a100 solar system
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Today’s APOD
Review Chapter 1, Kepler’s LawsRead Chapter 2: Gravity & Motion2nd Homework due Sept. 26Rooftop Session Tuesday evening,
9PMKirkwood Obs. open Wednesday Eve.,
8:30-10:30IN-CLASS QUIZ ON WEDNESDAY!!
The Sun Today
A100 Solar System
Today: the
Equinox
11:44 AM EDTtoday
http://apod.nasa.gov/apod/ap030923.html
Dr. Phil Plait (Sonoma St. U.) acting as the Bad Astronomer balanced three raw eggs on end in late October 1998
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 get more complexEpicycles 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
Astronomy in the Renaissance
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 OrbitsExplain 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
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”
Johannes Kepler (1571-1630)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
Kepler’s 1st Law
Planets move in elliptical orbits with the Sun at one focus of the ellipse
Words to rememberFocus vs. CenterSemi-major axisSemi-minor axisPerihelion, aphelionEccentricity
Definitions
• 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 & Dwarf Planets
Mercury 0.206 Saturn 0.054
Venus 0.007 Uranus 0.048
Earth 0.017 Neptune 0.007
Mars 0.094 Pluto 0.253
Jupiter 0.048 Ceres 0.079
Which orbit is closest to a circle?
Kepler’s 2nd
LawPlanets don’t move at constant speedsThe 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 2nd Law:
If the planet sweeps out equal areas in equal times, does it travel faster or slower when far from the Sun?
Same Areas
Kepler’s 3rd 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 3rd LawThird law can be used
to determine the semimajor axis, a, if the period, P, is known, a measurement that is not difficult to make
P2 = a3
Express the period in years
Express the semi-major axis in AU
Examples of Kepler’s 3rd Law
Express the period in yearsExpress the semi-major
axis in AU
Body Period (years)
Mercury 0.24
Venus 0.61
Earth 1.0
Mars 1.88
Jupiter 11.86
Saturn 29.6
Pluto 248
For Earth:
P = 1 year, P2 = 1.0
a = 1 AU, a3 = 1.0
P2 = a3
Examples of Kepler’s 3rd Law
Express the period in years Express the semi-major axis in AU
Body Period (years)
Mercury 0.2409
Venus 0.61
Earth 1.0
Mars 1.88
Jupiter 11.86
Saturn 29.6
Pluto 248
For Mercury:
P = 0.2409 yearsP2 = 5.8 x 10-2
a = 0.387 AUa3 = 5.8 x 10-2
P2 = a3
Examples of Kepler’s 3rd Law
Express the period in years Express the semi-major axis in AU
Body Period (years)
Mercury 0.2409
Venus 0.6152
Earth 1.0
Mars 1.88
Jupiter 11.86
Saturn 29.6
Pluto 248
For Venus:
P = 0.6152 yearsP2 = 3.785 x 10-1
What is the semi-major axis
of Venus?
P2 = a3
a = 0.723 AU
Examples of Kepler’s 3rd Law
Express the period in years Express the semi-major axis in AU
Body Period (years)
Mercury 0.2409
Venus 0.6152
Earth 1.0
Mars 1.88
Jupiter 11.86
Saturn 29.6
Pluto 248
For Pluto:
P = 248 yearsP2 = 6.15 x 104
What is the semi-major axis
of Pluto?
P2 = a3
a = 39.5 AU
Examples of Kepler’s 3rd Law
Express the period in years Express the semi-major axis in AU
Body Period (years)
Mercury 0.2409
Venus 0.6152
Earth 1.0
Mars 1.88
Jupiter 11.86
Saturn 29.6
Pluto 248
The Asteroid Pilachowski (1999 ES5):
P = 4.11 years
What is the semi-major axis of Pilachowski?
P2 = a3
a = ??? AU
Fill in the Table
Express the period in yearsExpress the semi-major axis in AU
Planet/Dwarf Planet
Period (years)
Semi-Major Axis (AU)
P2 a3
Mercury 0.2409 0.39 5.8 x 10-2 5.9 x 10-2
Venus 0.6152 0.72
Earth 1.0 1 1.0 1.0
Mars 1.8809 1.52
Jupiter 11.8622
5.2
Saturn 29.4577
9.54
Pluto 247.7 39.5
Comparing Heliocentric Models
Geocentric > HeliocentricThe 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?
ASSIGNMENTSthis week
Review Chapter 1, Kepler’s LawsRead Chapter 2: Gravity & Motion2nd Homework due Sept. 26Rooftop Session Tuesday evening,
9PMKirkwood Obs. open Wednesday Eve.,
8:30-10:30IN-CLASS QUIZ ON WEDNESDAY!!
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