The Mars rover
Opportunity is currently
exploring Endeavour
crater for clues about how
wet Mars was billions of
years ago. Tisdale 2, the
unusual rock structure
shown here, was probed
by Opportunity last week.
It is thought to be a
remnant thrown off during
the impact that created the
Odyssey crater. Chemical
analysis of Tisdale 2 has
shown it to have a
strangely high amount of
the element zinc.
Homework #1 has been posted on the class website.
Answers are to be submitted via the OnCourse “Original Test and Survey”
program. Work through the homework questions and arrive at all your
answers before going to OnCourse. Then, go to the A103 class page on
Oncourse, click on the “Original Test and Survey” button, and chose
Homework 1 from the pull-down menu. Input your answers. Once this is
accomplished, be sure to submit the homework. You cannot exit the
program and return to it later!
DO NOT SUBMIT UNTIL YOU HAVE GIVEN ALL YOUR ANSWERS – YOU
CANNOT GO BACK ONCE YOUR ANSWERS ARE SUBMITTED.
Understanding
the context of
our search
Celestial Sphere
Large imaginary spherical
surface centered on the
Earth.
Stars and other celestial
objects “fixed” on its
surface.
Conceptual Model, not a
physical model
Patterns Observed in the sky:
(observed facts)
Stars rise in the eastern sky and set in the western
sky
The Sun rises in the eastern sky and sets in the
western sky
The rising and setting locations for the Sun on the
horizon change in a recurring pattern
Relative to background stars, the Sun moves
slowly, approximately one degree per day, towards
the east
The sun follows the same path around the sky (on the
celestial sphere), repeating this journey once every year.
This path is called the “Ecliptic”
 Planets are always
found close to the
“ecliptic”, the apparent
annual path of the sun
through the sky.
 Mercury and Venus,
often referred to as the
inferior planets, are always
close to Sun in sky, with
Mercury staying the
closest to the Sun
Motions of the planets
 On short term (minutes, hours), planets appear to move with the
stars, east to west, making a full circuit around the sky (meridian to
meridian) in approximately one day
 On the longer timescale (days, weeks, months), planets move
slowly eastward relative to the stars: different planets moving at
different rates
Some planets occasionally reverse their motion
relative to the stars, moving slowly westward
relative to the stars, for a few days
apparent retrograde motion
The observed motions of the stars, sun,
moon, and planets in the sky provide us
with “observed facts”
What accounts for these observed facts?
(construct a model and then test it)
The Greeks developed a model for the
Universe that lasted for nearly 15
centuries.
It did a reasonably good job explaining
these motions.
Ptolemy and later scientists were
strongly influenced by the belief of
Plato that …
“all natural motion is circular”
● Earth is at center
(Geocentric)
● Sun orbits Earth
●Planets orbit on
small circles
(epicycles) whose
centers orbit the
Earth on larger
circles (this explains
retrograde motion)
Ptolemy’s
Geocentric Model
Apparent retrograde motion in geocentric model
 Planet orbits lie in
approximately the
same plane (this
explains why the
planets are always
near the ecliptic)
 Inferior planet
epicycles were fixed
to the Earth-Sun line
(this explained why
Mercury & Venus
never stray far
from the Sun).
Geocentric Model
Ptolemy’s Geocentric Model
● Relied upon circles upon circles (epicycles &
defferents) to explain the motions of planets
and the sun.
● Tied to Plato & Aristotle’s belief that “all
natural motion is circular”
● With modifications (e.g., additions of epicycles
upon epicycles), remained the standard
through the middle-ages.
Ptolemy’s model fit the data and made accurate
predictions, but was horribly contrived!
Plato proposed that the orbits of
the planets have what shape?
conical
circular
elliptical
equal-angular
epicycles
Plato proposed that the orbits of
the planets have what shape?
conical
circular
elliptical
equal-angular
epicycles
The diurnal (daily) motion of stars is due to
the motion of the earth around the sun
the rotation of the earth
the epicyclic nature of the celestial sphere
the rotation of the celestial sphere
The diurnal (daily) motion of stars is due to
the motion of the earth around the sun
the rotation of the earth
the epicyclic nature of the celestial sphere
the rotation of the celestial sphere
What is the ecliptic?
when the Moon passes in front of the Sun
the constellations commonly used in astrology to
predict the future
the Sun's daily path across the sky
the Sun's apparent path across the celestial
sphere
What is the ecliptic?
when the Moon passes in front of the Sun
the constellations commonly used in astrology to
predict the future
the Sun's daily path across the sky
the Sun's apparent path across the celestial
sphere
About how long does it take the Sun to complete
one “trip” around along the ecliptic around the
entire sky?
One day
One month
One year
The time varies from one trip to the next
This never happens
About how long does it take the Sun to complete
one “trip” around along the ecliptic around the
entire sky?
One day
One month
One year
The time varies from one trip to the next
This never happens
The Revolution Begins!
Nicolaus Copernicus (1473-1543)
He thought Polemy’s
model was contrived
Yet he believed in circular
motion
De Revolutionibus
Orbium Coelestium
Copernicus’ Heliocentric Model
●Sun is at center of the Universe
●Earth orbits the Sun like any other planet
●Earth rotates
●Circular orbits for all planets
●Inferior planet orbits are smaller
●Planets move at constant velocities in their
orbits
●Retrograde motion occurs when we “lap” Mars
& the other superior planets
Copernicus’ Heliocentric Model
●Retrograde motion occurs when we “lap” Mars
& the other superior planets
Simpler, more “elegant”
But, it still required some epicycles in order to make
accurate predictions
because
It was still wedded to Aristotle's circular orbit paradigm
Predictions were not much better than those of Ptolemy
Tycho Brahe (1546-1601)
●
Greatest observer of his
day
• Charted accurate
positions of planets
(accurate positions of
the planets were not
fully available)
Tycho Brahe…
was motivated by inadequacy of existing
predictions
made very accurate observations of positions
(this was prior to the development of the
telescope)
advocated a model in which Sun orbits Earth
because he could not observe stellar parallax
The parallax problem troubled the Greeks and
Tycho. It led both to reject a heliocentric universe.
The problem was that stars are too distant to produce a parallax
large enough to be seen with the technology of those time.
1600 – Tycho brought Johannes Kepler to bear
on problem. He assigned him the task of
understanding the motions of Mars.
Kepler had great faith in Tycho's
measurements; they placed strong constraints
on model
Johannes Kepler (1571-1630)
●
Hired by Tycho to analyze his
observations of planetary
positions, particularly Mars
●
Greatest theorist of his day
●
Believed that “forces” made the
planets move
●
Developed his three laws of
planetary motion
Kepler's Laws
1. The Law of Orbits: All planets move in
elliptical orbits, with the sun at one focus.
2. The Law of Areas: Planets move faster in
their orbit the closer they are to the Sun.
3. The Law of Periods: Planets on larger orbits
take longer to complete an orbit than planets
smaller orbits.
Kepler’s First Law
Each planet’s orbit around the Sun is an
ellipse, with the Sun at one focus.
Ellipse: defined by points located such that the sum of the
distances from the two foci is constant
Animation by Michael Kossin
x2/a2
+
y2/b2
=1
focus
y
The circle is a
special form of
an ellipse
Semimajor axis = a
X
Semiminor axis = b
Eccentricity
e2 = 1 - b2/a2
Kepler’s Second Law
● A planet moves along its orbit with
a speed that changes in such a way
that a line from the planet to the
Sun sweeps out equal areas in equal
intervals of time.
● Consequence: planets move faster
when they are closer to the sun and,
conversely, planets spend more time
in the more distant parts of their
orbits
A good animation demonstrating this law can be found at:
www.physics.sjsu.edu/tomley/Kepler12.html
Kepler’s Third Law
The ratio of the cube of a planet’s
average distance from the Sun
“a” to the square of its orbital
period “P” is the same for each
planet.
3
2
a / P = constant
The constant is the
same for all planets
Consequence: Planets with larger
orbits have longer orbital
periods.
A good animation demonstrating this law can be found at:
www.physics.sjsu.edu/tomley/Kepler3.html
3
2
a / P = constant
Earth:
a = 1 AU, P = 1 year
So, if we measure the size of a planet’s orbit in
AU and its orbital period in Earth years, then
constant in the 3rd Law is 1 AU3 yr-2
Jupiter:
a = 5.203 AU,
P = 11.86 years