The

Memphis Astronomical SocietyPresents

A SHORT COURSEin

ASTRONOMY

CHAPTER 2

THE SKY AND THE EARTH

Dr. William J. BuslerAstrophysical 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.

INTERMISSIONINTERMISSION

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 north-south 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 perpen-

dicular 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 perpen-

dicular 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”.)

Precession of the Equinoxes

Ecliptic

Present (Polaris) Celestial Equator (V.E. in Pisces)

Thuban Equator (V.E. in Aries)

Vega Equator (V.E. in Capri-cornus)

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”.

T H E E N DT H E E N D