Download Celestial Equator

The
Memphis Astronomical Society
Presents
A SHORT COURSE
in
ASTRONOMY
CHAPTER 2
THE SKY AND THE EARTH
Dr. William J. Busler
Astrophysical Chemistry 439
SKY MAPS
• First, select the proper set of sky maps for your
latitude.
• Then, using the date/time guide which should have
come with your sky maps, select the proper monthly
sky map for the current date and time.
SKY MAPS
• Hold the map so that the direction you are facing
corresponds to the edge (horizon) of the map which
is down.
• What you see on that portion of the map should
correspond to what is visible in that area of the sky.
CONSTELLATIONS
• Scientifically meaningless.
• Mythologically interesting.
• Patterns are made up of relatively nearby stars
in our Galaxy (less than 1000 light-years
away).
• 88 constellations altogether.
• Learn the major constellations for each season
first; use them to find the others.
• Learn the names of all the first-magnitude
stars, then other important stars.
The ROTATION of the EARTH
• The Earth rotates eastward on its axis, making
one rotation per day.
• This diurnal (daily) motion is what causes the
Sun to appear to rise and set each day.
• Diurnal motion also causes the stars to exhibit
the same motion during the night.
CIRCUMPOLARITY
• The Earth’s axis of rotation points toward
Polaris, the North Star; as a result, Polaris
remains stationary, while all the other stars
wheel around the North Star during the night.
• Stars close to Polaris never set -- they are
circumpolar.
• Those farther away from Polaris go below the
horizon.
• The farther a star is from Polaris, the more
time it spends below the horizon.
Circumpolar Star Trails over Kitt Peak
The ROTATION of the EARTH
• A star located on the celestial equator is up for
12 hours and down for 12 hours.
• (The celestial equator divides the heavens into
northern and southern hemispheres.)
• Stars north of the celestial equator are above
the horizon more than they are below it.
• Stars south of the celestial equator are below
the horizon more than they are above it.
Equatorial Star Trails
The Effect of LATITUDE
• The observer’s latitude affects the altitude of
Polaris, i.e., its angular distance above the
horizon.
• At the north pole, the observer’s latitude = 90;
the altitude of Polaris = 90 (i.e., directly
overhead).
• At the equator, the observer’s latitude = 0; the
altitude of Polaris = 0 (i.e., on the northern
horizon).
• At Memphis, the observer’s latitude = 35; the
altitude of Polaris is 35.
The Effect of LATITUDE
• At Memphis, the circumpolar constellations are
those within 35 of Polaris.
• These include Ursa Minor, Ursa Major (“Big
Dipper” portion), Cassiopeia, Cepheus, and
Draco.
• At the north pole, the circumpolar constellations
include all those within 90° of Polaris, i.e., the
entire northern celestial hemisphere.
• At the north pole, Polaris is stationary overhead;
all the other stars move along parallel to the
horizon as the Earth rotates.
The Effect of LATITUDE
• At the equator, the circumpolar constellations
would include all those within 0° of Polaris,
i.e., none.
• At the equator, Polaris is stationary on the
northern horizon; all the other stars rise
vertically in the east, move across the sky for
12 hours, and set in the west, remaining below
the horizon for 12 hours.
• At the equator, all stars are eventually visible.
• At Memphis, all stars within 35° of the south
celestial pole are never seen.
The REVOLUTION of the EARTH
• The Earth revolves around the Sun once each
year, moving in an eastwardly direction.
• This annual (yearly) motion causes the
constellations seen at a given time each night
to advance with the seasons.
• In other words, the diurnal and annual motions
of the Earth have the same effect on what is
seen in the sky.
• As a result, the constellations of the opposite
season are seen just before sunrise.
The REVOLUTION of the EARTH
• The annual and diurnal motions of the Earth
have the same effect on what is seen in the sky.
•
•
•
•
12 months of revolution = 24 hours of rotation.
1 month of revolution = 2 hours of rotation.
2 weeks of revolution  1 hour of rotation.
1 day of revolution = 4 minutes of rotation.
• In other words, the same stars rise 4 minutes
earlier each night. (More later!)
CELESTIAL COORDINATES
• Zenith: The overhead point as seen from the
observer’s position.
• Meridian: The north-south line passing
through the zenith.
• Celestial Equator: An imaginary line around
the sky directly above the Earth’s equator.
• The celestial equator is the projection of the
plane of the Earth’s equator onto the celestial
sphere, 90° from the celestial poles.
• The celestial equator divides the northern and
southern celestial hemispheres.
CELESTIAL COORDINATES
• The celestial equator appears to run from the
eastern horizon to the western horizon.
• At the Earth’s equator, the celestial equator
passes through the zenith.
• In the northern (terrestrial) hemisphere, the
celestial equator does not pass overhead, but
instead passes south of the zenith by an angular
distance equal to the observer’s latitude.
• At Memphis, the celestial equator passes 35°
south of the zenith.
• At the north pole, the celestial equator runs
around the horizon.
INTERMISSION
CELESTIAL COORDINATES
• The ecliptic is the plane of the Earth’s orbit
projected onto the celestial sphere.
• The 12 constellations along the ecliptic are
known as the constellations of the zodiac.
• As the Earth orbits the Sun, the Sun appears to
move eastward along the ecliptic at the rate of
about 1° per day, or one “sign” per month.
• The Moon and nearly all the other planets orbit
in essentially the same plane as does the Earth.
• Therefore, the Moon and planets will also be
found close to the ecliptic, against the
background of the constellations of the zodiac.
CELESTIAL COORDINATES
• The Earth’s axis is tilted 23.5° from the vertical
(with respect to the plane of its orbit).
• As a result, the celestial equator is inclined to the
ecliptic by 23.5°.
• Therefore, the ecliptic and equator intersect at
two points (the equinoxes), and are separated by
a maximum of 23.5° at two points (the solstices).
• The vernal equinox is the intersection point at
which the Sun (on the ecliptic) crosses the
celestial equator going north. This event marks
the beginning of spring.
• The vernal equinox is located in Pisces.
CELESTIAL COORDINATES
• The autumnal equinox is the intersection point
at which the Sun (on the ecliptic) crosses the
celestial equator going south. This event
marks the beginning of autumn.
• The autumnal equinox is in Virgo.
• When the Sun is at an equinox, i.e., on the
celestial equator, it behaves like any other star
on the celestial equator: it is up for 12 hours
and down for 12 hours. In other words, days
and nights are 12 hours each all over the world
at the time of the equinoxes.
• (The term “equinox” means “equal night”.)
CELESTIAL COORDINATES
• The solstices mark the two points where the
ecliptic is at its maximum distance (23.5°) from
the celestial equator.
• When the Sun is near the solstices, its northsouth position (declination) remains nearly
constant for several days before it heads back
toward the celestial equator.
• Hence the word solstice, which means “the Sun
standing still”.
CELESTIAL COORDINATES
• The summer solstice is in Gemini, near Castor’s
foot.
• When the Sun is at the summer solstice, 23.5°
north of the celestial equator, it is up much
longer than it is down (i.e., days are longer than
nights by the maximum amount).
• When the Sun reaches the summer solstice, this
“longest day” marks the beginning of summer.
CELESTIAL COORDINATES
• The winter solstice is in Sagittarius.
• When the Sun is at the winter solstice, 23.5°
south of the celestial equator, it is down much
longer than it is up (i.e., nights are longer than
days by the maximum amount).
• When the Sun reaches the winter solstice, this
“shortest day” marks the beginning of winter.
CELESTIAL COORDINATES
• Declination: On the celestial sphere, lines of
declination are parallels to the celestial equator,
analogous to lines of latitude on Earth.
• Declination (Dec or ) is measured from the
celestial equator (0°) to the north celestial pole
(+90°), or to the south celestial pole (-90°).
• Degrees of declination are subdivided into
minutes and seconds:
• 60' (minutes) = 1°.
• 60" (seconds) = 1'.
CELESTIAL COORDINATES
• Right Ascension: Analogous to lines of longitude
on Earth.
• Lines of right ascension (RA or ) run from pole
to pole, perpendicular to the celestial equator.
• The zero-hour (0h) line intersects the equator (and
the ecliptic!) at the vernal equinox in Pisces.
• The 6h line passes through the summer solstice in
Gemini.
• The 12h line passes through the autumnal equinox
in Virgo.
• The 18h line passes through the winter solstice in
Sagittarius.
CELESTIAL COORDINATES
• Note that right ascension is measured eastwardly
along the equator, starting at the vernal equinox.
• Note that 24h is the same as 0h.
• Hours of right ascension are subdivided into
minutes and seconds. However, these are not
equivalent to the minute and second subdivisions
of degrees of declination! (Note that their
symbols are different as well!)
• 360° of declination = circle = 24h right ascension.
• 15° of declination = 1h of right ascension.
• 15' of declination = 1m of right ascension.
• 15" of declination = 1s of right ascension.
The Celestial Coordinate System
SIDEREAL TIME
• The Earth rotates on its axis every 23h56m with
respect to the stars; this is called the sidereal day.
• Meanwhile, the Earth’s revolution carries it a
little farther around its orbit.
• Consequently, the Earth must rotate a little longer
(4 min) to bring the same point on the Earth into
alignment with the Sun as on the previous day.
• I.e., the solar day is exactly 24h long, while the
sidereal day is 23h56m long.
• This 4-minute difference causes each star to rise 4
minutes earlier each night.
In A, the spot on the Earth with
the arrow is facing the Sun -- it
is noon there.
The next day, 23h56m later, the
Earth has made one complete
rotation (to B) with respect to
the stars.
However, the Earth must still
rotate another 4 minutes (to C)
in order to face the Sun (noon)
again.
SIDEREAL TIME
• Our clocks run on solar time, because it is
convenient to have the Sun in approximately the
same place in the sky at the same clock time each
day throughout the year.
• Meanwhile, the stars keep sidereal time. Sidereal
time is defined as the hour of RA on the meridian.
• Over the course of a year, this 4-minute daily
interval adds up to another whole day.
• Thus, there are 366.25 sidereal days per year.
• A mechanical clock (or a telescope clock drive)
can be made to keep sidereal time by setting it to
run faster than normal by 4 minutes per day.
THE SEASONS
• The Earth’s axis is tilted 23.5° from the perpendicular to the plane of its orbit around the Sun.
• The northern hemisphere of the Earth tilts toward
the Sun in summer and away from it in winter.
• At the equinoxes, the Sun is up 12 hours and
down 12 hours.
• In summer, the Sun is north of the celestial
equator, and is therefore up more than down.
• In winter, the Sun is south of the celestial
equator, and is therefore down more than up.
• Besides the length of daylight, the angle of
insolation leads to seasonal temperature changes.
The Seasons
THE SEASONS
• The arctic circle is the parallel of latitude located
23.5° from the north pole; i.e., 90° - 23.5° = 66.5°.
• Within (north of) the arctic circle, the Sun
becomes circumpolar around the time of the
summer solstice. (“Land of the Midnight Sun”.)
• Conversely, near the winter solstice, the Sun
remains below the horizon, “day” and night.
• At the north pole, the Sun is constantly up from
the first day of spring until the first day of autumn,
then down again until the next spring.
• The Sun rises only because of its motion along the
ecliptic, not the Earth’s rotation.
PRECESSION
• The Earth’s axis is tilted 23.5° from the perpendicular to the plane of its orbit around the Sun.
• Due to the gravitational pull of the Moon on the
Earth’s equatorial bulge, the Earth’s axis slowly
wobbles.
• This causes the north celestial pole to trace out a
circle in the sky 23.5° in radius, centered on the
north ecliptic pole in Draco, every 26,000 years.
• The north ecliptic pole is perpendicular to the
plane of the ecliptic -- the “axis” of the Solar
System.
PRECESSION
• As a result of precession, therefore, there is a
succession of “North Stars”.
• At the time of the construction of the pyramids,
Thuban ( Draconis) was the pole star.
• After Polaris, the stars along the eastern edge of
Cepheus will serve as pole stars.
• In 12,000 AD, Vega will be the north star.
The Precession Circle
PRECESSION
• The equinoxes also precess westward; the ecliptic
remains fixed but the Earth’s “wobble” moves the
equator westward.
• The vernal equinox spends about 2,200 years in
each constellation of the zodiac before moving into
the next one toward the west.
• 2000 years ago, the vernal equinox was in Aries.
(It is sometimes still called the “first point of
Aries”.)
Ecliptic
Present
(Polaris)
Celestial
Equator
(V.E. in
Pisces)
Thuban
Equator
(V.E. in
Aries)
Precession of the Equinoxes
Vega
Equator
(V.E. in
Capricornus)
PRECESSION
• The vernal equinox is now in Pisces, the next
constellation toward the west -- we are in the
“Christian era”.
• Eventually, the vernal equinox will move farther
westward into Aquarius -- the “dawning of the
Age of Aquarius”.
• Precession slowly changes the right ascension and
declination of every star; consequently, star atlases
must be drawn for a particular “epoch”.
THE END