Transcript Orbital Motion

A100
Solar System
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’s APOD
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 get more complex
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
Astronomy in the
Renaissance
Nicolaus Copernicus (1473-1543)
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
Heliocentric Models
with Circular Orbits
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
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 remember
Focus vs. Center
Semi-major axis
Semi-minor axis
Perihelion, aphelion
Eccentricity
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 Law
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 2nd Law:
Same Areas
If the planet sweeps out
equal areas in equal times,
does it travel faster or
slower when far from the
Sun?
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
2
P
=
3
a
Kepler’s 3rd 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
2
P
=
3
a
Examples of
Kepler’s 3rd Law
Body
Period
(years)
Mercury 0.24
Venus
0.61
Earth
1.0
Mars
1.88
Jupiter
11.86
Saturn
29.6
Pluto
248
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
For Mercury:
Examples of
Kepler’s 3rd Law P = 0.2409 years
P2 = 5.8 x 10-2
Body
Period
(years)
Mercury 0.2409
Venus
0.61
Earth
1.0
Mars
1.88
Jupiter
11.86
Saturn
29.6
Pluto
248
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 3rd Law
Body
Period
(years)
For Venus:
P = 0.6152 years
P2 = 3.785 x 10-1
Mercury 0.2409
Venus
0.6152
Earth
1.0
Mars
1.88
Jupiter
11.86
Saturn
29.6
Pluto
248
 Express the period in years
 Express the semi-major axis in AU
What is the
semi-major axis
of Venus?
P2 = a3
a = 0.723 AU
Examples of
Kepler’s 3rd Law
Body
Period
(years)
For Pluto:
P = 248 years
P2 = 6.15 x 104
Mercury 0.2409
Venus
0.6152
Earth
1.0
Mars
1.88
Jupiter
11.86
Saturn
29.6
Pluto
248
 Express the period in years
 Express the semi-major axis in AU
What is the
semi-major axis
of Pluto?
P2 = a3
a = 39.5 AU
Examples of
Kepler’s 3rd Law
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?
 Express the period in years
 Express the semi-major axis in AU
P2 = a3
a = ??? AU
Fill in the Table
Planet/
Dwarf
Planet
Period
(years)
SemiMajor
Axis (AU)
Mercury 0.2409
0.39
Venus
0.6152
0.72
Earth
1.0
1
Mars
1.8809
1.52
Jupiter
11.8622
5.2
Saturn
29.4577 9.54
Pluto
247.7
P2
a3
5.8 x 10-2
5.9 x 10-2
1.0
1.0
39.5
Express the period in years
Express the semi-major axis in AU
Comparing Heliocentric Models
Geocentric > Heliocentric
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?
ASSIGNMENTS
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!!