AST210 notes (for quiz 1)

8/10/2019 AST210 notes (for quiz 1)

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Celestial Sphere: the imaginary sphere of heavenly objects that seems to center on the observer

Celestial Pole: the point on the celestial sphere directly above a pole of the Earth

Constellation:

(from Latin meaning “stars together”) is an area of the sky containing a pattern of stars named

for a particular object, animal or person. Earliest constellation were defined by the Sumeranians as early as 2000 BC

Different civilizations saw different “patterns” in the sky

Our modern constellations draw from the Greeks and Romans

The 88 constellations used today were established by international agreement. They cover the

entire celestial sphere and have specific boundaries

are accidental patterns of stars. The stars in a constellation are at different distances from us

and move relative to each other in different directions and with different speeds.

Astronomers use constellations as a convenient way to identify parts of the sky.

Measuring the Positions of Celestial Objects

Angular separation: (of two objects) the angle between two lines originating from the eye of theobserver toward the two objects.

1° = 60 arc-minutes; 1 arc-minute = 60 arc-seconds

10° ~ fist held at arm’s length

1° ~ little finger held at arm’s length



Coordinates of the Earth

Latitude: position north or south of the equator

Longitude: position east or west of prime meridian (runs along Greenwich, England)

Celestial Coordinates

Declination (of an object on the Celestial Sphere): the angle north or south of the celestial equator

Celestial Equator: a line on the celestial sphere directly above the Earth’s equator *-90°, 90°]

Right Ascension (of an object): angle around the celestial sphere, measuring eastward from the vernal

equinox, where the sun crosses the equator moving northward.

Parallels between The Coordinates of the Earth and the Celestial Coordinates

Longitude and Latitude: uniquely define the position of an object on Earth.

Right Ascension and Declination: define the position of an object on the celestial sphere

Greenwich: defines the Prime meridian on the Earth’s Surface

Vernal Equinox: defines the Zero Right Ascension line (Equator is divided into 24 hrs; 60 mins; 60sec)

Sun’s Motion across the Sky

The sun seams to rise in the east and set in the west just like the rest of the stars As time goes on, the Sun appears to move constantly eastward among the stars

The time it takes for the sun to return to the same place among the stars is about 365.25 days

The Sun and the Seasons

Observation in the Northern Hemisphere

o

Sun rises and sets farther North in the summer than in the Winter

o

Sun is in the sky longer each day in the summer than in the winter

Explanation

o

Sun reaches a point higher in the sky in the summer, than in the winter.

o

Each portion of the Earth’s surface receiving more energy in a given amount of time in

the summer than in winter.o

Sunlight passes through more atmosphere in winter than in summer, resulting in more

scattering and absorption in the atmosphere.

Distance of the Earth from the Sun does not vary much during the year and thus is not a

determining factor for the seasons

The orientation of the Earth with respect to the Sun is the main reason for the seasons.

The Earth’s rotational axis is tilted 23.5° from the line drawn perpendicular to the ecliptic plane.

This tilt remains the same anywhere along the Earth’s orbit around the Sun.

Altitude: height of a celestial object (e.g. Sun) measured as an angle above the horizon

Summer & Winter Solstices: points on the celestial sphere where the Sun reaches its northernmost and

southernmost positions respectively.Vernal & Autumnal Equinoxes: points on the celestial sphere where the Sun crosses the celestial

equator while moving north and south respectively.

Leap Year and the Calendar

Tropical Year (365.242190 days): determines the seasons and is the time the Sun it takes to return to

the vernal equinox

Julian calendar: 365 days + 1 day added at the end of February every 4 years (Average of 365.25 days)Note: The difference between the tropical and Julian year caused the calendar to get out of synchronization with the seasons.



Gregorian calendar: has 365.2425 days

Leap Year rule: Every year whose number is divisible by four is a leap year, except century years, unless

they are divisible by 400.

The Moon’s Phases

Rotation: spinning of an object about an axis that passes through it.

Revolution: orbiting of one object around another.Note: The rotation and revolution period of the Moon are equal.

Phases (of the Moon): the changing appearance of the Moon during its cycle (caused by the relative

positions of the Earth, Moon and Sun)

Why do we see phases of the Moon?

Lunar phases are a consequence of the Moon’s 27.3 day (elliptical) orbit around the Earth

Angular size of the Moon as seen from Earth varies somewhat.

Half of Moon is illuminated by the Sun and half is dark.

We see a changing combination of the bright and dark faces as Moon orbits.

Phases of the Moon: Waxing Crescent, First Quarter, Waxing Gibbous, Full Moon, Waning

Gibbous, Third (or Last) Quarter, Waning Crescent, New Moon.

Elongation: The angle of the Moon (or Planet) from the Sun in the sky.

Sidereal Period: time required for one revolution (or rotation) of a celestial object with respect to

distant stars.

Sidereal Revolution (of the Moon): 27 1/3 days

Synodic Period: time interval between successive similar alignments of a celestial object with respect to

the Sun.

Synodic revolution (of the Moon): 29 ½ days

Lunar Month is the Moon’s synodic period or the time between successive phases: 29d 12h 4m 9s.

We only see one side of the MoonSynchronous Rotation: the Moon rotates exactly once with each orbit.

What causes Eclipses?

The Earth and Moon cast shadows

When either passes through the other’s shadow, we have an eclipse

Lunar Eclipses

An eclipse in which the Moon passes into the shadow of the Earth

Lunar Eclipses can occur only at full moon.

Lunar Eclipses can be penumbral, partial or total. Eclipse season: time of the year during which a solar or lunar eclipse is possible

A Lunar eclipse does not occur at each full Moon because the Moon’s plane of revolution is

tilted 5° compared to the Earth’s plane of revolution around the Sun.

Only during the 2 eclipse seasons that occur each year are the Earth and Moon positioned so

that the Moon will enter the Earth’s shadow during a full Moon.

o

Lunar eclipse during full moon

o

Solar eclipse during new moon



Umbra: portion of a shadow that receives no direct light from the light source.

Penumbra: portion of a shadow that receives direct light from only part of the light source

Penumbral Lunar eclipse: Eclipse of the Moon in which the Moon passes through the Earth’s penumbra

but not through its umbra.

Total Lunar eclipse: Eclipse of the Moon in which the Moon is completely in the umbra of the earth’s

shadow.Note: A total eclipse of the Moon is never totally dark because some light is refracted toward the moon by the Earth’s atmosp here.

Most of this refracted light reaching the Moon is red; the blue portion has been scattered out.

Partial Lunar eclipse: Eclipse of the Moon in which only part of the Moon passes through the umbra of

the Earth’s shadow.

Solar eclipse: Eclipse of the Sun in which light from the Sun is blocked by the Moon

Total Solar eclipse: Eclipse in which light from the normally visible portion of the sun (the photosphere)

is completely blocked by the Moon.

Corona: The Outer atmosphere of the Sun – is visible during a total solar eclipse

Partial Solar eclipse: Only part of the Sun’s disk is covered by the Mon.

Annular Solar eclipse: Eclipse in which the Moon is too far from the Earth for its disk to cover that of the

Sun completely, so the outer edge of the Sun is seen as a ring or annulus.Note: When the Moon is far away during a solar eclipse, the eclipse will be annular.

Two conditions must be met to have an eclipse

It must be a full moon (for a lunar eclipse) or a new moon (for a solar eclipse)

The Moon must be at or near one of the two points in its orbit where it crosses the ecliptic plane

(its nodes)

Predicting Eclipses

Eclipses recur with in the 18yr 11 1/3 day Saros cycle (but type and location may vary)

The Moon: Summary: Why do we see phases of the Moon?

o

Half the Moon is lit by the Sun; half is in shadow, and its appearance to us is determined

by the relative positions of Sun, Moon and Earth.

What causes Eclipses?

o

Lunar Eclipse: Earth’s shadow on the Moon.

o

Solar Eclipse: Moon’s shadow on Earth

o

Tilt of Moon’s orbit means eclipses occur during two periods each year.

Science and Its Ways of Knowing

Scientific Method: A never-ending cycle of hypothesis, prediction, data gathering and verification

Scientific Hypothesis: An educated guess made in describing the results of an experiment orobservation. It can be wildly speculative but must be testable.

Scientific Fact: A close agreement by competent observers of a series of observations of the same

phenomenon

Scientific Law or Principle: A scientific hypothesis that has been repeatedly tested and has not been

contradicted.



Scientific Model: A description of a phenomenon, based on observation, experiment and theoretical

considerations. It is a set of ideas that accounts for a set of observations in nature. It is not necessarily

the truth or reality, but a description that allows prediction of future events.

Scientific Theory: a synthesis of a large body of information that encompasses well-tested (by

repeatable experiments) and verified hypotheses about certain aspects of the natural world. No theory

can be proven to be true, but data can prove a theory to be false.Note: A scheme is not usually called a theory until its ideas are shown to fit observed data successfully.

Criteria for Scientific Model

The model must fit the data

The model must make predictions that can be tested and be of such nature that it would be

possible to disprove the model (falsifiability)

The model should be as simple as possible

o

Occam’s razor: The principle that the best explanation is the one that requires the

fewest unverifiable assumptions

Scientific Method (~16th

century)

Recognize a problem Formulate a hypothesis (i.e. solution)

Predict consequences of hypothesis

Perform experiments (or observations) to test hypothesis

Find simplest general rule which organizes (2), (3) and (4) [above bullet points] into a theory

The Greek Geocentric Model

The Greeks were interested in astronomy because of a pure philosophical desire to understand

how the universe works as opposed to other civilizations who were more interested in astrology

for agricultural predictions.

o

They believed in and looked for a sense of symmetry, order and unity in the cosmos

o

They took the first steps in creating a unified model of the universe Thales of Miletus (~600 BCE): Sun and stars as balls of fire, not gods

o

Taught Anaximander who taught Pythagoras.

Pythagoras (~530 BCE): Nature can be described with Mathematics.

o

Orbit of moon is inclined to Earth’s equator

o

Earth is spherical (due to roundness of Earth’s shadow on moon during lunar eclipses)

o

Venus the Morning Star is the same planet as the Evening Star.

o

Travelled and studied in various places (especially Egypt)

o

Founded a cult-like society of Pythagoreans, who postulated a spherical universe with

central “fire” containing force controlling all motions. The Earth, Moon, Sun and 5

naked-eye planets all move around it.

Plato (~380 BCE): Spheres moving in circular orbits Aristotle: Absence of parallax for the stars in the sky implied that the Earth must be at the

center of the solar system.Note: This is a valid argument given the limitations of observations those days. (i.e. logical argument, but wrong

conclusion due to incomplete data)

o Parallax: The apparent shifting of nearby objects with respect to distant ones as the

position of the observer changes.

d[parsecs]; p[arcseconds]



Note: Stellar Parallax was not observed until 1838; the greatest annual shift observed for any star is only 1.5 arcseconds

(parallax angle is half of that)

Note: Closest star system α Centauri is 4.4 light years = 1.34 parsecs away.

o

Saw the difference in the “natural” behaviour of Earthly objects compared to heavenly

objects. He believed two different sets of rules existed, one for Earthly objects and one

for celestial objects.

o

Aristotle’s Model of Heavens (based on spheres)

Stationary Earth at the center of the solar system

Sun is located on a sphere around the Earth, inside the celestial sphere of the

stars. The axes of the two spheres were tilted with respect to one another.

Sun is further away than the Moon: Moon’s crescent phase shows that it

passes between Earth and Sun.

Earth is spherical

Only on a sphere do all falling bodies seek the centre

As one travels North, more of the Northern sky is exposed while

southern stars disappear below the horizon.

During lunar eclipses, the Earth’s shadow on the Moon is always circular

Moon is spherical: line between lit and unlit side changes curvature with phase

of moon.

On Earth, things fall down toward the centre and stop

In the Heavens, things move in circles, and keep on moving.

Ptolemy (~150 AD): Ptolemaic model – the most comprehensive geocentric model

o

Published the Ptolemaic model on his book called the Almagest

Observations of Planetary Motion

Five Planets are visible to the naked eye: Mercury, Venus, Mars, Jupiter, Saturn

The Planets lack the simple, uniform motion of the Sun and Moon.

o

Retrograde Motion: Planet sometimes stop their eastward motion among the stars and

move westward for a while.

The Planets always stay near the ecliptic

o

Mercury and Venus never appear very far from the position of the Sun in the sky (i.e.

their elongation is small)

o

Elongation: angle in the sky from an object to the Sun

A Model of Planetary Motion: Epicycles Ptolemy’s geocentric model explained the planetary motions using epicycles.

o Epicycle: The circular orbit of a planet, the center of which revolves around the Earth in

another circle.

The model retained the idea of perfect heavenly circles and uniform speeds.

o

It explains why the planets never move far from the ecliptic.

o

It treated Mercury and Venus as special cases in order to explain their small elongations.



Rotations

Solar day: amount of time that elapses between successive passages of the Sun across the meridian.

Meridian: imaginary line that runs from north to south, passing through the observer’s zenith

Sidereal day: the amount of time that passes between successive passages of a given star across the

meridian.Note: The Earth’s solar day and sidereal day differ by about 4 minutes

Units of Distance in Astronomy

Astronomical Units (AU): Used to measure distances in a planetary system. It is the average distance

between Earth and Sun

Light Year: Used to measure even greater distances. It is the distance light travels in 1 year.

The Scale of the Universe

Nearest star other than the Sun is about 4460 miles away

The diameter of the galaxy on this scale would be about 164,000,000 miles.

Tools of Astronomy: Powers of Ten

Measuring the size of the Earth

Eratosthenes (276 – 195 BC): first person to clearly understand the shape and approximate size

of the Earth.

o

Compared shadows at noon during summer solstice at two different locations.

o

Sun must be directly overhead (at the Zenith) in Syene

o

Sun’s direction was off the vertical by 7° in Alexandria

o

7° difference was due to the Earth’s curvature

o

Earth’s circumference ~ 360/7 = 50 times the distance between Alexandria and Syene

o

Earth’s diameter: C = πd

Combining the calculations of Aristarchus and Eratosthenes, the ancient Greeks had for the first

time measurements of the radii of Earth, Moon and Sun and their relative distances. Had to wait until 1769 AD (transit of Venus) to observe the actual value of the astronomical unit

and thus the true dimensions of the solar system.

Q: Why was the Earth-centred Ptolemaic model accepted for 1300 years instead of the heliocentric

model computed by Aristarchus and Eratosthenes?

A: Because Aristotle’s argument held sway and a stationary Earth was demanded. No parallaxes were

observed until well after the Copernican and Keplerian revolutions.

Aristarchus’s Heliocentric Model

400 years before Ptolemy, around 280 BC, the Greek philosopher Aristarchus proposed a

moving-Earth solution to explain celestial motions. He introduced the concept of a spinning

Earth and the first heliocentric model, 1800 years before Copernicus.

Even though Aristarchus could not explain the lack of observable parallax (Aristotle’s argument),

he believed that the Sun was at the center of the solar system because it was much bigger in

size than the Earth.

Based on observations, he concluded the Sun was about 20 times farther from the Earth than

the Moon is. He showed that the Earth is 3 times larger than the Moon in diameter, and the Sun

is 20 times larger than the moon in diameter. This implies the Sun is about 7 times larger than

the Earth in diameter.



Aristarchus was the first to create a map of the solar system. He simply did not have the scale

for it.

Aristarchus: Relative distances of Moon and Sun

Through the measurement of angle MES (Moon, Earth, Sun), the ration of EM (Earth, Moon) and

ES (Earth, Sun) can be found

o

MES = 87°; EM/ES = 1/19 (what Aristarchus found)

o

MES = 89° 51 EM/ES = 1/400 (actual)

The Marriage of Aristotle and Christianity

St. Thomas Aquinas blended the natural philosophy of Aristotle and Ptolemy’s work with

Christian beliefs. He wanted no conflict between faith and reason.

A central, unmoving Earth fir perfectly with Christian thinking and a literal interpretation of the

Bible. Humans at the centre of God’s creation.

People during the Middle Ages placed a great reliance on authority, especially authorities of the

past, Bible, earlier churchmen, church superiors, Aristotle. Arguments tended to be supported

by reference to authorities rather than individual experience and experiment.

o

Fall of Byzantium to Turks in 1453 led to the emigration of scholars with the

accumulated knowledge of the Arabs into Europe. This was new to the then-backward

Europeans (Probably knowledge from Moors in Andalucia, southern Spain also

contributed.)

Nicolaus Copernicus and the Heliocentric Model

Lecture 3, 4, 5

GAP

Lecture 7

Applications of Kepler’s and Newton’s laws

Tides: Effect of sun

Precession of the Earth

Orbits of Comets



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AST210 notes (for quiz 1)