II. What We See in the Sky

1. Celestial Sphere with "fixed" stars

• The stars don't change their position w.r.t. each other.

A) Orientation on Earth and sky

• Determine position on celestial sphere like on the globe (sphere of the Earth)

We use the same lines on Earth and projected onto the sky

B) Coordinates in the sky:

a)

North Celestial Pole (NCP)	(always above horizon in Durham).
South Celestial Pole	(always below horizon in Durham).
Celestial Equator	(only 1 half above the horizon)

b) Declination: degrees N or S of celestial equator (like being on a certain Parallel)

c) NCP at 90^o N of equator

• height of NCP above horizon = latitude of observer.

2. Apparent rotation of the sky from East to West

(Earth turns W to E = counterclockwise, when we look down onto Northern Hemisphere)

A) How do stars on certain positions move over the sky?

1. On celestial equator:
   • Passes through horizon due E, due W.
   • Is up 1/2 day; and down 1/2 day.
2. On N declination:
   • is up more than 1/2 day,
   • Star is high in sky when on meridian
   • Star rises, sets: NE, NW on far North declination: stars never set (examples: Big and Little Dipper)
3. On S declination:
   • up less than 1/2 day
   • star is low in sky when on meridian star rises
   • sets: SE, SW on far South declination: stars never rise
4. Daily motion: object is always highest in sky when on meridian.

B) Sidereal day

• refers to motion of stars: sidereal day = 23h 56m 4s
• shorter than solar day
• Sun is not fixed in the sky w.r.t. the stars

3. Sun.

A) Apparent annual eastward motion with respect to the stars.

Observed by:

a) Solar day (noon to noon) is longer than sidereal day.

Eastward motion of sun is due to:

• Earth orbits sun in one year, counterclockwise looking down onto northern hemisphere.  

b) Westward progression of constellations in the sky during year:

• constellations set and rise earlier every day

After some time a constellation which is east of the previous one is seen at the same position in the sky, when observing at the same time of the night.

 Sun's motion across the sky completed after 1 year

• definition of one Year

B) Change in declination during year:

Observed by:Change of

1. Rising and setting points on horizon (more N in summer than winter)
2. Length of daylight.
3. Height of sun at noon.

These values are different for different latitudes on Earth!

4. Declination of sun on the celestial sphere

C) Ecliptic: apparent annual path of sun with respect to the stars.

The ecliptic:

• runs through the constellations of the Zodiac
• is a Great Circle on celestial sphere
• has an Inclination of 23 1/2 degrees w.r.t. celestial equator

Due to:

• Earth's orbit planar and sun in the plane --> Great Circle.
• Earth's axis tilted Þ Inclination.

(does not prove the earth goes around the sun)

Leads to Seasons:

• Height of sun in sky at noon --> more direct sunlight in summer etc.
• Length of daylight varies

Leads to Climates:

• Arctic, Antarctic (sun up in summer, down in winter)
• N, S temperate (regions with significant change of height of the sun)
• Tropics (sun always high)

D) Sun clock is not exact over the year (called Analemma)

Solar day not exactly 24^h (varies over the year) but annual average very close to 24h

This is due to:

• Ecliptic is at oblique angle to equator
• Earth's orbital speed changes
• Earth - Sun distance changes over the year

4. Moon

A) Apparent motion of the Moon

a) Eastward with respect to sun and stars

Due to:

• Moon orbits counterclockwise when looking down onto Northern Hemisphere.
• Moon's orbital period shorter than Earth's

b) Phases: Sunlit side 'points' toward sun.

Crescent moon close to sun:

• sets soon after sunset (waxing crescent)
• or rises shortly before sunrise (waning)

Full moon opposite to sun:

• rises at sunset; sets at sunrise  

Boundary between light and dark on the moon is an arc

• Early proof that moon is spherical

Half moon at right angle to the sun in the sky

• Early deduction that Sun is very far away & very large.

Earthshine observed on new moon and crescent

• Sunlight reflecting off Earth onto moon (daVinci ca. 1500)  

c) Synodic month (refers to phases)

• Longer than sidereal month (Moon in same position w.r.t. the stars)

Synodic month originally used as definition of Month

From month to month each phase (e.g. full) of the moon progresses eastward through the stars.

B) Moon's orbit

1. Great circle (almost) close to ecliptic

• Full moon opposite sun:
• high in sky in winter
• and low in sky in summer.

Moon's orbit inclined 5 degrees to ecliptic

Due to:

• Moon's orbit and Earth in one plane --> Great Circle.
• Moon's orbital plane inclined to earth's orbital plane Þ Inclination.

b) Nodes progress westward

Due to:

• Sun's gravitational pull on Moon.
• Full cycle = 18.6 years (affects when eclipses occur).

C) Eclipses

Reason:

• Shadow play (Sun, moon, Earth exactly aligned!)
• Solar eclipsesduring new moon.
• Lunar eclipsesduring full moon.

But not every new or full moon, only when new or full moon near ecliptic (i.e. node).

Eclipse seasons:

• Line of nodes must be toward sun.
• About 6 months apart (less than 6 months)

a) Lunar Eclipses:

Types:

• Partial (Earth's shadow line seen on moon)
• Total (No direct sunlight on moon)

But: moon not completely dark during total eclipse

• some sunlight reaches the moon through the Earth's atmosphere

Uses of lunar eclipses:

• Early proof that Earth is spherical (curved shape of shadow line)
• First measurement of moon's size and distance (size of Earth's shadow)

b) Solar Eclipses:

Types:

• Total: (sun fully covered by moon)
• Annular: (ring of sunlight, varying with distance of the moon)
• Partial: (Sun and moon not exactly aligned)

Uses of full eclipses:

Study solar atmosphere

in Chapter VIII

• much fainter light of the upper layers of the atmosphere becomes visible

We see: sunlight scattered by electrons & dust

- General Relativityin Chapter X

(Bending of starlight by gravitational forces)

5. Calendar

Based on:

A)Sun	day	(one circle over the sky)
	year	(journey along the ecliptic) = 365.24 days
B)Moon	month	(m6; one full cycle of lunar phases)
	sidereal month m6; 28 days	Synodic month m6; 29.5 days

All "wandering" objects in the sky (as known in ancient times)

• Week=7 days; 1/4 of a month

Symbolic association with days

Sunday	Sun
Monday	Moon
Tuesday	Mars (Mardi in French)
Wednesday	Mercury (Mercredi in French)
Thursday	Jupiter(= Thor in Germanic heaven)
Friday	Venus(= Freya " )
Saturday	Saturn

6. Planets

Apparent motion of the planets with respect to the sun and stars.

• Always close to ecliptic (In the southern half of the sky over Durham)

A) Appear to move through the stars on nearly great circles close to the ecliptic

Due to:

• The sun is in the center of the orbital plane of the planets.
• Planet orbits are inclined to Earth's orbit, but not by much.

Mercury, Venus always	appear close to sun	(inferior planets)
Mars, Jupiter, Saturn can	appear far from sun	(superior planets)

B) Mercury, Venus

We can see them either right before sunrise or right after sunset:  

We define:

1. Superior Conjunction with Sun = invisible
2. Maximum Eastern Elongation = "evening star"
3. Inferior Conjunction with Sun = invisible
4. Maximum Western Elongation ="morning star"
5. Superior Conjunction with Sun =invisible

Best time to see Mercury: At maximum Elongation, in particular: in Spring after sunset or in Fall before sunrise

• Synodic period: (e.g. from one inferior conjunction to next inferior conjunction) as seen from Earth with respect to the sun
• Sidereal period (orbit around sun with respect to stars; the planet's 'year') as seen from the sun with respect to the stars
• Synodic longer than sidereal because earth moves too (everything counterclockwise).
• Apparent motion in the sky mostly eastward (along with sun) with respect to stars.

C) Mars, Jupiter, Saturn.

• Apparent motion always westward with respect to sun, but:
• mainly eastward with respect to the stars. (like sun).

We define:

1. Superior Conjunction with Sun
2. Emerges as morning star
3. Western quadrature on meridian @ sunrise
4. Opposition - opposite sun; rises at sunset, on meridian at midnight

Best time to observe:

• closest to Earth
• brightest

Winter opposition best:

• high in sky (like full moon)

(The constellations of the Zodiac are high in the sky on winter nights and low in the sky on summer nights.)

5. Eastern quadrature- on meridian @ sunset
6. Approaches sun as evening star
7. Superior Conjunction

Apparent motion of Mars, Jupiter, and Saturn, is eastward with respect to stars except near opposition

--- The motion at opposition is called "Retrograde":

Apparent westward motion with respect to stars as Earth speeds by the planet

(Planets draw loops in the sky with respect to the stars)

After one Earth year the planet appears further east with respect to the stars:

Due to:

• All planets orbit the sun counterclockwise when looking down onto Northern Hemisphere.