Download Planets in the Sky

It's spring for the
northern hemisphere
of Mars and spring on
Mars usually means
dust storms. This
sharp image shows
the evolving dust
storm (brown swath
across polar ice)
extending from the
large dark region
known as Mare
Acidalium below the
polar cap.
Homework #3 is due Monday,
Feb. 15, 2:30 pm.
Exam 1: Wednesday, Feb. 17
Review session: Monday, Feb. 15, 7 pm til ?,
Location to be announced
1. Which planets are visible at 9 pm? At 3 am?
2. Mercury and Venus appear in the sky only shortly after sunset, at
which time they are called “evening stars”, OR shortly before
sunrise (“morning stars”). What are these two planets currently?
3. The orbit planes of all of the planets are near a plane for which
we have already discussed. What is the name of this plane?
What defines it?
4. Do we expect to ever see either the inferior planets (Venus &
Mercury) or the inferior planets (all the rest) close to the North
Celestial Pole? At southern celestial latitudes? Explain.
Inner solar system
Outer solar system
Jupiter
Venus
Earth
Mars
Mercury
Saturn
Planets in the Sky
There are five “naked eye” planets
1. Mercury
2. Venus
3. Mars
4. Jupiter
5. Saturn
They are all quite bright.
They have been well known to throughout
human existence
Where are these seen
relative to the sun?
“Naked eye” planets in the sky
Mercury: always close to Sun in sky
Venus: always close to Sun in sky
 Mars: no restrictions on distance from Sun in sky
 Jupiter: no restrictions on distance from Sun in sky
 Saturn: no restrictions on distance from Sun in sky
What causes these differences?
Where are these seen on
the celestial sphere?
 Planets are always
close to the “ecliptic”,
the apparent annual
path of the sun through
the sky.
This is a consequence of
the planets orbiting in
planes that are near
each other.
How do the planets move
on the Celestial Sphere?
Motions of the planets
 On short term (diurnal motion), planets appear to move
with the stars, east to west, making a full circuit around the
sky (meridian to meridian) in approximately one day
 Most of the time, planets move slowly eastward each day
relative to the stars: different planets at different rates
What causes these motions?
Some planets occasionally reverse their motion
relative to the stars, moving slowly westward
relative to the stars, for a few days
apparent retrograde motion
What causes this?
What causes this?
We have now set the stage for discussing
the historical development of astronomy
What causes the observed motions of the
stars, sun, moon, and planets in the sky?
The Greeks developed a model for the
Universe that lasted for nearly 15
centuries.
It did a reasonably good job explaining
these motions.
Claudius Ptolemy (100-170 CE)
Developed a model of the
universe designed to fit
the observational data.
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 model fit the data and made accurate
predictions, but was horribly contrived!
● Although the geocentric model of
Ptolemy gained dominance,
Aristarchus of Samos actually
proposed that the earth rotated
daily and revolved around the sun
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.
The ancient Greeks rejected the notion that
the Earth orbits the sun. Why?
●
●
●
It ran contrary to their senses.
If the Earth revolved about the Sun, then
there should be a “great wind” as we
moved through the air.
Greeks knew that we should see stellar
parallax if we orbited the Sun – but they
could not detect it.
Parallax Angle
Apparent shift of a star’s position due
to the Earth’s orbiting of the Sun
Possible reasons why stellar
parallax was undetectable:
1.
Stars are so far away that stellar parallax is too small
for naked eye to notice
2.
Earth does not orbit Sun; it is the center of the
universe
Unfortunately, with notable exceptions like Aristarchus, the
Greeks did not think the stars could be that far away,
and therefore rejected the correct explanation (1)…
Thus setting the stage for the long, historical showdown
between Earth-centered and Sun-centered systems.
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!
The Copernican Revolution
●
●
Copernicus, Tycho, Kepler, and Galileo.
Kepler’s three laws of planetary motion
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
Retrograde
Motion
(1) Planets, including the
Earth, orbit the Sun
(2) Planets closer to the
Sun have shorter orbital
periods than planets
farther from the Sun
As we “pass” a planet, it
appears to move backwards
(as seen from Earth)
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
Suggested webpage to visit for more insight into Tycho Brahe,
Johannes Kepler, and the development of Kepler’s Laws:
http://csep10.phys.utk.edu/astr161/lect/history/kepler.html
Johannes Kepler (1571-1630)
●
Greatest theorist of his day
●
a mystic
●
there were no heavenly spheres
●
forces made the planets move
●
Developed his three laws of
planetary motion
Kepler’s First Law
1 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
o
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 planets
spend more time
in the more
distant parts of
their orbits
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
3
2
a / P = constant
Consequence: Planets with larger orbits have
longer orbital periods.
Earth:
a = 1 AU, P = 1 year
So, if we use distance in AU and time in years,
the constant in the 3rd Law is 1 AU3 yr-2
Jupiter:
a = 5.203 AU,
P = 11.86 years
Kepler’s Laws are extremely accurate in
their predictions of planetary motions.

They are “empirical”, i.e., they are derived
from experiment, experience, and
observation rather than from theory or logic

Isaac Newton subsequently demonstrated
that Kepler’s laws are the natural outcome
of gravity.
