Chapter 2: The Sky

Constellations

Sagittarius, the Archer

Scorpius, the Scorpion

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In ancient times, constellations only

referred to the brightest stars that

appeared to form groups, representing mythological figures.

Today, constellations are well-defined regions of the sky, irrespective of the presence or absence of bright stars in those regions.

• The stars of a constellation only appear to be close to one another.

• Usually, this is only a projection effect.

• The stars of a constellation may be located at very different distances from us.

Stars are named by a Greek letter (α, β, γ,) according to their relative brightness within a given constellation followed by the possessive form of the constellation name:

Betelgeuse = α Orionis,

Rigel = β Orionis

Betelgeuse

Rigel

Orion

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This stamp shows the constellation Orion.

Why does this look odd to residents of northern hemisphere?

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The Magnitude Scale

First introduced by Hipparchus

(160 - 127 B.C.):

More quantitatively:• 1st mag. stars appear 100 times brighter than 6th mag. stars

• 1 mag. difference = a factor of 2.512 in apparent brightness

• Brightest stars = 1st magnitude

• Faintest stars (unaided eye) = 6th magnitude

(The greater the magnitude, the fainter the star!)

Example:

Betelgeuse

Rigel

Magnitude = 0.41 mag

Mag. diff. Intensity Ratio

1 2.512

2 2.512 x 2.512= (2.512)2 = 6.31

… …

5 (2.512)5 = 100 (definition)

Magnitude = 0.14 mag

For a magnitude difference of

0.41 – 0.14 = 0.27,

we find an intensity ratio of

(2.512)0.27 = 1.28

Intensity is a precise term for brightness and expresses the amount of light energy received by each square meter every second. (Units: joules/m2/sec)

The magnitude scale system can be extended toward negative numbers (very bright) and positive numbers > 6 (faint objects):

•Sirius (brightest star in the sky): mv = –1.42

•Full moon: mv = –12.5

•Sun: mv = –26.5

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The “Concept Art Portfolio” helps with visual understanding ofimportant concepts

The Celestial Sphere — A model of the sky

• Nadir: Point on the celestial sphere directly underneath (never visible!)

• Zenith: Point on the celestial sphere directly overhead

• Celestial equator: projection of Earth’s equator onto the c.s.

• North celestial pole: projection of Earth’s north pole onto the c.s.

[ More general view of the celestial sphere ]

• The ecliptic is shown crossing the celestial equator at an angle of 23.5°.

• Do not confuse the ecliptic plane with the horizon plane of the previous slide*.

*The ecliptic (the plane of Earth’s orbit) always makes 23.5° with the celestial equator, while the horizon makes an angle that depends on the person’s latitude.

Skip this slide at first reading—Come back during or after Chapter 3

• Celestial equator culminates 90° – ℓ above the horizon.

ℓ

90° - ℓ

• From geographic latitude – ℓ (southern hemisphere), you see the celestial south pole ℓ degrees above the horizon.

• From geographic latitude +ℓ (northern hemisphere), you see the celestial north pole ℓ degrees above the horizon.

The Celestial Sphere — A model of the sky

Example: New York City: ℓ ≈ 40.7°

Horizon

North

north celestial pole

40.7°

South

49.3°

Celestial Equator

The south celestial pole is not visible from the northern hemisphere.

Horizon

Apparent Motion of the Celestial Sphere

Horizon System• The horizon system is a convenient system to use to locate stars and other celestial objects from one’s local vantage point.

•Altitude (“height”) is angular distance from the horizon.

AltitudeHeight

AzimuthDirection

East

Horizon

Star

•Azimuth (“direction”) locates the place on the horizon just below the star.

Terrestrial Coordinate System• The terrestrial coordinate

system is used to locate places on Earth

• Latitude describes distance north or south of the equator

• Longitude describes distance east or west from the zero point. The zero point is located on the equator, directly south of Greenwich, England, along the prime meridian.

Longitude lines Latitude lines

Equatorial System

• The equatorial system uses right ascension (or hour angle) and declination to locate stars on the celestial sphere.

• Right Ascension (RA) = projection of longitude onto the celestial sphere.

• Declination (Dec) = projection of latitude onto the celestial sphere.

Lines ofright ascension

Lines of declination

Precession

Gravity is pulling on a spinning top.→ Wobble around the vertical.

Sun and Moon are pulling on the spinning Earth.

The resulting “wobble” of Earth’s axis of rotation around the vertical w.r.t. the orbital plane takes about 26,000 years and is called

precession.

Bulging Earth

• As a result of precession, the north celestial pole follows a circular pattern on the sky, once every 26,000 years.

• It will be closest to Polaris ~ A.D. 2100.

• ~ 12,000 years from now, it will be close to Vega in the constellation Lyra.

**There is nothing special about Polaris. (neither particularly bright nor nearby, etc.)