User’s Guide to the Sky:
Patterns and Cycles
Astronomy 101
Lecture by: Prof. Barsony
Sub: Abby Fuller
Find this lecture at
http://www.physics.sfsu.edu/~afuller
/117L/117L.htm
Perspectives on Astronomy
Seeds & Backman
Chapter 2 (cont’d.)
Part III. Cycles
•
•
•
Eclipses
Seasons
Precession
Solar Eclipses
Which way is the Sun in this picture?
http://en.wikipedia.org/wiki/Umbra
The umbra (Latin: "shadow") is the darkest part of a
shadow. From within the umbra, the source of light is
completely blocked by the object causing the shadow. This
contrasts with the penumbra , where the light source is
only partially blocked and there is only a partial shadow.
Penumbras occur only when the source of light is not a
point source. As the sun is an extended, visible disc, unlike
the stars, which are point sources, shadows cast by sunlit
objects, viewed on Earth, have penumbras.
Ingredients for a Total Solar Eclipse
• By coincidence, the angular size of the Moon, as seen from
Earth, is approximately the same as the angular size of the
Sun seen from Earth. This allows for the possibility of the
Moon’s face completely obscuring the Sun.
• A total solar eclipse occurs only when the Moon is directly
between the Sun and the Earth.
• Since the umbra of the Moon’s shadow barely touches
Earth, the region over which totality occurs on Earth is
relatively small (270 km or 170 miles across).
• Because of the orbital motion of the Moon, combined with
the rotational motion of the Earth, the path of totality
sweeps across the Earth’s surface at over 1000 mph or
1600 km/hr.
Questions
• By coincidence, how much farther is the Sun than
the Moon?
(Ans. 390 x on average)
• How much larger is the Sun’s diameter than the
Moon’s?
(Ans. 400 x)
• What phase is the Moon in during a solar eclipse?
(Ans. New Moon)
• Why isn’t there a total solar eclipse each New Moon?
(Ans. The Moon’s orbit is inclined to Earth’s orbit
around the Sun by 5o)
If you ever get a chance, you should really
see a total solar eclipse for yourself.
Because our eyes have a much higher
dynamic range (seeing both very bright and
very dim light at the same time) than any
cameras, the photographs of totality shown
here in the last two images, cannot do justice
to what you actually can see with your own
eyes during a total solar eclipse (but only
during the few short minutes of totality!)
Annular Eclipse
http://apod.nasa.gov/apod/ap980824.html
This picture of an annular eclipse of the Sun was taken by a video camera.
An annular solar eclipse occurs when the Moon's angular size is slightly
less than the Sun's angular size. Therefore, when the Moon is directly in
front of the Sun, the edges of the Sun are still visible. This solar ring is so
bright that the Moon's surface normally appears dark by comparison. The
angular sizes of the Sun and Moon change slightly because of the elliptical
nature of the Moon's and Earth's orbit. A total solar eclipse would have
occurred were the Moon much closer to the Earth.
Since looking into the Sun directly will blind you, you should
use this method to see the Sun’s disk during most portions of a
solar eclipse. Only during the few minutes of totality is it safe
to look directly towards the Sun (but with special, filter
glasses on).
Lunar Eclipses
Ingredients for a Lunar Eclipse
• Occurs when the Moon moves through the shadow of the
Earth.
• A total lunar eclipse occurs when the Moon moves through
the umbra of the Earth’s shadow.
• A partial lunar eclipse occurs when the Moon moves
through the penumbra of the Earth’s shadow.
• It typically takes a few hours for the Moon to travel
through the Earth’s entire shadow during a lunar eclipse.
Questions
• What phase is the Moon in during a lunar eclipse?
(Ans. Full Moon)
• Why isn’t there a lunar eclipse each Full Moon?
(Ans. The Moon’s orbit is inclined to Earth’s orbit
around the Sun by 5o)
Orientation of Earth’s and Moon’s Umbral Shadows
To Sun
(For clarity, the diameters of the Earth and the Moon have been enlarged to twice
their size relative to a true scale drawing.)
The Moon’s orbital plane, indicated by the dashed line with the arrows on its
end, is tilted with respect to the Earth’s orbital plane around the Sun, whose
orientation is indicated by the solid, left-pointing arrow.
This mismatch between the two orbital planes accounts for the ease
with which the Full Moon can miss Earth’s shadow (therefore, no
lunar eclipse), or how easily Moon’s umbra can miss Earth’s surface
during New Moon (therefore, no solar eclipse).
The combination of light scattered by all Earth’s sunrises and sunsets
lights the totally eclipsed Moon’s face in a copper glow.
Seasons
The Seasons
• Refer to cyclical climatic changes in Earth’s
“temperate” zones: warmth in summer, cold
in winter
• In summer, Sun is in sky longer, days are
longer, in winter days are shorter
• In summer, Sun attains higher altitude in the
sky than in winter
A few terms we’ll need to know for further discussion of the seasons
Object in Sky
Altitude: The elevation of an object, in angular
measure (e.g., degrees) from your horizon
Azimuth: The angle around your horizon,
measured from North, in degrees. East is at
90o azimuth, S at 180o, W at 270o.
Altitude
angle
Your
horizon
The Sun reaches its highest altitude in the sky at local noon.
The altitude of the Sun at noon varies from its highest point in
mid-summer, to its lowest point, in mid-winter.
The azimuth of sunrise varies from northeast to southeast, whereas the
azimuth of sunset varies from northwest to southwest. Both of these
azimuth variations progress with the seasons.
The Sun rises due East and sets due West only twice a year:
at the equinoxes.
Tilt of Earth’s Rotational Axis Relative to an Axis Perpendicular to
the Earth-Sun Line is Responsible for the Seasons
Direction perpendicular Direction of Earth’s
to Earth-Sun lineca
rotational axis =
NCP
Northern
Summer
To Sun
To SCP
Southern
Winter
Earth’s Rotational Axis is
tilted 23.5o away from the
direction perpendicular to the
Earth-Sun line
Sun at its furthest north as seen
from Earth.
Celestial Equator
Tilt of Earth’s Rotational Axis Relative to an Axis Perpendicular to
the Earth-Sun Line is Responsible for the Seasons
Perpendicular to
Earth-Sun Line
Northern
Winter
Celestial Equator
Sun at its furthest
South, as seen
from Earth
To Sun
Southern
Summer
6 months later...
To SCP
To NCP
Kinesthetic Astronomy: Key Point for Seasons
Although Earth orbits the Sun, the direction of its spin
axis*does not change* during the year as it orbits.
1. One person will represent the Sun. Please come up and
stand in the middle of the stage.
2. The rest of us will be Earth. Let’s orbit (walk around
the Sun) once, with our spin axis (head-to-toe line)
perpendicular to the Sun-Earth axis.
3. Now, let’s orbit (walk around the Sun) with our spin axis
tilted *at a constant angle* (from the waist up is OK) as
we orbit the Sun.
4. OK to go back to your places & sit down.
You have experienced that in the course of your orbit
around the Sun (i.e., during the year) your head
(Northern hemisphere) is sometimes tilted towards the
Sun, and sometimes tilted away from the Sun, although
your tilt (spin axis) does not change during the course
of the year.
The amount of energy received from the Sun depends on the
angle at which the Sun’s rays strike a surface. Just as with
collecting rain in a bucket, you collect the most water if the
rain is pouring straight down, and collect no water if the
bucket is angled sideways (perpendicular to the incident rain).
The same is true for receiving solar energy.
Receive more energy per unit area. Receive less energy per unit area.
The intersection point
between the Celestial Equator and the
ecliptic, when the Sun’s apparent
position, as seen from Earth, starts
going South
When the Sun
reaches its
Southernmost point
in the sky.
The plane traced out by
the Earth-Sun line
When the Sun reaches its
Northernmost point in the sky.
The intersection point between the Celestial Equator
and the ecliptic, when the Sun’s apparent position, as
seen from Earth, starts going North
Seasons defined by 4 Events
Precession
Precession is the result of torques acting on a spinning body which
tend to change the direction of its spin axis
Axis of precession
Direction
NCP
perpendicular to
Earth-Sun line
To Sun
For Earth, the main such torque is due to the Sun’s gravitational pull
Earth’s Precession Period is 26,000 years
It is observable in the changing direction of the Celestial Pole among the constellations.
Circles around the Earth Become
Orbits around the Sun
Perspectives on Astronomy
Seeds & Backman
Chapter 3
Astronomy 101
Prof. Barsony
Theories of the Heavens
•
•
•
•
Aristotle - Earth centered, stationary Earth,
circular orbits, uniform speed
Ptolemy - Slightly off-Earth centered, stationary
Earth, epicyclic circular orbits, uniform speed
Copernicus - Sun centered, circular orbits,
uniform speed, rotating Earth
Brahe, Kepler - Sun centered, elliptical orbits,
variable speed, rotating Earth
Aristotle
384-322 BC
Aristotle's cosmological work ``On The Heavens” is the most
influential treatise of its kind in the history of humanity. It was
accepted for more than 18 centuries from its inception (around
350 B.C.) until the works of Copernicus in the early 1500s. In
this work Aristotle discussed the general nature of the cosmos
and certain properties of individual bodies.
Earth
solarsystem.nasa.gov/.../ display.cfm?ST_ID=525
Aristotle proposed that Earth was the center of the Universe and
above it the Moon, Sun, and 5 planets orbited Earth, held in
place by crystal spheres. Higher than all were the fixed stars,
which also revolved around Earth, all embedded in the outermost
sphere. Beyond the sphere of the stars the universe continued
into the spiritual realm where material things cannot be.
Question:
What were the 5 known planets in Aristotle’s time?
Earth
solarsystem.nasa.gov/.../ display.cfm?ST_ID=525
The discoveries of Uranus and Neptune required telescopes.
The proof that each is a planet was: 1) Motion against the background
stars & 2) An extended appearance, unlike stars which appear point-like.
Uranus was discovered by Caroline and
William Herschel on March 13, 1781.
Neptune was discovered September 23, 1846,
at a position that was predicted mathematically.
Its presence was deduced from the deviations
observed in the orbit of Uranus.
Aristotle also claimed that while Earth was corruptible and
imperfect, the heavenly objects were perfect and not made of the
four elements of the world (believed to be fire, water, air, and
earth) but rather of an entirely different element called
quintessence (=fifth element), which was also perfect.
Aristotelian Motion
The idea that all bodies, by their very nature, have a natural way
of moving is central to Aristotelian cosmology. Movement is,
therefore, endowed to bodies, and is not, he states, the result of
the influence of one body on another.
Some bodies naturally move in straight lines, others naturally are
at rest. There is yet another natural movement: the circular motion.
By Aristotelian logic: since to each motion there
must correspond a substance, there ought to be
some bodies that naturally move in circles. Aristotle
then proclaims that such things are the heavenly
bodies as they are made of a more exalted and
perfect substance than all earthly objects.
Since the stars and planets are made of this exalted substance
and then move in circles, it is also natural, according to Aristotle,
for these objects to be spheres. The cosmos is then made of a
central earth (which he accepted as spherical) surrounded by the
moon, sun and stars all moving in circles around it.
In the fully developed
Aristotelian system,
the spherical Earth is
at the center of the
universe. The planets
are attached to
anywhere from 47 to
55 concentric spheres
that rotate around the
Earth *in the same
direction*.
Aristotle says that to
determine the exact
number of spheres,
one should consult
the astronomers.
Problem: Retrograde Motion
Throughout the night, the
celestial sphere appears to rotate
towards the West around the
North Celestial Pole, as shown
by the blue arrow.
In general, Mars traces a path
from West to East in relation to
the distant stars, except for
episodes of “retrograde”
motion, when Mars appears to
move East to West relative to
the background stars.
Kentfield, CA
latitude: +37.952o
longitude: -122.556o
http://www.heavens-above.com
Kentfield, CA
latitude: +37.952o
longitude: -122.556o
http://www.heavens-above.com
Kentfield, CA
latitude: +37.952o
longitude: -122.556o
http://www.heavens-above.com
Kentfield, CA
latitude: +37.952o
longitude: -122.556o
http://www.heavens-above.com
Kentfield, CA
latitude: +37.952o
longitude: -122.556o
http://www.heavens-above.com
Plato gave his students a major problem to work on.
Their task was to find a geometric explanation for the apparent
motion of the planets, especially the strange retrograde
motion. One key observation is that near and during the time
of retrograde motion, Mars appears significantly brighter in the
sky than at other times. What might this mean? Plato and his
students were also constrained by the Pythagorean worldview,
in which the Earth is supposed to be the unmoving center of
the planetary motions.
Aristarchus
Plato’s student,
Aristarchus, developed
a Sun-centered model
that could explain the
retrograde motion of
Mars, with the planets
moving on circular
paths.
zebu.uoregon.edu/2004/hum399/lec04.html
Aristarchus’ Sun-centered model was not accepted because
of the ``obvious’’ observations against a moving Earth.
Ancient astronomers believed that Earth did not move because they saw no parallax.
Parallax is the apparent shift of an object against a background caused by a change in
the observer’s position.
Question: In the example above, what is
``the change in the observer’s position’’?
Orders of Magnitude=Powers of 10
On an interstellar scale, parallax created by the different orbital
positions of the Earth causes “nearby” stars to appear to move
relative to the more distant stars.
Because of the great distances to the stars, this effect is so small
it is undetectable without extremely precise measurements.
Recall the human eye can distinguish a difference of 1 arcminute
in angular measure, at best. This is about 1/30 of the diameter of
the full moon.
The displacement of the nearest star, Proxima Centauri, when
seen from opposite sides of the Earth’s orbit around the Sun
(e.g., six months apart), is 0.77233 arcseconds. An arcsecond =
1/60 of an arcminute, so the parallax of the nearest star is
0.77233 x 1/60 arcminute= 0.01287 arcminutes or ~77 times
smaller than the human eye can detect.
384-322 BC
.
Ptolemy
85-165 A.D.
A more complicated model to save the Earth-centered Universe
In order to preserve the geocentric (Earth-centered)
cosmology of the time and to account for retrograde
motion, Ptolemy had to make a model using epicycles.
In the Ptolemaic system, the planets are assumed to
move in a small circle, called an epicycle, which, in turn
moves around a larger circle, called a deferent. Both
circles rotate counterclockwise.
equant
epicycle: small circle
The deferent was a circle centered on a point
half-way between the equant and the Earth.
The epicycle rotated on the deferent with
uniform motion, not with respect to the
center, but with respect to an off-center point
called the equant.
deferent: large circle
Earth
A visualization of epicycles:
http://www.astronomynotes.com/history/epicycle.htm
(shows animation of how Ptolemy’s epicycles solved the problem of retrograde motion)
.
Nicolaus Copernicus
1473-1543
On the Revolution of
the Celestial Spheres
De Revolutionibus Orbium Coelestium In the Copernican model,
the Sun, instead of the
I. Fixed stars
Earth, is at the center. The
II. Saturn
eventual acceptance of the
III.Jovis=Jupiter
Copernican model was
IIII. Mars
such a large shift in
humanity’s conception of
V. Earth
the Universe and our place
VI. Venus
in it, that the modern
VII. Mercury
English word “revolution”
referring to a large change,
originates from the title of
Copernicus’ work.
1543
In the Copernican system, the Earth is just
another planet (the third outward from the
Sun), and the Moon is in orbit around the Earth,
not the Sun. The planets, including the Earth,
revolve about the Sun in concentric circles.
The closer-in planets move faster in their
circular orbits than the further out ones.
The stars are distant objects that do not
revolve around the Sun. Instead, the Earth is
assumed to rotate once in 24 hours, causing
the stars to appear to revolve around the Earth
in the opposite direction.
Retrograde Motion and Varying Brightness of the Planets
The Copernican system, by banishing the idea that
the Earth was the center of the Solar System,
immediately led to a simple explanation of both the
varying brightness of the planets and retrograde
motion: The planets in such a system naturally vary
in brightness because they are not always the same
distance from the Earth. The retrograde motion could
be explained in terms of geometry and a faster
motion for planets with smaller orbits.
http://csep10.phys.utk.edu/astr161/lect/retrograde/copernican.html
Copernicus’ system still required epicycles
to account for detailed observations of the
planets’ motions, since he incorrectly clung
to the idea of uniform circular motion.
However, fewer epicycles were required
than in the Ptolemaic system.
.
Tycho Brahe & Johannes Kepler
1546-1601
1571-1630
Tycho, himself, did not
believe in the
Copernican system.
He, instead, devised
his own peculiar, geoheliocentric system, in
which the sun orbits
the Earth and the stars
and other planets orbit
the sun.
The Geometry of Ellipses
•
A circle consists of all the points that are the
same distance, r, (for radius) from a point (the
center of the circle).
•
An ellipse consists of all the points the sum of
whose distances from two points (the foci of the
ellipse) is a constant
• The semi-major axis, a, of an
ellipse is 1/2 its longest axis
• The sem-minor axis, b, of an
ellipse is 1/2 its shortest axis
http://mathworld.wolfram.com/Ellipse.html
• The eccentricity, e, of an ellipse is a measure
of its departure from circularity. It is the ratio
of the distance between the foci and the major
axis of the ellipse. A circle has e=0 (the two
foci coincide at the center). A line segment has
eccentricity = 1 (the foci lie on the ellipse).
b
Kepler’s Three Laws of Planetary Motion
I.
II.
Empirical Laws: Based purely on observational evidence
The orbits of the planets are ellipses, with the Sun at one focus.
A line from a planet to the Sun sweeps out equal areas in equal
intervals of time.
III. If P = planet’s orbital period and a is the semi-major axis of its
orbit, then P2 a3
.
Galileo Galilei
1564-1642
Galileo was the first astronomer
to use a telescope
Looking through the
telescope, he discovered
Moons Orbiting Jupiter
This shows heavenly bodies that are not orbiting Earth, but another planet!
Galileo was the first astronomer to use a telescope
Discovered Phases of Venus, disproving
Ptolemaic
system
b) Viewed
through Galileo’s
a) If Venus moved in an epicycle
on the Earth-Sun line, it would
always appear as a crescent.
telescope, Venus is seen to go
through a full set of phases,
consistent with the Copernican
world-view, and contradicting the
Ptolemaic one.
Summary of "Letters on Sunspots": At Galileo’s time, it was believed
that the heavens are pure, and hence if it was known that
blemishes could appear and disappear on the face of the sun
itself, the incorruptibility and inalterability of the heavenly
bodies was destroyed. Hence, Galieleo’s contemporary, the
Jesuit priest, Scheiner, accounted for the sunspots by assuming
a number of small planets revolve about (or beneath) the sun,
and hence obstruct our vision to create sunspots.
He even
proposed that they could be stars. However, Galileo was bold
enough to place the location of the spots right on the surface of
the sun, or at least no farther from it than clouds are from the
earth. His evidence of his theory was undisputed for it was
mathematical. However, as to the nature of the spots, he
remained uncommitted, though he did not hesitate to reason
about this matter by analogy with terrestrial phenomena, a very
radical departure at the time.
from "Discoveries and Opinions of Galileo (1st Publication)" [Page 80 - 145]
Heliocentric, Keplerian model of Solar System
was eventually accepted.
Obstacles overcome, based on observations
• An unmoving Earth at the center of all celestial bodies
(contrary evidence: Jupiter’s moons, Venusian phases)
• All heavenly bodies moving at uniform speed, in circular
orbits (Kepler’s laws best explain planetary motions)
• Heavenly objects “perfect”, and not of the same substance
as Earth (the imperfection of sunspots)
Scientific, Critical Thinking
• Recognition that current world-view is
temporary, and subject to revision and
improvement as we learn more from
evidence, observations, experimentation.
• A scientific theory should have explanatory
power, and have predictable, testable
consequences.
The End
No Class Monday, 1 September
We’ll resume w/Chpt. 3 one week
from today, Wed. 3 September