User’s Guide to the Sky:

Patterns and Cycles

Perspectives on AstronomySeeds & Backman Chapter 2 (cont’d.)

Astronomy 101Lecture by: Prof. Barsony

Sub: Abby FullerFind this lecture at

http://www.physics.sfsu.edu/~afuller/117L/117L.htm

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.

http://en.wikipedia.org/wiki/Umbra

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)

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).

Orientation of Earth’s and Moon’s Umbral Shadows

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

Altitude: The elevation of an object, in angular measure (e.g., degrees) from your horizon

Object in Sky

Your horizon

Altitude angle

Azimuth: The angle around your horizon, measured from North, in degrees. East is at 90o azimuth, S at 180o, W at 270o.

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

To Sun

Direction perpendicular to Earth-Sun lineca

Direction of Earth’s rotational axis = NCP

Earth’s Rotational Axis is tilted 23.5o away from the direction perpendicular to the Earth-Sun line

Celestial Equator

Northern Summer

Southern Winter

Sun at its furthest north as seen from Earth.

To SCP

To Sun

6 months later...

Celestial Equator

Northern Winter

Southern Summer

To NCPPerpendicular to Earth-Sun Line

Sun at its furthest South, as seen from Earth

To SCP

Tilt of Earth’s Rotational Axis Relative to an Axis Perpendicular to the Earth-Sun Line is Responsible for the Seasons

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.

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.

4. OK to go back to your places & sit down.

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.

Seasons defined by 4 Events

The plane traced out by the Earth-Sun line

The intersection point between the Celestial Equator and the ecliptic, when the Sun’s apparent position, as seen from Earth, starts going North

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 Northernmost point in the sky.

When the Sun reaches its Southernmost point in the sky.

Precession

Precession is the result of torques acting on a spinning body which tend to change the direction of its spin axis

For Earth, the main such torque is due to the Sun’s gravitational pull

To Sun

NCPDirection perpendicular to Earth-Sun line

Axis of precession

Earth’s Precession Period is 26,000 yearsIt is observable in the changing direction of the Celestial Pole among the constellations.

Circles around the Earth Become Orbits around the Sun

Perspectives on AstronomySeeds & Backman Chapter 3

Astronomy 101Prof. 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

Aristotle384-322 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.

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.

solarsystem.nasa.gov/.../ display.cfm?ST_ID=525

Earth

Moon

Sun

solarsystem.nasa.gov/.../ display.cfm?ST_ID=525

Earth

Moon

Sun

Question:What were the 5 known planets in Aristotle’s time?

Mercury

Venus

Mars

JupiterSaturn

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.

Uranus was discovered by Caroline and William Herschel on March 13, 1781.

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.

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

http://www.heavens-above.com

Kentfield, CA latitude: +37.952o

longitude: -122.556o

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

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.

Plato gave his students a major problem to work on.

Plato’s student, Aristarchus, developed a Sun-centered model that could explain the retrograde motion of Mars, with the planets moving on circular paths.

Aristarchus

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.

Ptolemy

384-322 BC

.

85-165 A.D.

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.

A more complicated model to save the Earth-centered Universe

epicycle: small circle

deferent: large circle Earth

equant

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.

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

De Revolutionibus Orbium Coelestium

1543

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 humanity’s 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’ work.

I. Fixed starsII. Saturn

III.Jovis=JupiterIIII. Mars

V. Earth

VI. VenusVII. Mercury

Sol = Sun

On the Revolution of the Celestial Spheres

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, 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

http://mathworld.wolfram.com/Ellipse.html

• 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

b• 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).

Kepler’s Three Laws of Planetary Motion

I. The orbits of the planets are ellipses, with the Sun at one focus.

II. 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 P2a3

Empirical Laws: Based purely on observational evidence

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

a) If Venus moved in an epicycle on the Earth-Sun line, it would always appear as a crescent.

b) Viewed through Galileo’s 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

• 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)

Obstacles overcome, based on observations

was eventually accepted.

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.

No Class Monday, 1 September

We’ll resume w/Chpt. 3 one week from today, Wed. 3 September

The End