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Lecture Notes
ASTR 1000
Fall 2009
Slide Set #1
Celestial Motions
Dr. H.A. McAlister
Dept. of Physics & Astronomy
Georgia State University
The Constellations
•
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 a Orionis.
Orion’s second brightest star, Rigel, is also called b Orionis.
•
The twelve constellations lying along the projection of the
Earth’s orbit onto the sky (the ecliptic) comprise the zodiac.
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
north celestial pole
Earth’s
spin
axis
north pole
equator
celestial equator
south pole
celestial
sphere
south celestial pole
Terrestrial Coordinates
N
* Greenwich
* Atlanta
latitude
Equator
longitude
S
For Atlanta:
latitude = 33o 45’ N
longitude = 84o 23’ W
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.)
t1
Time from t1 to t3 is the “synodic month”
(This is the time between repetition of phases
and equals about 29.5 days. This is what we
use for our calendar.)
t2
t3
Lunar Phases
first
quarter
waxing
gibbous
waxing
crescent
sunset
full
moon
noon
midnight
sunrise
waning
gibbous
Earth
third
quarter
waning
crescent
new
moon
to the Sun
Questions About Lunar Phases
•
What is the time interval between new and full moons?
two weeks
•
What time does the full moon culminate?
midnight
•
What time does the new moon culminate?
noon
•
What time does the new moon rise?
sunrise
•
What is the phase of the moon that culminates at sunset?
first quarter
•
What is the phase of the rising moon at sunset?
full
•
What is the phase of the setting moon at midnight?
first quarter
“Earthshine”
waxing
crescent
Moon
Sunlight reflected off day lit side of Earth
illuminates dark part of crescent moon.
to the Sun
Earth
The effect is most obvious just before and
just after new moon
The Tides
4. On the far side, the
Earth is effectively pulled
Moonward away from the
water, yielding another
high tide.
3. The water on the near side of
the Moon is pulled away from
Earth, raising a high tide.
Earth
Moon
2. The presence of the Moon
produces a gravitational attraction
on the Earth whose strength varies
inversely with distance from the
Moon.
1. Imagine a perfectly spherical
Earth uniformly flooded by an ocean.
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
Summer Solstice – 21 June
tropic of
Cancer
arctic
circle
equator
antarctic
circle
Winter Solstice – 21 December
tropic of
Cancer
arctic
circle
equator
antarctic
circle
tropic of
Capricorn
Vernal Equinox – 21 March
arctic
circle
tropic of
Cancer
equator
tropic of
Capricorn
antarctic
circle
Autumnal Equinox – 21 September
arctic
circle
tropic of
Cancer
equator
tropic of
Capricorn
antarctic
circle
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 sun never sets for observers north of the arctic
circle on the day of the summer 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.
Tilt of Earth’s Spin Axis
W
N
S
E
winter
solstice
equinox
summer
solstice
The sun rises on the east point and sets on the west point on the days of the equinoxes, giving
equal periods of “day” and “night”.
The sun is in the sky for the longest duration on the summer solstice and illuminates
the 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.
•
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.
•
If the Earth’s spin axis were not tilted by some angle,
we would have no seasons.
Precession of Earth’s Spin Axis
5. Spin axis now points to
Polaris. 13,000 years from now,
Vega will be our “pole star”
4. Earth responds to this pull
by slowly “precessing” its spin
axis around a circle in the sky
once every 26,000 years
23.5o
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
1. The rotation of the Earth distorts it
into an “oblate” spheroid flattened at
the poles
Shadows and Eclipses
Penumbra
Umbra
Earth
Sun
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 orbit
with respect to the ecliptic
A lunar eclipse lasts for many hours and can be seen from the majority of the
Earth’s surface
Eclipse of the Sun (Solar Eclipse)
Earth’s Orbit
Moon’s Orbit
Occurs at New Phase when Moon is also at the “line of nodes” of its orbit
with respect to the ecliptic
A solar eclipse lasts for only for a few minutes and can only be seen from very restricted
locations on the Earth’s surface
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’s
webpage on eclipses:
www.williams.edu/
astronomy/IAU_eclipses/
Total Solar Eclipse of 21 June 2001 from Zimbabwe
See Richard Monk’s
webpage 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 Ocean
25 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
normal “direct” (eastward) motion
retrograde motion
Mars
East
West
The night sky facing south
The Geocentric Explanation
All motions are circular
epicycle
Mars
stationary Earth
+
.
equant
deferent
center
deferent
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!
The Heleocentric Explanation
direct motion
retrograde motion
around “opposition”
Sun
direct motion
Earth
Mars
First proposed in detail by Nicolaus Copernicus in ~1505
but not published until De Revolutionibus in 1543.
Oppositions of Mars
“Unfavorable”
Opposition
Earth is at perihelion
closest approach is
68 million miles
Mars is at aphelion
“Favorable”
Opposition
Earth is at aphelion
closest approach is
34 million miles
Mars is at perihelion
Oppositions of Mars occur at 26-month intervals
On 27 Aug 2003, Mars had its most favorable opposition in 73,000 years
Orbital Configurations
for an Inferior Planet
Maximum Eastern
Elongation
Earth
Inferior
Conjunction
Superior
Conjunction
Sun
Maximum Western
Elongation
Orbital Configurations
for a Superior Planet
Eastern Quadrature
Opposition
Earth
Sun
Western Quadrature
Conjunction
Giants of the Heliocentric Theory
•
Nicolaus Copernicus (1473-1543) – Developed the Heliocentric
Theory but waited until just before his death to release his great
book, De Revolutionibus.
•
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.
Kepler’s First Law
Planets revolve around the sun in elliptical orbits with the
sun located at one focus of the ellipse
planet
+
focus
center
sun
focus
Kepler’s Second Law
The line from the sun to a planet sweeps out equal areas in
equal time intervals.
t1
t2
areaA
t4
aphelion
(slowest)
perihelion
(fastest)
areaB
areaA = areaB if t2-t1 = t4-t3
t3
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
•
New Stars – Discovered that his telescopes revealed far more stars
than are accessible to the unaided eye.
•
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.
•
Rings of Saturn – Galileo reported that Saturn had “ears” as his
telescopes couldn’t quite make out the true nature of the rings.
•
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.
•
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.