Test 1

• Test covers Chapters 1-3• Part 1: Short questions and problems• Part 2: bonus problems, extra points• Show your work everywhere• Don’t forget to prepare formula sheet• Bring your calculator• Textbook and lecture notes are not

allowed

How to prepare:

• Read chapters and lecture notes

• Pay extra attention to chapter summary

• Answer review questions

• Solve homework problems

Remember and check UNITS Remember and check UNITS for all terms in the formulas!!!for all terms in the formulas!!!

Indicate units on your formula sheet

Express all terms in correct units before plugging in the formula

Check your answer for right unit

Chapter 1

• Scale of different objects: planets, sun, orbits of planets, interstellar distances, Milky Way galaxy, distances between galaxies, Universe

• No need to memorize exact numbers, but try to remember the order of magnitude!

• It will help you to check whether your answers make sense

107 mplanets

109 mSun andstars

1017 m~ 3 pcdistancebetweenstars

1021 m~ 10 kpcgalaxy

1011 m~ 1 AUSolar System

1025 m~ 500 MpcLargeststructure

1026 m~ GpcHubbleradius

Distance scale

1022 m~ 1 MpcDistancebetweengalaxies

New units of distance

1 AU = 1.5x1011 m (orbits of planets)

1 light-year (ly) ~ 1016 m ~ 105 AU (interstellar distances)

1 ly = c1 year (the distance the light travels in 1 year)

Velocity of light in vacuum: c = 3 108 m/s

1 parsec (pc) 3.26 ly = 3 1016 m

Kpc, Mpc, Gpc

Chapter 2,3

Relationship between magnitudes and intensities

Define the magnitude scale so that two stars that differ by 5 magnitudes have an intensity ratio of 100.

100;5 B

AAB I

Imm

512.2100;1 5 B

AAB I

Imm

AB mm

B

A

I

I )512.2(

)(5

2100)( 5

ABABB

A mmLogmmI

ILog

B

AAB I

ILogmm 5.2)(

90o-L

Apparent motion of the sun, moon, stars, and planets

Drawn for northern latitudes, these are the paths the sun takes across the sky on the equinoxes and solstices. Can you see that the summer path is longer (and therefore that the summer sun stays in the sky longer)?

90o-L

Seasons - summary1. Seasons are NOT caused by varying distances from the Earth to the Sun

2. The primary cause of seasons is the 23.5 degree tilt of the Earth's rotation axis with respect to the plane of the ecliptic.

Note: the Earth is actually closest to the Sun in January 4!

The Seasons in the Northern Hemisphere

Perihelion: 147.09 × 106 km; Aphelion: 152.10 × 106 km

Thus, we experience Summer in the Northern Hemisphere when the Earth is on that part of its orbit where the N. Hemisphere is oriented more toward the Sun and therefore:

1. the Sun rises higher in the sky and is above the horizon longer, 2. The rays of the Sun strike the ground more directly.

Likewise, in the N. Hemisphere Winter the hemisphere is oriented away from the Sun, the Sun only rises low in the sky, is above the horizon for a shorter period, and the rays of the Sun strike the ground more obliquely.

Ice Ages - cause

• Atmospheric composition, especially greenhouse gases and dust;

• Changes in the Earth’s orbit and inclination;• The motion of tectonic plates resulting in

changes in the landmass distribution;• Variations in the solar output;• The impact of large meteorites;• Eruptions of supervolcanoes

Cycles of glaciation - cause

• Theory: cyclic climate changes due to variations in the Earth’s orbital parameters– Precession (26,000 yr cycle)– Eccentricity (varies from 0.00 to

0.06 with 100,000 and 400,000 yr cycles)

– Axis tilt (varies from 24.5o to 22.1o with 41,000 yr cycle

Milutin Milankovitch 1920

• Varies from 0.00 to 0.06 (currently 0.017)• Periodicity 100,000 and 400,000 yr• Eccentricity cycle modulates the amplitude of the precession cycle

26,000 yr cycle

An effect called precession causes the Sun's vernal equinox point to slowly shift westward over time, so a star's RA and dec will slowly change by about 1.4 degrees every century (a fact ignored by astrologers), or about 1 minute increase in a star's RA every twenty years. This is caused by the gravitational pulls of the Sun and Moon on the Earth's equatorial bulge (from the Earth's rapid rotation) in an effort to reduce the tilt of the Earth's axis with respect to the ecliptic and the plane of the Moon's orbit around the Earth (that is itself slightly tipped with respect to the ecliptic).

Very good agreement in general, but some findings are still contradictory

The response of the climate system to external variations is highly nonlinear: small external variations can trigger large changes in climate. Example: ice-albedo positive feedback loop.

Milankovitch theory:

The Phases of the MoonFrom Earth, we see different portions of the Moon’s surface lit by the sun, causing the phases of the Moon.

Lunar Phases

The Phases of the Moon (2)• The Moon orbits Earth in a sidereal period of 27.32 days.

27.32 days

EarthMoon

Fixed direction in space

The Phases of the Moon (2)

• The Moon’s synodic period (to reach the same position relative to the sun) is 29.53 days (~ 1 month).

Fixed direction in space

Earth

Moon

Earth orbits around Sun => Direction toward Sun

changes!

29.53 days

Synodic period defines the cycle of lunar phases

Integrate over the mass distributionIn the Earth’s body

Tides

Spring and Neap TidesThe Sun is also producing tidal effects, about half as strong as the Moon.

• Near Full and New Moon, those two effects add up to cause spring tides.

• Near first and third quarter, the two effects work at a right angle, causing neap tides.

Spring tides

Neap tides

Effects of tides

• Slow down the rotation of earth

• Seabed slips under the water bulges • Friction slows down the rotation• The day was 18 hours long 900 million yr ago

The Tidally-Locked Orbit of the Moon

The Earth also exerts tidal forces on the moon’s rocky interior that slow down its rotation.

It 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.

Effects of tides1. Synchronization of the rotational and orbital period

2. Tides cause the heating of the interiors of the interacting bodies

3. If the bodies are too close to each other, they can be disrupted by tides (Roche limit).

Why not every new and full moon??

Eclipses

Moon’s orbit is tilted by 5o from the ecliptic

1. The moon should be at one of the nodes – crossing the plane of the earth’s orbit2. The line of nodes should point at the sun

For an eclipse to occur,

Conditions for Eclipses

A solar eclipse can only occur if the moon passes a node near new moon.

The moon’s orbit is inclined against the ecliptic by ~ 50.

A lunar eclipse can only occur if the moon passes a node near full moon.

How come that the Moon can eclipse the Earth??

Solar Eclipses

Accidentally, they have almost the same angular sizes!

Earth-Moon system to scale

Angular diameter (rad) = Linear diameter

Distance

180 degrees = radian

(rad) = L/D

(deg) = (rad)180/

distance)(

size)linear (rad)(

D

L

D

L 265,206rad)(265,206)arcsec(

radian = 180 degrees

DL

Convert from radian to arcseconds:

arcsec206265 arcsec3600180

deg180

rad1

1 deg = 60 arcmin = 3600 arcsec

Note units!!

Small Angle Formula

D

L

2arctan2rad)(

rad)(265,206)arcsec(

radian = 180 degrees

DL

Convert from radian to arcseconds:

arcsec206265 arcsec3600180

deg180

rad1

1 deg = 60 arcmin = 3600 arcsec

Note units!!

Exact Formula

Small Angle Formula

(SLIDESHOW MODE ONLY)

Moon: = 3476 km

384000 km= 0.0091 rad = 0.5 deg

Sun: =1.4106 km

1.5108 km= 0.0093 rad = 0.5 deg

Very close!

Solar Eclipses

The sun appears approx. as large in the sky (same angular diameter ~ 0.50) as the moon.

When the moon passes in front of the sun, the moon can cover the sun completely, causing a total solar eclipse.

Umbra is below 270 km in diameterIt moves at 1600 km/hrTotal eclipse lasts for not more than 7.5 min

Total Solar Eclipse

Prominences

Chromosphere and Corona

Solar Atmosphere Revealed

Diamond Ring Effect

Moon’s orbit is elliptical -> when the moon is in apogee, umbra does not reach the earth -> annular eclipse

Annular Solar Eclipses

The angular sizes of the moon and the sun vary, depending on their distance from Earth.

When Earth is near perihelion, and the moon is near apogee, we see an annular solar eclipse.

Perigee Apogee Perihelion Aphelion

Moon’s orbit is more elliptical than the earth’s orbit

Solar Eclipses: 2002-2012Approximately 1 total solar eclipse per year

The Saros Cycle

Saros cycle: 18 years, 11 days, 8 hours

Repeats in one place every 3 cycles, or ~ 54 yr 1 month