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Users Guide to the Sky:


New Moon) Why isn't there a total solar eclipse each New ... how easily Moon's umbra can miss Earth's surface during New Moon (therefore, no solar eclipse) ... – PowerPoint PPT presentation

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Title: Users Guide to the Sky:

Users Guide to the Sky
  • Patterns and Cycles

Astronomy 101 Lecture by Prof. Barsony Sub Abby
Fuller Find this lecture at http//www.physics.sf /117L/117L.htm
Perspectives on Astronomy Seeds Backman
Chapter 2 (contd.)
Part III. Cycles
  • Eclipses
  • Seasons
  • Precession

Solar Eclipses
Which way is the Sun in this picture?
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 Moons
    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 Moons 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 Earths
    surface at over 1000 mph or 1600 km/hr.

  • By coincidence, how much farther is the Sun than
    the Moon?

(Ans. 390 x on average)
  • How much larger is the Suns diameter than the

(Ans. 400 x)
  • What phase is the Moon in during a solar eclipse?

(Ans. New Moon)
  • Why isnt there a total solar eclipse each New

(Ans. The Moons orbit is inclined to Earths
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
Annular Eclipse
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 Suns
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).
(No Transcript)
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 Earths shadow.
  • A partial lunar eclipse occurs when the Moon
    moves through the penumbra of the Earths
  • It typically takes a few hours for the Moon to
    travel through the Earths entire shadow during a
    lunar eclipse.

  • What phase is the Moon in during a lunar eclipse?

(Ans. Full Moon)
  • Why isnt there a lunar eclipse each Full Moon?

(Ans. The Moons orbit is inclined to Earths
orbit around the Sun by 5o)
Orientation of Earths and Moons 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 Moons orbital plane, indicated by the dashed
line with the arrows on its end, is tilted with
respect to the Earths 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 Earths shadow (therefore, no lunar
eclipse), or how easily Moons umbra can miss
Earths surface during New Moon (therefore, no
solar eclipse).
The combination of light scattered by all Earths
sunrises and sunsets lights the totally eclipsed
Moons face in a copper glow.
(No Transcript)
The Seasons
  • Refer to cyclical climatic changes in Earths
    temperate zones warmth in summer, cold in
  • 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 well 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 Earths Rotational Axis Relative to an
Axis Perpendicular to the Earth-Sun Line is
Responsible for the Seasons
Direction perpendicular to Earth-Sun lineca
Direction of Earths rotational axis NCP
Earths Rotational Axis is tilted 23.5o away from
the direction perpendicular to the Earth-Sun line
Northern Summer
To Sun
Sun at its furthest north as seen from Earth.
Southern Winter
Celestial Equator
Tilt of Earths 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...
Kinesthetic Astronomy Key Point for Seasons
Although Earth orbits the Sun, the direction of
its spin axisdoes not change during the year as
it orbits.
  • 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. Lets orbit
(walk around the Sun) once, with our spin axis
(head-to-toe line) perpendicular to the Sun-Earth
  • Now, lets 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 Suns 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 Suns apparent
position, as seen from Earth, starts going South
When the Sun reaches its Southernmost point in
the sky.
When the Sun reaches its Northernmost point in
the sky.
The plane traced out by the Earth-Sun line
The intersection point between the Celestial
Equator and the ecliptic, when the Suns apparent
position, as seen from Earth, starts going North
Seasons defined by 4 Events
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 perpendicular to Earth-Sun line
To Sun
For Earth, the main such torque is due to the
Suns gravitational pull
Earths 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
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

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 display.cfm?ST_ID525
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.
What were the 5 known planets in Aristotles time?
Moon display.cfm?ST_ID525
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
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
Kentfield, CA latitude 37.952o
longitude -122.556o
Kentfield, CA latitude 37.952o
longitude -122.556o
Kentfield, CA latitude 37.952o
longitude -122.556o
Kentfield, CA latitude 37.952o
longitude -122.556o
Plato gave his students a major problem to work
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.
Platos student, Aristarchus, developed a
Sun-centered model that could explain the
retrograde motion of Mars, with the planets
moving on circular paths.
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 observers
Question In the example above, what is the
change in the observers position?
Orders of MagnitudePowers 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 Earths 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
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.
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
A visualization of epicycles http//www.astronom (shows animation
of how Ptolemys epicycles solved the problem of
retrograde motion)
Nicolaus Copernicus
On the Revolution of the Celestial Spheres
De Revolutionibus Orbium Coelestium
In the Copernican model, the Sun, instead of the
Earth, is at the center. The eventual
acceptance of the Copernican model was such a
large shift in humanitys conception of the
Universe and our place in it, that the modern
English word revolution referring to a large
change, originates from the title of Copernicus
I. Fixed stars
II. Saturn
IIII. Mars
V. Earth
VI. Venus
VII. Mercury
Sol Sun
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
Retrograde Motion and Varying Brightness of the
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.
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
Tycho Brahe Johannes Kepler
Tycho, himself, did not believe in the Copernican
system. He, instead, devised his own peculiar,
geo-heliocentric 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

  • 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 e0 (the
    two foci coincide at the center). A line segment
    has eccentricity 1 (the foci lie on the

Keplers Three Laws of Planetary Motion
Empirical Laws Based purely on observational
  • 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.
  • If P planets orbital period and a is the
    semi-major axis of its orbit, then P2? a3

Galileo Galilei
Galileo was the first astronomer to use a
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
Discovered Phases of Venus, disproving Ptolemaic
b) Viewed through Galileos telescope, Venus is
seen to go through a full set of phases,
consistent with the Copernican world-view, and
contradicting the Ptolemaic one.
a) If Venus moved in an epicycle on the Earth-Sun
line, it would always appear as a crescent.
Summary of "Letters on Sunspots" At Galileos
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,
Galieleos 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 Jupiters moons,
    Venusian phases)
  • All heavenly bodies moving at uniform speed, in
    circular orbits (Keplers 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,
  • A scientific theory should have explanatory
    power, and have predictable, testable

No Class Monday, 1 September Well resume
w/Chpt. 3 one week from today, Wed. 3 September
The End