Lecture NotesASTR 1000

Fall 2009Slide Set #1

Celestial Motions

Dr. H.A. McAlisterDept. of Physics & Astronomy

Georgia State University

• 88 constellations in the sky. Those in the northern celestial hemisphere named by the Greeks. Constellations in the extreme southern sky were named in modern times.

• Subsets of constellations are called asterisms. For example, the “Big Dipper” is an asterism of the constellation Ursa Major (the big bear).

• While constellations were named by the Greeks, Arabic names have been mostly adopted for individual stars. Stars within a constellation are assigned Greek letters in accordance with their brightest. For example, the brightest star in Orion has the Arabic name Betelgeuse, but it is also known as Orionis. Orion’s second brightest star, Rigel, is also called Orionis.

• The twelve constellations lying along the projection of the Earth’s orbit onto the sky (the ecliptic) comprise the zodiac.

The Constellations

Winter Sky – Facing North

Winter Sky – Facing South

Orion as Depicted by

J. Hevelius(1690)

(Note that this is as viewed from outside

celestial sphere)

Spring Sky – Facing North

Spring Sky – Facing South

Celestial Motions

• The rotation of the Earth about its spin axis once every 24 hours causes diurnal effects including day and night and the rising and setting of celestial objects.

• The revolution of the Earth about the sun once every 365.2422… days produces annual effects such as the sun appearing to move with respect to the stars along a path in the sky called the ecliptic. The twelve constellations lying along the ecliptic comprise the zodiac.

• The apparent motions of celestial objects on the sky are the combined result of diurnal and annual motions and, in the case of the planets their own orbital motions around the sun.

The Celestial Sphere

celestial equator

celestialsphere

south celestial pole

north celestial pole

south pole

north pole

equator

Earth’sspinaxis

N

S

Equator

* Greenwich

* Atlanta

longitudelatitude

For Atlanta: latitude = 33o 45’ N longitude = 84o 23’ W

Terrestrial Coordinates

t1

t2

t3

Lunar Months

All motions are counterclockwise

Time from t1 to t2 is the “sidereal month” (This is time required for realignment with respect to the stars and equals 27.3 days.)

Time from t1 to t3 is the “synodic month”(This is the time between repetition of phasesand equals about 29.5 days. This is what weuse for our calendar.)

Earth

noonmidnight

sunset

sunrise

to the Sun

sunlight

sunlight

Lunar Phases

fullmoon

newmoon

firstquarter

thirdquarter

waningcrescent

waxingcrescent

waxinggibbous

waninggibbous

Questions About Lunar Phases

• What is the time interval between new and full moons?

• What time does the full moon culminate?

• What time does the new moon culminate?

• What time does the new moon rise?

• What is the phase of the moon that culminates at sunset?

• What is the phase of the rising moon at sunset?

• What is the phase of the setting moon at midnight?

two weeks

midnight

noon

sunrise

first quarter

full

first quarter

Earth

to the Sun

sunlight

sunlight

“Earthshine”waxing

crescent

MoonSunlight reflected off day lit side of Earthilluminates dark part of crescent moon.

The effect is most obvious just before andjust after new moon

The Tides

Earth

Moon

1. Imagine a perfectly spherical Earth uniformly flooded by an ocean.

2. The presence of the Moon produces a gravitational attraction on the Earth whose strength varies

inversely with distance from the Moon.

3. The water on the near side of the Moon is pulled away from

Earth, raising a high tide.

4. On the far side, the Earth is effectively pulled Moonward away from the water, yielding another high tide.

Moon Factoids

• A “blue moon” is when more than one full moon occurs in the same calendar month.

• The moon undergoes “synchronous” rotation and revolution (i.e. the periods of rotation and revolution are identical), so one side of the moon always faces the Earth.

• The “harvest moon” involves the rising of the full moon in late September and early October. Due to the angular tilt of the moon’s orbital plane with that of the Earth, the bright moon appears to rise at about the same time in the early evening when the moon is full at the time of the “autumnal equinox”.

Moon Myths

• The phase of the moon has no effect on human behavior.

• There is no such thing as the “dark side of the moon.”

• We did indeed land humans on the moon in the six Apollo landings between July 1969 and December 1972.

• For more about “lunatics”, the “moon hoax” and other astronomical pseudoscience, see:

www.astrosociety.org/education/resources/pseudobib.html

Tilt of Earth’s Spin Axis

23.5o tilt

The Earth’s spin axis is tilted by 23.5 degrees off vertical with respect to the “ecliptic plane” (plane of the Earth’s orbit around the sun)

The spin axis remains essentially parallel to itself during the course of the year

sunlight

sunlight

Summer Solstice – 21 June

equator

antarcticcircle

arcticcircle

tropic ofCancer

sunlight

sunlight

Winter Solstice – 21 December

equator

antarcticcircle

arcticcircle

tropic ofCapricorn

tropic ofCancer

sunlight

sunlight

Vernal Equinox – 21 March

equator

antarcticcircle

arcticcircle

tropic ofCancer

tropic ofCapricorn

sunlight

sunlight

Autumnal Equinox – 21 September

equator

antarcticcircle

arcticcircle

tropic ofCancer

tropic ofCapricorn

The Culminating Sun

• The sun culminates in the zenith (i.e. straight overhead) at noon for observers located on the tropic of Cancer (latitude = 23.5o N) on the day of the summer solstice.

• The sun culminates in the zenith at noon for observers located on the tropic of Capricorn (latitude = 23.5o S) on the day of the winter solstice.

• The sun culminates in the zenith (i.e. straight overhead) at noon for observers located on the equator (latitude = 0o) on the days of the equinoxes.

Other Seasonal Extremes

• The sun never rises for observers north of the arctic circle on the day of the winter solstice

• The above conditions are reversed for the antarctic circle.

• The sun moves 360o around the horizon for observers located at the north and south poles on the days of the equinoxes.

• The sun never sets for observers north of the arctic circle on the day of the summer solstice

Tilt of Earth’s Spin Axis

NS

W

Ewintersolstice

summersolstice

equinox

The sun rises on the east point and sets on the west point on the days of the equinoxes, givingequal periods of “day” and “night”.

The sun is in the sky for the longest duration on the summer solstice and illuminatesthe northern hemisphere most directly.

Temperature Effect

• Summer days are longer and the sun is more intense (due to the more direct illumination angle). Thus summer is hotter than winter.

• If the Earth’s spin axis were not tilted by some angle, we would have no seasons.

• There is a lag of the seasons when comparing the dates of the solstices with the actual extremes in temperature because it takes time to heat up the oceans and atmosphere at the onset of summer and to cool them off at the onset of winter.

Precession of Earth’s Spin Axis

1. The rotation of the Earth distorts it into an “oblate” spheroid flattened

at the poles

2. Moon’s orbital plane is tilted by 5o from our equator

3. Moon’s gravitational pull on Earth attempts to pull

bulge into lunar orbital plane

23.5o

4. Earth responds to this pull by slowly “precessing” its spin axis around a circle in the sky

once every 26,000 years

5. Spin axis now points to Polaris. 13,000 years from now,

Vega will be our “pole star”

Sun

Shadows and Eclipses

Penumbra

Umbra Earth

Eclipse of the Moon (Lunar Eclipse)

Earth’s Orbit

Moon’s Orbit

Occurs at Full Phase when Moon is also at the “line of nodes” of its orbitwith respect to the ecliptic

A lunar eclipse lasts for many hours and can be seen from the majority of theEarth’s surface

Eclipse of the Sun (Solar Eclipse)

Occurs at New Phase when Moon is also at the “line of nodes” of its orbitwith respect to the ecliptic

A solar eclipse lasts for only for a few minutes and can only be seen from very restrictedlocations on the Earth’s surface

Earth’s Orbit

Moon’s Orbit

Total and Annular Eclipses

Vertex of Umbral shadow is at or below Earth’s surface, so a total eclipse is possible

Vertex of Umbral shadow is above Earth’s surface, so only an annular eclipse is possible

Example of a Solar Eclipse Path

See Richard Monk’swebpage on eclipses:www.williams.edu/astronomy/IAU_eclipses/

Total Solar Eclipse of 21 June 2001 from Zimbabwe

See Richard Monk’swebpage on eclipses:www.williams.edu/astronomy/IAU_eclipses/

Bailey’s Beads

Solar Corona

“Diamond Ring”

Upcoming Lunar and Solar Eclipses

Solar Eclipses:

15 Jan 2009 (annular) – Asia & Africa 11 July 2010 (total) – South Pacific Ocean 4 Jan 2011 (partial) – Europe, Africa & central Asia 1 Jun 2011 (partial) – east Asia, far N. America, Iceland

1 Jul 2011 (partial) – south Indian Ocean25 Nov 2011 (annular) – south Africa, Antactica, Tasmania, New Zealand

The next total solar eclipses visible from the U.S. will be on 21 Aug 2017 and 8 Apr 2024. The 2017 eclipse will be visible from Georgia.

Lunar Eclipses:

31 Dec 2009 – not U.S.15 Jan 2010 (annular) – not U.S.26 Jun 2010 (partial) – not U.S.21 Dec 2010 (total) – all U.S.15 Jun 2011 (total) – not U.S.10 Dec 2011 (total) – all U.S.

Motions of the “Wanderers” – The Planets

The night sky facing south

WestEast

normal “direct” (eastward) motion retrograde motion

Mars

The Geocentric Explanation

stationary Earth

+ .deferentcenter

deferent

equant

epicycle

All motions are circular

Epicycle moves at constant angular rate about the equant

Adjustable parameters include diameters of epicycle & deferent, distance of equant from deferent center, and rates of motion along epicycle & deferent

Developed in detail around 140 AD by Claudius Ptolemy and very successfully used for 1500 years!

direct

retrograde

Mars

The Heleocentric Explanation

Sun

Earth Mars

direct motion

direct motion

retrograde motionaround “opposition”

First proposed in detail by Nicolaus Copernicus in ~1505 but not published until De Revolutionibus in 1543.

Oppositions of Mars

“Favorable”Opposition

Earth is at aphelion

closest approach is 34 million miles

Mars is at perihelion

“Unfavorable” Opposition

Earth is at perihelion

closest approach is 68 million miles

Mars is at aphelion

Oppositions of Mars occur at 26-month intervalsOn 27 Aug 2003, Mars had its most favorable opposition in 73,000 years

Earth

Maximum EasternElongation

Maximum WesternElongation

InferiorConjunction

SuperiorConjunction

Orbital Configurations for an Inferior Planet

Sun

Opposition

Eastern Quadrature

Western Quadrature

Earth Conjunction

Orbital Configurations for a Superior Planet

Sun

Giants of the Heliocentric Theory

• Tycho Brahe (1546-1601) – Greatest pre-telescopic observer, produced extensive observations of Mars that were critical to proving the Heliocentric Theory.

• Johannes Kepler (1571-1630) – Hired as Tycho’s assistant but only gained access to Tycho’s complete data after Tycho’s premature death. Kepler discovered three “laws of planetary motion” that revolutionized the understanding of the solar system.

• Galileo Galilei (1564-1642) – First used the telescope for observing the night sky in 1609. His discoveries were monumental and included proof of the Heliocentric Theory.

• Isaac Newton (1642-1727) – Developed the Law of Universal Gravitation and three laws of motion that completely explain Kepler’s Laws of Planetary Motion.

• Nicolaus Copernicus (1473-1543) – Developed the Heliocentric Theory but waited until just before his death to release his great book, De Revolutionibus.

Kepler’s First Law

Planets revolve around the sun in elliptical orbits with the sun located at one focus of the ellipse

+focus focuscenter

sun

planet

Kepler’s Second Law

The line from the sun to a planet sweeps out equal areas in equal time intervals.

t1

t2areaA

t3

t4

areaBareaA = areaB if t2-t1 = t4-t3

perihelion(fastest)

aphelion(slowest)

Kepler’s Third Law

For any two planets, the ratio of their mean distance from the sun cubed equals the ratio of their orbital periods squared.

(D1/D2)3 = (P1/P2)2

Planets far from the sun take longer to orbit the sun than do planets nearer the sun.

Galileo’s Telescopic Discoveries

• Lunar Feature – Found the moon to have craters, mountains and complicated terrain. He also reported spots on the sun, although it turns out they had first been reported centuries earlier by Chinese astronomers.

• Satellites of Jupiter – Discovered four large moons of Jupiter (still often referred as the “Galilean satellites”) which clearly orbited Jupiter and contradicted the geocentric premise that all bodies move around the Earth.

• Rings of Saturn – Galileo reported that Saturn had “ears” as his telescopes couldn’t quite make out the true nature of the rings.

• Phases of Venus – He discovered that Venus exhibited a complete cycle of phases, which it could not do under the constraints of the geocentric theory. This was proof of the heliocentric theory.

• New Stars – Discovered that his telescopes revealed far more stars than are accessible to the unaided eye.