.C.), extensive observations of the planetary positions existed. Note, however, the accuracy of these data were limited.

• An important philosophical issue of the time was how to explain the motion of the Sun, Moon, and planets.

What is a model?

• A model is an idea about how something works.

• It contains assumptions about certain things, and rules on how certain things behave.

• Ideally, a model will explain existing observations and be able to predict the outcome of future experiments.

Aristotle (385-322 B.C.)

• Aristotle was perhaps the most influential Greek philosopher. He favored a geocentric model for the Universe: The Earth is at the center of the Universe. The heavens are ordered, harmonious, and

perfect. The perfect shape is a sphere, and the natural motion was rotation.

Geocentric Model

• The motion of the Sun around the Earth accounts for the rising and setting of the Sun.

• The motion of the Moon around the Earth accounts for the rising and setting of the Moon.

• You have to fiddle a bit to get the Moon phases.

Geocentric Model

• The fixed stars were on the “Celestial Sphere” whose rotation caused the rising and setting of the stars.

• The constellations rise and set each night, and individual stars make a curved path across the sky.

• The curvature of the tracks depend on where you look.

Geocentric Model

• The fixed stars were on the “Celestial Sphere” whose rotation caused the rising and setting of the stars.

• However, the detailed motions of the planets were much harder to explain…

Planetary Motion

• The motion of a planet with respect to the background stars is not a simple curve. This shows the motion of Mars.

• Sometimes a planet will go “backwards”, which is called “retrograde motion.”

Planetary Motion• Here is a plot of the path

of Mars.• Other planets show similar

behavior.

Image from Nick Strobel Astronomy Notes (http://www.astronomynotes.com/)

http://www.astronomynotes.com/

Aristotle’s Model

• Aristotle’s model had 55 nested spheres.

• Although it did not work well in detail, this model was widely adopted for nearly 1800 years.

Better Predictions

• Although Aristotle’s ideas were commonly accepted, there was a need for a more accurate way to predict planetary motions.

• Claudius Ptolomy (85-165) presented a detailed model of the Universe that explained retrograde motion by using complicated placement of circles.

Ptolomy’s Epicycles

• By adding epicycles, very complicated motion could be explained.


Image from Nick Strobel’s Astronomy Notes (http://www.astronomynotes.com/).



• Ptolomy’s model was considered a computational tool only.

• Aristotle’s ideas were “true”. They eventually became a part of Church dogma in the Middle Ages.

The Middle Ages

• Not much happened in Astronomy in the Middle Ages (100-1500 A.D.).

Next:

The Copernican Revolution

The Sun-Centered Model• Nicolaus Copernicus

(1473-1543) proposed a heliocentric model of the Universe.

• The Sun was at the center, and the planets moved around it in perfect circles.

The Sun-Centered Model• The Sun was at the

center. Each planet moved on a circle, and the speed of the planet’s motion decreased with increasing distance from the Sun.

The Sun-Centered Model• Retrograde motion

of the planets could be explained as a projection effect.

The Sun-Centered Model• Retrograde motion

of the planets could be explained as a projection effect.

Image from Nick Strobel’s Astronomy Notes (http://www.astronomynotes.com/)


Copernican Model

• The model of Copernicus did not any better than Ptolomy’s model in explaining the planetary motions in detail.

• He did work out the relative distances of the planets from the Sun.

• The philosophical shift was important (i.e. the Earth is not at the center of the Universe).

Tycho Brahe (1546-1601)

• Tycho was born in a very wealthy family.

• From an early age, he devoted himself to making accurate astronomical observations.

• He received a great deal of support from the king of Denmark, including the use of his own island.

Tycho

• Tycho lived before the invention of the telescope.• His observations of Mars were about 10 times more

accurate than what had been done before.

Johannes Kepler (1571-1630)

• Kepler was a mathematician by training.

• He believed in the Copernican view with the Sun at the center and the motions of the planets on perfect circles.

• Tycho hired Kepler to analyize his observational data.

Johannes Kepler (1571-1630)

• Kepler was a mathematician by training.

• He believed in the Copernican view with the Sun at the center and the motions of the planets on perfect circles.

• Tycho hired Kepler to analyize his observational data.

• After years of failure, Kepler dropped the notion of motion on perfect circles.

Kepler’s Three Laws of Planetary Motion

• Starting in 1609, Kepler published three “laws” of planetary motion:



1. Planets orbit the Sun in ellipses, with the Sun at one focus.

Ellipses

• An ellipse is a “flattened circle” described by a particular mathematical equation.

• The eccentricity tells you how flat the ellipse is: e=0 for circular, and e=1 for infinitely flat.

Ellipses

• You can draw an ellipsed with a loop of string and two tacks.




2. The planets sweep out equal areas in equal times. That is, a planet moves faster when it is closer to the Sun, and slower when it is further away.

Kepler’s Second Law

• The time it takes for the planet to move through the green sector is the same as it is to move through the blue sector.

• Both sectors have the same area.





3. (Period)2 = (semimajor axis)3

Kepler’s Third LawPeriod P2 distance d3

Mercury 0.241 0.058 0.387 0.058

Venus 0.615 0.378 0.723 0.378

Earth 1.000 1.000 1.000 1.000

Mars 1.881 3.538 1.524 3.540

Jupiter 11.857 140.588 5.203 140.852

Saturn 29.424 865.772 9.537 867.432

The Kepler’s Law Simulator

• There are some animations on the web illustrating Kepler’s Laws:

– http://www.astro.utoronto.ca/~zhu/ast210/kepler.html

http://www.astro.utoronto.ca/~zhu/ast210/kepler.html

Heliocentric or Geocentric?

• The year is around 1610. The “old” school is Aristotle and a geocentric view. The “new” school is the heliocentric view (Copernicus and Kepler).

• Which one is correct?




• Observational support for the heliocentric model would come from Galileo.




• Observational support for the heliocentric model would come from Galileo.

• Theoretical support for the heliocentric model would come from Isaac Newton.

Next:

Who Wins?

Galileo Galilei (1564-1642)• Galileo was one of

the first to use a telescope to study astronomical objects, starting in about 1609.

• http://www.pacifier.com/~tpope/index.htm

http://www.pacifier.com/~tpope/index.htm

http://www.pacifier.com/~tpope/index.htm

Galileo Galilei (1564-1642)

• Galileo was one of the first to use a telescope to study astronomical objects, starting in about 1609.

• His observations of the moons of Jupiter and the phases of Venus provided strong support for the heliocentric model.

Jupiter’s Moons

• The 4 objects circled Jupiter, and not the Earth!

Jupiter’s Moons

• You can watch Jupiter’s moons move from one side of Jupiter to the other in a few days.

Jupiter’s Moons

• Not all bodies go around the Earth!

Venus

• Venus, the brightest planet, is never far from the Sun: it sets at most a few hours after sunset, or rises at most a few hours before sunrise.

Venus

• Venus, the brightest planet, is never far from the Sun: it sets at most a few hours after sunset, or rises at most a few hours before sunrise.

• It is never out in the middle of the night.

Venus

• Galileo discovered that Venus had phases, just like the Moon.

Venus


• Furthermore, the crescent Venus was always larger than the full Venus.

Venus


• Furthermore, the crescent Venus was always larger than the full Venus.

• Conclusion: Venus shines by reflected sunlight, and it is closer to Earth when it is a crescent.

Venus in the Geocentric View

• Venus is always close to the Sun on the sky, so its epicycle restricts its position.

• In this view, Venus always appears as a crescent.

Venus in the Heliocentric View

• In the heliocentric view, Venus orbits the Sun closer than the Earth does.

• We on Earth can see a fully lit Venus when it is on the far side of its orbit.

Venus in the Heliocentric View

• The correlation between the phases and the size is accounted for in the heliocentric view.

• Galileo’s observations of Jupiter and Venus strongly favored the heliocentric view of the Universe.


• Galileo was put before the Inquisition and forced to recant his views.


• Galileo was put before the Inquisition and forced to recant his views.

• Pope John Paul II admitted in 1992 that the Church was wrong to denounce Galileo.

Isaac Newton (1642-1727)

http://www-history.mcs.st-andrews.ac.uk/history/PictDisplay/Newton.html

http://www-history.mcs.st-andrews.ac.uk/history/PictDisplay/Newton.html


• Isaac Newton was born the year Galileo died.



• He was professor of mathematics at Cambridge University in England. (Steven Hawking currently hold’s Newton’s Chair at Cambridge).



• He was professor of mathematics at Cambridge University in England. (Steven Hawking currently hold’s Newton’s Chair at Cambridge).

• He was later the Master of the Mint in London, where first proposed the use of grooved edges on coins to prevent shaving.


• Newton was perhaps the greatest scientist of all time, making substantial contributions to physics, mathematics (he invented calculus as a college student), optics, and chemistry.


• Newton was perhaps the greatest scientist of all time, making substantial contributions to physics, mathematics (he invented calculus as a college student), optics, and chemistry.

• His laws of motion and of gravity could explain Kepler’s Laws of planetary motion.

Newton’s Laws of Motion

Newton’s Laws of Motion

1. A body in motion tends to stay in motion in a straight line unless acted upon by an external force.

2. The force on an object is the mass times the acceleration (F=ma).

3. For every action, there is an equal and opposite reaction. (For example, a rocket is propelled by expelling hot gas from its thrusters).

What is Gravity?

What is Gravity?

• Gravity is a force between all matter in the Universe.

What is Gravity?

• Gravity is a force between all matter in the Universe.

• It is difficult to say what gravity is. However, we can describe how it works.

What is Gravity?

• The gravitational force between larger bodies is greater than it is between smaller bodies, for a fixed distance.

What is Gravity?

• As two bodies move further apart, the gravitational force decreases. The range of the force is infinite, although it is very small at very large distances.

Newton’s Laws

• Using Newton’s Laws, we can…

Newton’s Laws

• Using Newton’s Laws, we can… Derive Kepler’s Three Laws.

Newton’s Laws

• Using Newton’s Laws, we can… Derive Kepler’s Three Laws. Measure the mass of the Sun, the Moon, and

the Planets.

Newton’s Laws

• Using Newton’s Laws, we can… Derive Kepler’s Three Laws. Measure the mass of the Sun, the Moon, and

the Planets. Measure the masses of distant stars in binary

systems.

Laws of Physics

• The models of Aristotle and Ptolomy were based mainly on beliefs (i.e. that motion should be on perfect circles, etc.).

• Starting with Newton, we had a physical model of how the planets moved: the laws of motion and gravity as observed on Earth give a model for how the planets move.

• All modern models in Astronomy are based on the laws of Physics.

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