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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?
1.
2.
3.
4.
5.
East to West
West to East
North to South
South to North
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 …
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
27.32 days
• The Moon orbits Earth
in a sidereal period of
27.32 days.
Moon
Earth
Fixed direction in space
The Phases of the Moon
Fixed direction in space
29.53 days
Earth
Moon
Earth orbits around Sun =>
Direction toward Sun changes!
• The moon’s synodic
period (to reach the
same position relative
to the sun) is 29.53
days (~ 1 month).
What is the orientation of the
moon’s orbit with respect to the
Earth’s orbit around the sun?
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?
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
Introduced to explain retrograde
(westward) motion of planets
The ptolemaic system was considered
the “standard model” of the Universe
until the Copernican Revolution.
Kepler’s third law of planetary
motion states:
1.
2.
3.
4.
5.
The planets revolve around the sun in perfect circles.
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.
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.
The orbital period of a planet’s motion around the sun is
proportional to its average distance to the sun.
The mass of a planet is proportional to its average
distance to the sun.
Kepler’s Third Law
3. A planet’s orbital period (P) squared is
proportional to its average distance from the
sun (a) cubed:
Py2 = aAU3
(Py = period in years; aAU = distance in AU)
Orbital period P known → Calculate average distance to the sun, a:
aAU = Py2/3
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?
1.
2.
3.
4.
5.
450,000 km/s
45,000,000,000 km/s
150,000 km/s
300,000 km/s
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 …
1.
2.
3.
4.
5.
is a perfect circle whose orbital plane remains stable
even over many centuries.
is an ellipse whose orientation remains stable even
over many centuries.
is a perfect circle, and its orbital plane gradually
becomes more and more inclined against the plane of
the orbits of all other planets.
is an ellipse whose orbital plane gradually becomes
more and more inclined against the plane of the orbits
of all other planets.
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?
1.
2.
3.
4.
5.
Radio waves
Infrared light
Ultraviolet light
X-rays
Gamma-rays
The Electromagnetic Spectrum
Wavelength
Frequency
Need satellites
to observe
High
flying air
planes or
satellites
The Chandra Space Telescope
observes …
1.
2.
3.
4.
5.
Radio waves
Infrared light
Ultraviolet light
X-rays
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 …
1.
2.
3.
4.
5.
Contained in the protons in the nucleus.
Contained in the neutrons in the nucleus.
Contained in both protons and neutrons in
the nucleus.
Contained in electrons.
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?
1.
2.
3.
4.
5.
Photosphere, chromosphere, core, radiation zone, corona
Core, radiation zone, chromosphere, corona, photosphere
Core, chromosphere, radiation zone, photosphere, corona
Core, corona, radiation zone, chromosphere, photosphere
Core, radiation zone, photosphere, chromosphere, corona
The Sun’s Interior Structure
Flow of energy
Photosphere
Energy transport
via convection
(explained soon)
Energy transport
via radiation
Energy generation
via nuclear fusion
Temp, density and pressure decr. outward
Structure of the Sun
Apparent surface
of the sun
Heat Flow
Only visible
during solar
eclipses
Solar interior
Temp. incr.
inward
How is energy produced in the
sun’s core transported outward in
the region immediately outside
the core?
1.
2.
3.
4.
5.
By radiative energy transport.
By convective energy transport.
By heat conduction.
By microwave heating.
By relativistic beaming.
The Sun’s Interior Structure
Flow of energy
Photosphere
Energy transport
via convection
(explained soon)
Energy transport
via radiation
Energy generation
via nuclear fusion
Temp, density and pressure decr. outward
Which of the following provides
evidence that convective energy
transport plays a role in the sun?
1.
2.
3.
4.
5.
Spicules
Granulation
Prominences
Sunspots
The Aurora Borealis
Granulation
… is the visible consequence of convection
How does the region around a
sunspot appear when viewed in
ultraviolet light?
1.
2.
3.
4.
5.
Also as a dark spot, just like in visible light and
exactly coinciding with the visible-light sunspot.
As a small bright spot exactly coinciding with the
visible-light sunspot.
As a rather large bright region around the sunspot.
As a rather large dark region around the sunspot.
Sunspots do not leave any trace in the sun’s
ultraviolet image.
Sun Spots
Active Regions
Visible
Ultraviolet
Cooler regions of the photosphere (T ≈ 4240 K).
Sirius A has an absolute magnitude of
MA = 1.4, while Sirius B has MB = 11.6.
This means that …
1.
2.
3.
4.
5.
Sirius A is about 10 times more massive than Sirius B.
Sirius B is about 10 times more massive than Sirius A.
Sirius A is about 100 times brighter than Sirius B.
Sirius B is about 100 times brighter than Sirius A.
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 DM ~ 10
DM = 5  Flux ratio 100
DM = 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?
1.
2.
3.
4.
5.
Deneb’s diameter must be 900 times larger than Vega’s
Deneb’s diameter must be 30 times larger than Vega’s.
Deneb must be 900 times more massive than Vega.
Deneb must be 30 times more massive than Vega.
Deneb must have a 900 times stronger magnetic field
than Vega.
The Size (Radius) of a Star
We 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 …
1.
2.
3.
4.
5.
distance vs. luminosity.
mass vs. luminosity.
mass vs. surface temperature.
luminosity vs. spectral type.
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
Luminosity versus Temperature (or spectral type)
Hertzsprung-Russell Diagram
Spectral type: O
Temperature
B
A
F
G
K
M
What is the minimum mass
that a protostar has to have in
order to ignite Hydrogen fusion
and become a real star?
1.
2.
3.
4.
5.
0.1 % of a solar mass.
1 % of a solar mass.
8 % of a solar mass.
25 % of a solar mass.
1 solar mass.
Minimum Mass of
Main-Sequence Stars:
Mmin = 0.08 Msun
Gliese 229B
At masses below
0.08 Msun, stellar
progenitors do not
get hot enouth to
ignite thermonuclear
fusion.
→ Brown Dwarfs
Which is the latest fusion
process that will occur in the
sun before it “dies”?
1.
2.
3.
4.
5.
Proton-proton chain
CNO cycle
Triple-alpha process
Oxygen -> Neon burning
Silicon -> Iron burning
Red Giant Evolution
(5 solar-mass star)
C, O
Inactive He
What will happen to the sun
when it has used up its hydrogen
supply in the core?
1.
2.
3.
4.
5.
Hydrogen burning will continue in a shell around a Helium
core, and the sun will expand to become a red giant.
The Helium core will collapse onto a white dwarf, and
Hydrogen burning will continue in a shell around the white
dwarf.
The sun will explode in a supernova explosion.
Hydrogen burning will continue in a shell around a Helium
core, and the sun will become a hot, O or B-type star.
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?
1.
2.
3.
4.
5.
Luminosity with distance.
Luminosity with size.
Mass with pulsation period.
Mass with rotation period.
Luminosity with pulsation period.
Cepheid Variables:
The Period-Luminosity Relation
The variability period of a
Cepheid variable is correlated
with its luminosity.
The more luminous it is, the
more slowly it pulsates.
=> Measuring a
Cepheid’s period, we
can determine its
absolute magnitude!
A “planetary nebula” is …
1.
2.
3.
4.
5.
The remnant of the protostellar disk around a newborn star out of which planets may form.
The remnant of the explosion of a sun-like star at the
end of its life.
The remnant of the explosion of a very massive star
(more than 8 solar masses) at the end of its life.
The combined image of many planets around a newborn star, which can not be inidividually resolved in
telescopes with moderate resolution.
A giant molecula cloud, out of which new stars and
planets might form.
The Formation of Planetary Nebulae
Two-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”?
1.
2.
3.
4.
5.
The birth of a new star.
The birth of a new planet.
The explosive disruption of a very massive star at
the end of its life.
The explosive onset of Hydrogen fusion on the
surface of a white dwarf in a binary system.
The explosive onset of Carbon/Oxygen fusion in a
white dwarf in a binary system.
Nova Explosions
Hydrogen accreted through the
accretion disk accumulates on
the surface of the WD
 Very hot, dense layer of nonfusing hydrogen on the WD surface
 Explosive onset of H fusion
Nova Cygni 1975
 Nova explosion
In many cases: Cycle of
repeating explosions every
few years – decades.
Which of the following will NOT
result in a supernova explosion?
1.
2.
3.
4.
5.
The core-collapse of a 20-solar mass star.
The accretion-induced collapse of a white dwarf.
The onset of the triple-alpha process in the Helium
core of a Red Giant.
The merging of two white dwarfs in a binary system.
None of the above. – I. e., all of the above will result
in supernova explosions.
A different kind of Supernova:
Type Ia Supernovae
White Dwarfs can not
be more massive than
~ 1.4 solar masses.
White Dwarf in a binary
system accreting matter
from a companion star.
Untill it becomes too
massive to be a
White Dwarf
 Collapse!
 Supernova
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?
1.
2.
3.
4.
5.
It will collapse to form a white dwarf.
It will collapse to form a neutron star.
It will collapse into a black hole.
It will collapse to form a brown dwarf.
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: r ~ 1014 g/cm3
→ Piece of neutron star matter of
the size of a sugar cube has a
mass of ~ 100 million tons!!!