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The celestial sphere, the coordinates system, seasons,
phases of the moon and eclipses
Chapters 2 and S1
The celestial sphere and the coordinates system
Chapter S1
How to find our way in the sky?
Let’s start with the Earth Coordinate System
Latitude: N-S of the equator, Longitude: E-W along equator
North celestial poleNorth
North Celestial Pole
South Celestial Pole
Cele
stia
l
Equ
ato
r
From Earth to Space
The Celestial Sphere • The Celestial Sphere: An
imaginary sphere of infinite radius centered on Earth.
• The extensions of the Earth North and South Pole define the North and South celestial poles.
• The projection of Earth equator defines the Celestial equator.
• Celestial Sphere can then be divided into a grid, just like the Earth is divided into a grid of latitude and longitude.
The Celestial Sphere: Motions
• Stars, planets and Sun are “attached” to this imaginary sphere.
• As the Earth rotates, the celestial sphere (with the stars attached to it) appears to rotate in the opposite direction.
• To explain the daily motions of the sky you can imagine the sphere rotating once in 23 hours 56 minutes (using a star as reference).
orth celestial poleNorth
North Celestial Pole
South Celestial Pole
Cel
esti
al E
quat
or
Celestial Sphere: Measuring Angles
Longitude (E – W along Equator) Right Ascension (RA)
Latitude (N – S of Equator) Declination (Dec)
The celestial coordinate system
RA, measured in hr, min, sec (0 to 24 hours)
1 hour = 60 min
1 min = 60 sec
(1 hour = 15 degrees of Earth rotation)
Dec, measured in degrees, arcmin,
arcsec (0 celestial equator, +90 north hemisphere, -90
south hemisphere)
1 degree = 60 arcminutes
1 arcminute = 60 arcseconds
The use of RA and Dec to locate objects in the celestial sphere
There are two coordinates that allow to locate an object in the sky: Azimuth and
Altitude. Their value depends in the location of the observer
Azimuth: Use as reference the north direction (close to Polaris) and the range of
values is from 0 to 360 degrees. 0 degrees is N, 90 degrees E, 180 is S and 270 is W.
Altitude: Use as reference the horizon. The range of values is from 0 degrees (horizon)
to 90 degrees (zenith)
Locating the star Vega and the Sun in the celestial sphere
Ecliptic: Apparent annual path of the Sun in the celestial sphere
The Sun crosses the celestial equator on March 21 (Spring equinox) and on September
21 (Fall equinox)
The Sun reaches a declination of +23.5 degrees on June 21 (Summer solstice)
The Sun reaches a declination of – 23.5 degrees on December 21 (Winter solstice)
Locating Polaris: RA: 0h 31m 49.084s Dec: +89d 15’ 50.79”
Using two stars in the Big Dipper (Ursa Major) constellation called the Pointers”
Locating Polaris (North star) in the celestial sphere
Angular Size Angular size of an object depends on two parameters
The physical size of the object
The distance to the object Angular size is measured in units of angle (degrees, arcmin and
arcsec)
Angular size = Physical Size
Distance
More specifically (See page 30, Mathematical Insight 2.1)
Angular Size = Physical size
360 degrees 2 x Pi x distance
Angular size = Physical size x 360 degrees/ (2 x Pi x distance)
Example: Physical size of the Moon
Angular size = 0.5 degrees
Distance = 380,000 km
Angular Units Estimating angular sizes
Practical Measurements
• The Moon and the Sun, coincidentally, have nearly the same angular size,
about 0.5 degrees.
• The Moon is about 380,000 km away but only 3,300 km diameter
• The Sun is 150,000,000 km away and about 1,400,000 km diameter
Celestial Sphere and the Observer
Horizon: flat plane where observer
stands
Zenith: the point directly above an
observer
Nadir: the point opposite to the zenith
An observer can see only half of the
celestial sphere from any location on
Earth
Apparent Motion of Stars
Earth rotates from W-E celestial sphere
seems to rotate E-W.
Depending on our location, we’ll see some
stars rising on the east and setting on the
west.
Depending on our location, some stars
never set. Those stars are called
circumpolar stars.
For someone standing at the equator, all stars rise and set.
For someone standing at the poles, all stars are circumpolar.
Observer located at the equator
Meridian: The circle that passes through the zenith and the
two celestial poles
Orientation of the sky relative to
the celestial sphere, for an
observer at the Earth’s equator
Rotating the diagram make it
easier to visualize the local sky
at the equator
Observer located at the north pole
Observer located at latitude 40 degrees N
The latitude is the angle from the zenith to
the Earth’s equator. “Up” point to the circle
on the celestial sphere with declination +40
degrees
Notice that the south pole is below the
horizon and invisible for an observer located
at 40 degrees N latitude
Rotating the diagram so the zenith is
up make it easier to visualize the
local sky.
The blue scale along the meridian
shows altitudes and directions in the
local sky.
Notice that the altitude of the north
celestial pole is 40 degrees which
correspond to the latitude of the
place
How can we estimate our latitude? Remember that the angle between the horizon and the object is called altitude The altitude of the north celestial pole, give us our latitude. Polaris is close to the north celestial pole. By estimating the altitude of Polaris we can estimate the latitude of the observer.
The path of the sun on the equinoxes and solstices at latitude 40 degrees north
(Latitude of Gainesville is about +29.65 degrees)
The path of the Sun on the equinoxes and solstices at latitude 0 degrees ( Observer at
equator)
Apparent Daily Motion of the Sun
The Sun:
Rises in the east
Sets in the west
Travels on an arc
across the sky
Solar day: 24 hours
Solar and Sidereal Days Solar day (relative to the Sun): It is the average time between two consecutive passes of the Sun through the meridian. It is on average 24 hours Sidereal day (Relative to stars): It is the time between two consecutive passes of a star through the meridian. It is on average 23 hours, 56 minutes, 4.1 seconds
Why is the Solar Day Longer?
The reason: Earth rotation on its axis + orbital motion around the Sun
The Earth has to travel an additional angle to have the Sun at the same position each day. 1 orbit = 1 full circle = 360 degrees Earth takes 1 year = 365 days to complete 1 orbit.
additional angle Earth has to rotate:
360 degrees/365 days = 0.986 degrees/day
How long does it take the Earth to cover ~ 1 degree? It takes 1 day to rotate 360 degrees on its axis 1 day = 24 hrs = 1440 minutes 1440 minutes/360 degrees = 4 min/degree
Solar day is 4 minutes longer
Apparent Annual Motion of the Sun
Because of Earth orbital motion, the Sun position relative to the stars is different every night.
Apparent Annual Motion of the Sun
The Sun apparent path relative to the stars is called the ECLIPTIC The Sun moves eastward relative to the stars on celestial sphere It moves ~ 1 degree per day. Why?
The 12 constellations through which the Sun moves are the constellations of the
ZODIAC What is a constellation? A constellation is a region of the sky limited by lines of RA and Dec. The ancients attached a figure to a constellation. The IAU defined 88 constellations that cover the celestial sphere
An example of a
constellation:
Orion the Hunter
The stars form the figure of
a Hunter but the stars are
located a different distances.
The stars in a constellation
are not physical related to
each other
The Zodiac constellations (All the Zodiac constellations lie along the ecliptic)
ZODIAC CONSTELLATIONS
• There are actually 13 (NOT 12) zodiac constellations
(Ophiuchus)
• Sky has changed since Babylonians came up with the
signs of the zodiac (Earth precession later)
• For example: August 4th is not Leo anymore, but
Cancer
• The Sun spends different times in different
constellations (they are not all the same size!)
• Scorpius only 7 days
• Virgo 47 days
The seasons Chapter 2
Section 2.2
Why do we have seasons?
TRUE OR FALSE?
We have seasons because the Earth is closer
to the Sun in summer and farther from the
Sun in winter.
Question
TRUE OR FALSE?
We have season because the Earth is closer to
the Sun in summer and farther from the Sun
in winter.
Question
Hint: When it is summer in America,
it is winter in Australia.
TRUE OR FALSE!
Earth is closer to the Sun in summer and farther
from the Sun in winter. Actually it is the opposite: Earth is closer to the Sun
during the north hemisphere winter and farter during the
north hemisphere summer (see another slide later)
• Seasons are opposite in the N and S hemispheres, so
distance cannot be the reason.
• The real reason for seasons involves Earth’s axis tilt.
What causes the seasons?
Seasons depend on how Earth’s axis affects the directness of sunlight.
Earth’s rotation axis is tilted by 23.5 degrees compared to the
direction perpendicular to the Earth’s orbital plane
23.5
The sun crosses the meridian higher during the summer. In the winter the sun crosses the meridian lower in the sky.
Seasons
Summary: The Real Reason for Seasons
• Earth’s axis points in the same direction (to Polaris) all year round, so its orientation relative to the Sun changes as Earth orbits the Sun.
• Summer occurs in an hemisphere when sunlight hits it more directly; winter occurs when the sunlight is less direct.
• AXIS TILT is the key to the seasons; without it, we would not have seasons on Earth.
Why doesn’t distance matter?
•Is there a change in
distance from the Sun
during the year?
• Yes, but the
variation of Earth–
Sun distance is
small—about 3%; this
small variation is
overwhelmed by the
effects of axis tilt.
How do we mark the progression of the
seasons?
•We define four special points:
summer (June) solstice
winter (December) solstice
spring (March) equinox
fall (September) equinox
We can recognize solstices and
equinoxes by Sun’s path across sky:
Summer (June) solstice:
highest path; rise and set at
most extreme north of due
east
Winter (December) solstice:
lowest path; rise and set at
most extreme south of due
east
Equinoxes: Sun rises
precisely due east and sets
precisely due west.
How does the orientation of Earth’s axis
change with time?
•The effect is called precession. •Although the axis seems fixed on human
time scales, it actually precesses over about
26,000 years.
Polaris won’t always be the North
Star.
Positions of equinoxes shift around
orbit; e.g., spring equinox, once in Aries,
is now in Pisces!
Long-Term Changes: Climatic Changes
In about 13,000 years the Earth North Pole will be closer to
the Sun in December. The Earth is at its shortest distance
from the Sun in January. How will this affect our seasons?
Moon phases and eclipses Chapter 2. section 2.3
Motion of the Moon
• The Moon rises in the east and sets in
the west moving across the sky in an
arc
• The Moon moves slowly eastward
against the stars (half a degree per
hour)
• The Moon returns to the same position
among the stars every 27.3 days (its
orbital period or sidereal period)
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Why do we see phases of the Moon?
• Lunar phases are a
consequence of the
Moon’s 27.3-day
orbit around Earth.
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Differences in angular diameter of the moon when it is at
apogee (farthest from Earth) and perigee (closest from Earth )
This is caused by the elliptical orbit of the moon.
Why do we see phases?
• The Moon emits no light of its own shines by reflecting light
from the Sun
• The half of the Moon facing the Sun is always lit
• We see a combination of lit and dark areas
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Phases of the Moon • Half of Moon is illuminated
by Sun and half is dark.
• We see a changing
combination of the bright and
dark faces as the Moon orbits
the Earth
• Depending on the angle
between the Moon and the
Sun as seen from Earth, is the
combination of bright and
dark areas that we see.
• Examples: At new moon, the
moon rises at sunrise and sets
at sunset
At full moon, the moon rises
at sunset and set at sunrise
Phases of the Moon • Phases change in a regular sequence over a 29.5 day period (synodic
period). It is the time required for a complete cycle of lunar phases
Question
• If the Sun sets at 6pm,
when does a full Moon
rise?
The time at which the moon rises depends on its phase (phase of the moon depends on the relative positions of the Sun, Moon & Earth)
• At 6 pm. The side of the Moon we see is facing the Sun, so when the Sun is setting, the Moon is rising.
Another way of looking at it:
• The Sun and the Moon are ~ 180 degrees apart. The moon and Sun rising times are 12 hrs apart. Sun rose at 6 am Moon at 6pm.
Another question
• If the Sun sets at 6pm,
when does a 1st quarter
Moon rise?
• The Moon and Sun rising times are now 6
hrs apart (~90 degrees).
If the Sun rose at 6 am,
the Moon will rise 6
hours later (noon).
• How about New Moon and 3rd quarter Moon?
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Phases of the Moon: 29.5-day cycle
Waxing • Moon visible in afternoon/evening
• Gets “fuller” and rises later each day
Waning • Moon visible in late night/early morning
• Gets “less full” and sets later each day
© 2010 Pearson Education, Inc.
Question
A. first quarter
B. waxing gibbous
C. third quarter
D. half moon
It’s 9 a.m. You look up in the sky and see a
moon with half its face bright and half dark.
What phase is it?
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A. first quarter
B. waxing gibbous
C. third quarter
D. half moon
It’s 9 a.m. You look up in the sky and see a
moon with half its face bright and half dark.
What phase is it?
Question
• Why do we always see the same face of the moon?
• The Moon and Earth are tidally locked Moon keeps the same
side towards Earth at all times.
A consequence of this is that :
Moon rotation period = Moon orbital period
As a person walks around you, in order for you to always see her face She must be slowly spinning around (“rotating on her axis”)
Phases of the Moon
Lunar and Solar Eclipses
Chapter 2
© 2010 Pearson Education, Inc.
What causes eclipses? • The Earth and the Moon cast shadows.
• When either passes through the other’s shadow, we have an
eclipse.
• Umbra: the dark central region of the shadow
• Penumbra: The lighter, outlying region of the shadow
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Lunar and solar eclipses
• A lunar eclipse occurs when the Earth lies
directly between the Sun and the Moon, so
that the Earth’s shadow falls on the Moon
• A solar eclipse occurs when the Moon lies
directly between the Sun and the Earth so
that the Moon’s shadow falls on Earth
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Lunar and solar eclipses
New Moon, a condition for a
← solar eclipse
Full Moon, a condition for
lunar eclipse →
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When can lunar eclipses occur?
• Lunar eclipses can occur
only at full moon.
• Lunar eclipses can be
Total: The moon passes
through Earth’s umbra
Partial: If the alignment is
not perfect, only part of
the full Moon passes
through the umbra
Penumbral: The Moon
passes through the Earth’s
penumbra
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When can solar eclipses occur?
• Solar eclipses can occur only at new moon.
• Solar eclipses can be partial, total, or annular.
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Types of solar eclipses • Total eclipse: The Moon’s umbra touches a small area of Earth’s
surface, no more than 270 km diameter. Because the Earth and the Moon
are moving, this area drift across the Earth’s surface and may cover a
total of 7,000 km. An observer located inside this strip will see a total
solar eclipse.
• Partial solar eclipse: If the observer is located in the penumbral part of
the shadow, only part of the Sun will be covered and the observer will
see a partial solar eclipse
• Annular solar eclipse: If the Moon is relatively far from Earth in its orbit
(Or the Earth closer to the Sun or a combination of both effects), the
Moon disk will not completely cover the disk of the Sun. It leaves a ring
around the Sun. In that case, the umbra of the Moon’s shadow will not
touch the surface of Earth. The observer will see a bright ring (the Sun)
around the Moon.
• The Earth and the Moon orbits are elliptical. Because of that, the
distances between the two bodies can varies.
• The Sun-Earth distance can change from 147 x10^6 to 152 x 10^6 km
• The Earth-Moon distance can change from 357,000 to 406,000 km
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Types of solar eclipses
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Why don’t we have an eclipse at every new
and full moon? – The Moon’s orbit is tilted 5° to ecliptic plane.
– So we have about two eclipse seasons each year, with a lunar
eclipse at new moon and solar eclipse at full moon.
© 2010 Pearson Education, Inc.
Summary: Two conditions must be met
to have an eclipse:
1. It must be full moon (for a lunar eclipse) or new moon (for a solar eclipse).
AND
2. The Moon must be at or near one of the two points in its orbit where it crosses the ecliptic plane (its nodes).
© 2010 Pearson Education, Inc.
Predicting Eclipses • Eclipses recur with the 18-year, 11 1/3-day saros cycle, but
type (e.g., partial, total) and location may vary.
• When will be the next total solar eclipse seen from the continental US?
• August 21, 2017 (about 4 years and 7 month from now)
© 2010 Pearson Education, Inc.
What have we learned?
• Why do we see phases of the Moon?
– 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?
– Lunar eclipse: Earth’s shadow on the Moon
– Solar eclipse: Moon’s shadow on Earth
– Tilt of Moon’s orbit means eclipses do not occur for
every new or full Moon. They occur during two
periods each year.