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### A100 Solar System

### ASSIGNMENTS in the sky, Kepler showed the orbit to be an this week

- Review Chapter 1, Kepler’s Laws
- Read Chapter 2: Gravity & Motion
- 2nd Homework due Sept. 26
- Rooftop Session Tuesday evening, 9PM
- Kirkwood Obs. open Wednesday Eve., 8:30-10:30
- IN-CLASS QUIZ ON WEDNESDAY!!

Today’sAPOD

The Sun Today

Today: the Equinox

11:44 AM EDT

today

Dr. Phil Plait (Sonoma St. U.) acting as the Bad Astronomer balanced three raw eggs on end in late October 1998

http://apod.nasa.gov/apod/ap030923.html

The Problem: Retrograde Motion

- In a simple geocentric model (with the Earth at the center), planets should drift steadily eastward through the sky against the background of stars
- But sometimes, the motion of the planets against the background stars reverses, and the planets move toward the west against the background stars

Retrograde Motion in a Geocentric Model

- Ptolemy accounted for retrograde motion by assuming each planet moved on a small circle, which in turn had its center move on a much larger circle centered on the Earth
- The small circles were called epicycles and were incorporated so as to explain retrograde motion

Epicycles did pretty well at predicting planetary motion, but…

Discrepancies remained

Very complex Ptolemaic models were needed to account for observations

More precise data became available from Tycho Brahe in the 1500s

Epicycles could not account for observations

Epicycles get more complexAstronomy in the Renaissance but…

- Could not reconcile Brahe’s measurements of the position of the planets with Ptolemy’s geocentric model
- Reconsidered Aristarchus’s heliocentric model with the Sun at the center of the solar system

Nicolaus Copernicus (1473-1543)

Heliocentric Models with Circular Orbits but…

- Explain retrograde motion as a natural consequence of two planets (one being the Earth) passing each other
- Copernicus could also derive the relative distances of the planets from the Sun

But a heliocentric model doesn’t solve all problems but…

- Could not predict planet positions any more accurately than the model of Ptolemy
- Could not explain lack of parallax motion of stars
- Conflicted with Aristotelian “common sense”

Using Tycho’s precise observations of the position of Mars in the sky, Kepler showed the orbit to be an ellipse, not a perfect circle

Three laws of planetary motion

Johannes Kepler (1571-1630)Kepler’s 1 in the sky, Kepler showed the orbit to be an st Law

- Planets move in elliptical orbits with the Sun at one focus of the ellipse
- Words to remember
- Focus vs. Center
- Semi-major axis
- Semi-minor axis
- Perihelion, aphelion
- Eccentricity

Definitions in the sky, Kepler showed the orbit to be an

- Planets orbit the Sun in ellipses, with the Sun at one focus
- The eccentricity of the ellipse, e, tells you how elongated it is
- e=0 is a circle, e<1 for all ellipses

e=0.02 e=0.4 e=0.7

Eccentricity of Planets in the sky, Kepler showed the orbit to be an & Dwarf Planets

Which orbit is closest to a circle?

Kepler’s 2nd Law in the sky, Kepler showed the orbit to be an

- Planets don’t move at constant speeds
- The closer a planet is to the Sun, the faster it moves
- A planet’s orbital speed varies in such a way that a line joining the Sun and the planet will sweep out an equal area each month
- Each month gets an equal slice of the orbital pie

Kepler’s 2 in the sky, Kepler showed the orbit to be an nd Law:

Same Areas in the sky, Kepler showed the orbit to be an

If the planet sweeps out equal areas in equal times, does it travel faster or slower when far from the Sun?

Kepler’s 3 in the sky, Kepler showed the orbit to be an rd Law

- The amount of time a planet takes to orbit the Sun is mathematically related to the size of its orbit
- The square of the period, P, is proportional to the cube of the semimajor axis, a

P2 = a3

Kepler’s 3 in the sky, Kepler showed the orbit to be an rd Law

- Third law can be used to determine the semimajor axis, a, if the period, P, is known, a measurement that is not difficult to make

- Express the period in years
- Express the semi-major axis in AU

P2 = a3

Examples of Kepler’s 3 in the sky, Kepler showed the orbit to be an rd Law

- Express the period in years
- Express the semi-major axis in AU

For Earth:

P = 1 year, P2 = 1.0

a = 1 AU, a3 = 1.0

P2 = a3

Examples of Kepler’s 3 in the sky, Kepler showed the orbit to be an rd Law

For Mercury:

P = 0.2409 years

P2 = 5.8 x 10-2

a = 0.387 AU

a3 = 5.8 x 10-2

P2 = a3

- Express the period in years
- Express the semi-major axis in AU

Examples of Kepler’s 3 in the sky, Kepler showed the orbit to be an rd Law

For Venus:

P = 0.6152 years

P2 = 3.785 x 10-1

What is the

semi-major axis

of Venus?

P2 = a3

a = 0.723 AU

- Express the period in years
- Express the semi-major axis in AU

Examples of Kepler’s 3 in the sky, Kepler showed the orbit to be an rd Law

For Pluto:

P = 248 years

P2 = 6.15 x 104

What is the

semi-major axis

of Pluto?

P2 = a3

a = 39.5 AU

- Express the period in years
- Express the semi-major axis in AU

Examples of Kepler’s 3 in the sky, Kepler showed the orbit to be an rd Law

The Asteroid

Pilachowski (1999 ES5):

P = 4.11 years

What is the semi-major axis

of Pilachowski?

P2 = a3

a = ??? AU

- Express the period in years
- Express the semi-major axis in AU

Fill in the Table in the sky, Kepler showed the orbit to be an

- Express the period in years
- Express the semi-major axis in AU

Comparing Heliocentric Models in the sky, Kepler showed the orbit to be an

Geocentric > Heliocentric in the sky, Kepler showed the orbit to be an

- The importance of observations!
- When theory does not explain measurements, a new hypothesis must be developed; this may require a whole new model (a way of thinking about something)
- Why was the geocentric view abandoned?
- What experiments verified the heliocentric view?

- Review Chapter 1, Kepler’s Laws
- Read Chapter 2: Gravity & Motion
- 2nd Homework due Sept. 26
- Rooftop Session Tuesday evening, 9PM
- Kirkwood Obs. open Wednesday Eve., 8:30-10:30
- IN-CLASS QUIZ ON WEDNESDAY!!

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