A User’s Guide to the Sky

Stars are named by a Greek letter (…) according to their relative brightness within a given constellation plus the

possessive form of the name of the constellation:

Betelgeuse = Orionis,

Rigel = Orionis

Betelgeuse

Rigel

Constellations

What is the Zodiac?

The Celestial Sphere• Zenith = point on

the celestial sphere directly overhead

• Nadir = point on the c. s. directly underneath (not visible!)

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

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

The Celestial Sphere

On the sky, we measure distances between objects as angles:The full circle has 360o (degrees),1o has 60’ (arc minutes),1’ has 60” (arc seconds).

Degrees & Arcseconds

There are 360° in a full circle.

Arcminutes: 1° = 60’Arcseconds: 1’ = 60”

Extended fist = 10°

Ɵ

Ɵ = 31 arcminutes

Brainstorm!1) How many arcseconds?

a. 1° b. 1/2° c. 2° d. 2’

2) Through how many degrees does the Earth rotate in 1 hour?

The Celestial Sphere (II)• From geographic

latitude l (northern hemisphere), you see the celestial north pole ldegrees above the horizon;

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

• The celestial equator culminates 90o – l above the horizon.

l

90o - l

Example:New York City: l ≈ 40.70

HorizonNorth

Celestial North Pole

40.7°

South

49.3°

Celestial Equator

The Celestial South Pole is not visible from the northern hemisphere.

Horizon

Apparent Motion of the Celestial Sphere

Looking north, you see stars circling counterclockwise around the celestial north pole.

Precession (I)

• Gravity is pulling on a slanted top => wobbling around the vertical.

• The Sun’s gravity is doing the same to the Earth.

• The resulting “wobbling” of the Earth’s axis of rotation around the vertical with respect to the Ecliptic takes about 26,000 years and is called precession.

Precession (II)

• As a result of precession, the celestial north 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 peculiar about Polaris at all (it is neither particularly bright nor nearby, etc.).

Brainstorm!1)Why do stars appear

to move east-west?

2)Does precession have any effect on the celestial poles or celestial equator?

3) How many rotations does Earth complete in 1 revolution?

4) What are the Sun’s motions?

The Magnitude ScaleFirst introduced by Hipparchus

(160–127 B.C.):

• Brightest stars: ~1st magnitude• Faintest stars (unaided eye): 6th magnitude

More quantitative:

• 1st magnitude stars appear 100 times brighter than 6th magnitude stars

• 1 magnitude difference gives a factor of2.512 in apparent brightness (larger magnitude => fainter object!)

Example:

Betelgeuse

Rigel

Magnitude = 0.41 magMagnitude Difference

Flux Ratio

1 2.5122 2.512 × 2.512 =

(2.512)2 = 6.31… …5 (2.512)5 = 100

Magnitude = 0.14 mag

For a magnitude differenceof 0.41 – 0.14 = 0.27, we

find an flux ratio of(2.512)0.27 = 1.28

The magnitude scale system can be extended towards negative numbers (very bright) and numbers > 6 (faint

objects):

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

Full Moon: mv = –12.5

Sun: mv = –26.5

The Magnitude Scale

Brainstorm!1) Which would appear

fainter to us when viewed from Earth with our eyes?

a. −4 magnitude starb. +4 magnitude starc. 0 magnitude star

2) If two stars have the same energy output, what would make one star appear fainter than the other, when viewed from Earth?

Cycles of the Sun and Moon

The Annual Motion of the Sun

• Due to Earth’s revolution around the Sun, the Sun appears to move through the zodiacal constellations.

• The Sun’s apparent path on the sky is called the ecliptic.

• Equivalent: The ecliptic is the projection of Earth’s orbit onto the celestial sphere.

The Seasons (I)

The Seasons (I)

• The Earth’s equator is inclined against the ecliptic by 23.5°.

• The different incidence angle of the Sun’s rays causes the seasons on Earth.

The Seasons (II)

The Seasons (III)

Northern summer = Southern winter

Northern winter = Southern summer

The Seasons (IV)

SunEarth in July

Earth in January

The Earth’s distance from the Sun has only a very minor influence on seasonal temperature variations.

Earth’s orbit (eccentricity greatly exaggerated)

Astronomical Influences on Earth’s Climate (I)

Factors affecting Earth’s climate:

• Eccentricity of Earth’s orbit around the Sun (varies over period of ~100,000 years)

• Precession (period of ~26,000 years)

• Inclination of Earth’s axis versus orbital plane

Milankovitch Hypothesis: Changes in all three of these aspects are responsible for long-term global climate changes (ice ages).

Astronomical Influences on Earth’s Climate (II)

Last glaciation

End of last

glaciation

Polar regions receiving less than average energy

from the Sun

Polar regions receiving more than average energy from

the Sun

Brainstorm!1) Refer to your

celestial sphere map. Locate the position of the Sun for each season.

2) Will the seasons on Earth ever change? Explain.

3) At what latitude is the Sun directly overhead, at noon, on the first day of our “summer”? What is this latitude called?

4) At what latitude is the Sun directly overhead, at noon, on the first day of our “winter”? What is this latitude called?

Motions of the Planets

Earth

VenusMercury

All planets in almost circular (elliptical) orbits around the Sun, in approx. the same plane

(ecliptic)

Sense of revolution:

counter-clockwise

(distances and times reproduced to scale)

The Moon is orbiting Earth in almost the same plane (ecliptic)

Mercury appears, at most, ~28° from the Sun.

•It can occasionally be seen shortly after sunset in the west or before sunrise in the east.

Venus appears, at most, ~46° from the Sun.

•It can occasionally be seen for a few hours (at most) after sunset in the west or before sunrise in the east.

Apparent Motion of the Inner Planets

The Phases of the Moon (I)

As the Moon orbits around Earth, we see different portions of the Moon’s surface lit by the Sun, causing the phases of the Moon.

The Tidally-Locked Orbit of the Moon

The Moon is rotating with the same period around its axis as it is orbiting Earth (tidally locked).

We always see the same side of the Moon facing Earth.

The Phases of the Moon (II)

New Moon → First Quarter → Full Moon

Evening Sky

The Phases of the Moon (III)

Full Moon → Third Quarter → New Moon

Morning Sky

Synodic vs SiderealSynodic motion

relates to an Earth rotation/revolution which results in the same view of the Sun or Moon

Sidereal motion is the process of returning to the same position with respect to the background stars

http://www.skywise711.com/Skeptic/Sidereal/sidereal.html

The Month is based on the motion of the Moon.

One synodic month = 29.53 days (complete cycle moon phases)

One sidereal month = 27.3 days (one moon orbit)

A DayThe day is based on the rotation of Earth.

A sidereal day = 23 h, 56m, 4.09 s A solar day = 24 hours

1 → 2Earth Observer re-

points to distant star (sidereal)

Earth rotates 360°

1 → 3Earth Observer re-

points to sun (synodic)

Brainstorm!

1) In general, what does sidereal time measure?

2) Why do we have leap year?

3) What is the change in position of the moon in the sky, in 24 hours? (Number of degrees)

Lunar Eclipses• Earth’s shadow

consists of a zone of full shadow, the

umbra, and a zone of partial shadow, the

penumbra.

• If the Moon passes through Earth’s full

shadow (umbra), we see a lunar eclipse.

• If the entire surface of the Moon enters

the umbra, the lunar eclipse is total.

A Total Lunar Eclipse (I)

A Total Lunar Eclipse (II)

• A total lunar eclipse can last up to 1 hour and 40 minutes.

• During a total eclipse, the Moon has a faint, red glow, reflecting sunlight scattered in the Earth’s atmosphere.

Typically,

there are

1 or 2

lunar

eclipses

per year.

Brainstorm!1) What is the phase of the Moon during a total

lunar eclipse?

2) Why is the shadow dark and then red, during a total lunar eclipse?

3) How often can an eclipse occur?

4) Which are more commonly seen, solar or lunar eclipses? Why?

Solar Eclipses (I)

The angular diameter of the Moon (~0.5o) is almost exactly the same as that of the Sun.This is a pure coincidence. The Moon’s linear diameter is much smaller than that of the Sun.

Solar Eclipses (II)

Due to the equal angular diameters, the Moon can cover the Sun completely when it passes in front of

the Sun, causing a total solar eclipse.

Total Solar Eclipse

The Moon’s shadow sweeps across the Earth, over points

from where we can see a solar eclipse.

Total Solar Eclipse

During a total solar eclipse, the solar chromosphere, corona, and prominences can be seen.

The Diamond Ring Effect

Earth’s and Moon’s orbits are slightly elliptical:

Sun

Earth

Moon

(Eccentricities greatly exaggerated!)

Perihelion = position closest to the sun

Aphelion = position

furthest away from

the Sun

Perigee = position closest to Earth

Apogee = position furthest away from

Earth

Annular Solar EclipsesThe angular sizes of the Moon and the Sun vary, depending on their distance from Earth.

When the Earth is near perihelion, and the Moon isnear apogee, we see anannular solar eclipse.

Perigee Apogee Perihelion Aphelion

An almost total, annular eclipse of May 30, 1984.

Approximately 1 total solar eclipse per year

Very Important Warning:Never observe the Sun directly with your bare eyes, not even during a partial solar eclipse!

Use specially designed solar

viewing shades, solar filters, or a

projection technique.

Brainstorm!1) What is the phase of the Moon during a

total solar eclipse?

2) The Moon is much smaller than the Sun. Why then is it possible for a solar eclipse to occur?