Final Exam Review

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The outer planets (Mars, Jupiter, …) are usually moving which way in the sky, against

the background of the stars?

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1. East to West

2. West to East

3. North to South

4. South to North

5. They remain stationary near the celestial poles.

The Motion of the Planets• All outer planets (Mars,

Jupiter, Saturn, Uranus, Neptune and Pluto) generally appear to move eastward along the Ecliptic.

• The inner planets Mercury and Venus can never be seen at large angular distance from the sun and appear only as morning or evening stars.

The moon’s siderial orbital period is …

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1. the time it takes to orbit once around Earth, back to the same position with respect to the stars.

2. the time it takes to orbit once around Earth, back to the same lunar phase.

3. the time it takes to orbit once around the sun.

4. the time it takes to orbit once around a glass of cidre.

5. Both a) and b) are correct; those two orbital periods are the same.

The Phases of the Moon

• 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

• 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

What is the orientation of the moon’s orbit with respect to the Earth’s orbit around the sun?

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1. They are exactly in the same plane.

2. The moon’s orbit is inclined by 5o against the Earth’s orbit.

3. The moon’s orbit is inclined by 23.5o against the Earth’s orbit.

4. The moon’s orbit is exactly perpendicular to the Earth’s orbit.

5. The moon’s orbit is identical to the Earth’s orbit.

Conditions for Eclipses (I)

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

A solar eclipse can only occur if the Moon passes a node near New Moon.

A lunar eclipse can only occur if the Moon passes a node near Full Moon.

Conditions for Eclipses (II)

Eclipses occur in a cyclic pattern.

→ Saros cycle: 18 years, 11 days, 8 hours

What were the epicycles in the Ptolomaic model of the “Universe”

supposed to explain?

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1. The fact that the planets orbit the sun.

2. The fact that the planets always seem to move westward in the sky.

3. The fact that the planets always seem to move eastward in the sky.

4. The fact that the planets move westward for some time, while they usually move eastward.

5. The fact that the planets move eastward for some time, while they usually move westward.

Epicycles

The ptolemaic system was considered the “standard model” of the Universe

until the Copernican Revolution.

Introduced to explain retrograde (westward) motion of

planets

Kepler’s third law of planetary motion states:

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1. The planets revolve around the sun in perfect circles.

2. On its elliptical motion around the sun, a planet moves faster when it is far away from the sun, and slower when it is closer to the sun.

3. The square of the orbital period of a planet’s motion around the sun is proportional to the third power of its average distance to the sun.

4. The orbital period of a planet’s motion around the sun is proportional to its average distance to the sun.

5. The mass of a planet is proportional to its average distance to the sun.

3.A planet’s orbital period (P) squared is proportional to its average distance from the sun (a) cubed:

Py2 = aAU

3

(Py = period in years; aAU = distance in AU)

Kepler’s Third Law

Orbital period P known → Calculate average distance to the sun, a:

aAU = Py

2/3

Average distance to the sun, a, known → Calculate orbital period P.

Py = aAU3/2

You see the headlights of a relativistic train which approaches you with a speed of

150,000 km/s (i.e., half the speed of light, c = 300,000 km/s). You have a detector that can measure the speed of the light signal. What

speed will it measure?

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1. 450,000 km/s

2. 45,000,000,000 km/s

3. 150,000 km/s

4. 300,000 km/s

5. Depends on the wind speed between the train and the detector.

Two postulates leading to Special Relativity (I)

1. Observers can never detect their uniform motion, except relative to other objects.

This is equivalent to:

The laws of physics are the same for all observers, no matter what their motion, as

long as they are not accelerated.

Two postulates leading to Special Relativity (II)

2. The velocity of light, c, is constant and will be the same for all observers, independent of their motion relative to the light source.

Mercury’s orbit …

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1. is a perfect circle whose orbital plane remains stable even over many centuries.

2. is an ellipse whose orientation remains stable even over many centuries.

3. is a perfect circle, and its orbital plane gradually becomes more and more inclined against the plane of the orbits of all other planets.

4. is an ellipse whose orbital plane gradually becomes more and more inclined against the plane of the orbits of all other planets.

5. is an ellipse whose major axis is slowly precessing in the plane of the orbit.

Perihelion Precession

Which of these forms of radiation can be observed directly with ground-based

telescopes?

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1. Radio waves

2. Infrared light

3. Ultraviolet light

4. X-rays

5. Gamma-rays

The Electromagnetic Spectrum

Need satellites to observe

Wavelength

Frequency

High flying air planes or satellites

The Chandra Space Telescope observes …

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1. Radio waves

2. Infrared light

3. Ultraviolet light

4. X-rays

5. Gamma-rays

The Chandra X-Ray Observatory• Launched in 1999• Extremely high angular

resolution (< 1 arc second)

• Very high sensitivity

Most of the mass of an atom is …

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1. Contained in the protons in the nucleus.

2. Contained in the neutrons in the nucleus.

3. Contained in both protons and neutrons in the nucleus.

4. Contained in electrons.

5. Equally distributed between protons, neutrons and electrons.

Atomic Structure

• An atom consists of an atomic nucleus (protons and neutrons) and a cloud of electrons surrounding it.

• Almost all of the mass is contained in the nucleus, while almost all of the space is occupied by the electron cloud.

Which of the following lists the layers of the sun in the correct

order, from inner to outer layers?

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1. Photosphere, chromosphere, core, radiation zone, corona

2. Core, radiation zone, chromosphere, corona, photosphere

3. Core, chromosphere, radiation zone, photosphere, corona

4. Core, corona, radiation zone, chromosphere, photosphere

5. Core, radiation zone, photosphere, chromosphere, corona

The Sun’s Interior Structure

Temp, density and pressure decr. outward

Energy generation via nuclear fusion

Energy transport via radiation

Energy transport via convection (explained soon)

Flo

w o

f en

erg

y

Photosphere

Structure of the Sun

Only visible during solar eclipses

Apparent surface of the sun

Hea

t F

low

Solar interior

Temp. incr. inward

How is energy produced in the sun’s core transported outward in

the region immediately outside the core?

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1. By radiative energy transport.

2. By convective energy transport.

3. By heat conduction.

4. By microwave heating.

5. By relativistic beaming.

The Sun’s Interior Structure

Temp, density and pressure decr. outward

Energy generation via nuclear fusion

Energy transport via radiation

Energy transport via convection (explained soon)

Flo

w o

f en

erg

y

Photosphere

Which of the following provides evidence that convective energy transport plays a role in the sun?

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1. Spicules

2. Granulation

3. Prominences

4. Sunspots

5. The Aurora Borealis

Granulation

… is the visible consequence of convection

How does the region around a sunspot appear when viewed in

ultraviolet light?

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1. Also as a dark spot, just like in visible light and exactly coinciding with the visible-light sunspot.

2. As a small bright spot exactly coinciding with the visible-light sunspot.

3. As a rather large bright region around the sunspot.

4. As a rather large dark region around the sunspot.

5. Sunspots do not leave any trace in the sun’s ultraviolet image.

Sun Spots

Visible Ultraviolet

Cooler regions of the photosphere (T ≈ 4240 K).

Active Regions

Sirius A has an absolute magnitude of MA = 1.4, while Sirius B has MB = 11.6.

This means that …

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1. Sirius A is about 10 times more massive than Sirius B.

2. Sirius B is about 10 times more massive than Sirius A.

3. Sirius A is about 100 times brighter than Sirius B.

4. Sirius B is about 100 times brighter than Sirius A.

5. Sirius A is about 10,000 times brighter than Sirius B.

The Magnitude Scale

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

(mv = 6)

More quantitative:

• 1st mag. stars apear 100 times brighter than 6th mag. stars

• 1 mag. difference gives a factor of 2.512 in apparent brightness (larger magnitude => fainter object!)

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

Magnitude difference M ~ 10

M = 5 Flux ratio 100

M = 10 Flux ratio 1002 = 10,000

The stars Deneb and Vega have about the same spectral shape (and hence,

surface temperature), but Deneb is 900 times brighter (more luminous) than

Vega. What does this tell you?

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1. Deneb’s diameter must be 900 times larger than Vega’s

2. Deneb’s diameter must be 30 times larger than Vega’s.

3. Deneb must be 900 times more massive than Vega.

4. Deneb must be 30 times more massive than Vega.

5. Deneb must have a 900 times stronger magnetic field than Vega.

The Size (Radius) of a StarWe already know: flux increases with surface temperature (~ T4);

hotter stars are brighter.

But brightness also increases with size:

A B

Star B will be brighter than star A.

Specifically: Absolute brightness is proportional to radius (R) squared, L ~ R2.

Example:

Both Spica B and Sirius B are B-type stars, but Sirius B is a white dwarf star, with a

radius ~ 560 times smaller than Spica B.

Thus, since L ~ R2, Sirius B is intrinsically

5602 ≈ 320,000

times fainter than Spica B.

The Hertzsprung-Russell (HR) Diagram organizes stars in a

plot of …

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1. distance vs. luminosity.

2. mass vs. luminosity.

3. mass vs. surface temperature.

4. luminosity vs. spectral type.

5. luminosity vs. distance.

Organizing the Family of Stars: The Hertzsprung-Russell Diagram

We know:

Stars have different temperatures, different luminosities, and different sizes.

To bring some order into that zoo of different types of stars: organize them in a diagram of

Luminosity versus Temperature (or spectral type)

Lum

inos

ity

Temperature

Spectral type: O B A F G K M

Hertzsprung-Russell Diagram

What is the minimum mass that a protostar has to have in order to ignite Hydrogen fusion

and become a real star?

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1. 0.1 % of a solar mass.

2. 1 % of a solar mass.

3. 8 % of a solar mass.

4. 25 % of a solar mass.

5. 1 solar mass.

Minimum Mass of Main-Sequence Stars:

Mmin = 0.08 Msun

At masses below 0.08 Msun, stellar progenitors do not get hot enouth to

ignite thermonuclear fusion.

→ Brown Dwarfs

Gliese 229B

Which is the latest fusion process that will occur in the

sun before it “dies”?

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1. Proton-proton chain

2. CNO cycle

3. Triple-alpha process

4. Oxygen -> Neon burning

5. Silicon -> Iron burning

Red Giant Evolution (5 solar-mass star)

Inactive He

C, O

What will happen to the sun when it has used up its hydrogen

supply in the core?

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1. Hydrogen burning will continue in a shell around a Helium core, and the sun will expand to become a red giant.

2. The Helium core will collapse onto a white dwarf, and Hydrogen burning will continue in a shell around the white dwarf.

3. The sun will explode in a supernova explosion.

4. Hydrogen burning will continue in a shell around a Helium core, and the sun will become a hot, O or B-type star.

5. Hydrogen burning will cease, and the core will begin to burn Helium into Carbon instead.

Evolution off the Main Sequence: Expansion into a Red Giant

H in the core completely converted into He:

“H burning” (i.e. fusion of H into He) continues in a shell

around the core.

Expansion and cooling of the outer layers of the star →

Red Giant

In Cepheid variables, what is correlated with what?

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1. Luminosity with distance.

2. Luminosity with size.

3. Mass with pulsation period.

4. Mass with rotation period.

5. Luminosity with pulsation period.

Cepheid Variables:The Period-Luminosity Relation

The variability period of a Cepheid variable is correlated

with its luminosity.

=> Measuring a Cepheid’s period, we

can determine its absolute magnitude!

The more luminous it is, the more slowly it pulsates.

A “planetary nebula” is …

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1. The remnant of the protostellar disk around a new-born star out of which planets may form.

2. The remnant of the explosion of a sun-like star at the end of its life.

3. The remnant of the explosion of a very massive star (more than 8 solar masses) at the end of its life.

4. The combined image of many planets around a new-born star, which can not be inidividually resolved in telescopes with moderate resolution.

5. A giant molecula cloud, out of which new stars and planets might form.

The Formation of Planetary NebulaeTwo-stage process:

Slow wind from a red giant blows away cool, outer layers of the star

Fast wind from hot, inner layers of the star overtakes the slow wind and excites it

=> Planetary Nebula

Formation of a Planetary Nebula

What is a “nova”?

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1. The birth of a new star.

2. The birth of a new planet.

3. The explosive disruption of a very massive star at the end of its life.

4. The explosive onset of Hydrogen fusion on the surface of a white dwarf in a binary system.

5. The explosive onset of Carbon/Oxygen fusion in a white dwarf in a binary system.

Nova Explosions

Nova Cygni 1975

Hydrogen accreted through the accretion disk accumulates on

the surface of the WD

Very hot, dense layer of non-fusing hydrogen on the WD surface

Explosive onset of H fusion

Nova explosion

In many cases: Cycle of repeating explosions every

few years – decades.

Which of the following will NOT result in a supernova explosion?

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1. The core-collapse of a 20-solar mass star.

2. The accretion-induced collapse of a white dwarf.

3. The onset of the triple-alpha process in the Helium core of a Red Giant.

4. The merging of two white dwarfs in a binary system.

5. None of the above. – I. e., all of the above will result in supernova explosions.

A different kind of Supernova:Type Ia Supernovae

White Dwarf in a binary system accreting matter from a companion star.

Untill it becomes too massive to be a

White Dwarf

Collapse!

Supernova

White Dwarfs can not be more massive than

~ 1.4 solar masses.

Type Ia Supernovae

Alternative Scenario: Merger of two white dwarfs

What will become of the core of a 15-solar-mass star at the end of

its life?

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1. It will collapse to form a white dwarf.

2. It will collapse to form a neutron star.

3. It will collapse into a black hole.

4. It will collapse to form a brown dwarf.

5. It will collapse to form a planet.

The Death of a Massive Star

Properties of Neutron Stars

Typical size: R ~ 10 km

Mass: M ~ 1.4 – 3 Msun

Density: ~ 1014 g/cm3

→ Piece of neutron star matter of the size of a sugar cube has a mass of ~ 100 million tons!!!