Download 07.5 midterm review

Review for first midterm
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Unregistered clickers: 90C33261 and A4B91508
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Midterm: Friday at 3-5pm
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bring scantrons and calculators!
Scientific notation — the rules
Move the decimal over to the left until it is after the first
digit. The number of places that you moved it is the
exponent x.
For small numbers (less than 1) then you move the
decimal to the right, and the exponent is negative
Significant figures
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The two rules of significant figures:
Your final answer should have the same degree of
precision as the least precise of your input values.
When doing calculations that involve several steps, use
more significant figures than necessary. Then round your
final answer to the correct number of significant figures.
This reduces the chance of round-off errors.
Unit conversions
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Jon is 7ft tall. How tall is he in meters? Use the fact that
1ft = 0.305m.
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There is a simple trick: just multiply by 1!
1ft = 0.305m
0.305m
1=
1ft
m
1 = 0.305
ft
Unit conversions
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Jon is 7ft tall. How tall is he in meters? Use the fact that
1ft = 0.305m.
•
There is a simple trick: just multiply by 1!
The celestial sphere — a useful picture
Polaris, the
north star
Imagine the stars as points of light fixed on a large
rotating sphere surrounding the Earth
The heliocentric model
The plane of the Earth’s
orbit is called the ecliptic
The heliocentric model
You can see
this region of
the sky in
December
You can see
this region of
the sky in June
The heliocentric model
People in the northern hemisphere only
ever see this part of the sky
People in the southern hemisphere
only ever see this part of the sky
The Earth’s axis of rotation is not perpendicular to
the ecliptic — there is a 23○ axis tilt. This means that
the equator is also tilted at 23○ from the ecliptic.
The axis of rotation points in the same direction
(approximately towards Polaris) throughout the
Earth’s orbit
The cause of the seasons
Th reason
The
warmerthe
in
i summer
h in
i winter
i almost
When the
lightiti isifrom
sun than
arrives
c
on the
is that the sunlight is more concentrated
perpendicular
light
isy the most
ground when—
g
the i.e.
Sun isthe
high
gher
in the sky.
concentrated — you expect higher temperatures.
This happens during the summer.
The cause of the seasons
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When it’s summer in the northern hemisphere, it’s
winter in the southern hemisphere
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The difference between the seasons is minimized near
the equator, because the angle that the sunlight impacts
the Earth doesn’t vary as much
The cause of the seasons
At summer solstice, the path of the sun is highest on the
sky. This is the longest day of the year
The cause of the seasons
At winter solstice, the path of the sun is lowest on the
sky. This is the shortest day of the year
The cause of the seasons
At spring equinox and the fall equinox, the path of the
sun is in between — and it rises due east, and sets due
west
The phases of the Moon
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02_MoonriseSetVsPhase.htm
The Moon — synchronous rotation
Eclipses
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Lunar eclipse — the Moon goes into the Earth’s shadow
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Solar eclipse — the Moon blocks out the sun, so (part
of) the Earth is in the Moon’s shadow
Eclipses — lunar eclipse
Eclipses — solar eclipse
Eclipses — when do they occur?
Eclipses — when do they occur?
Notice also that the plane of the Moon’s orbit is
actually slightly tilted from the ecliptic. So the moon
doesn’t usually pass directly in front (or behind) the
Earth — it is a bit lower, or a bit higher.
The heliocentric model — retrograde motion
Retrograde motion — the planets move across the
celestial sphere, but occasionally they change
directions for a while
The heliocentric model — retrograde motion
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mars_retrograde_motion.htm
The history of astronomy
We’ve gone from a picture where the Earth is the center of
a perfect and unchanging Universe, surrounded by
concentric spheres containing the planets and the stars…
…to a picture where we are orbiting the Sun, which is just
one of billions of stars in the Milky Way, which is just one
of billions of galaxies in an expanding Universe, which
originated in a big bang 14 billion years ago.
The ancient Greek understanding of the universe
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Ancient thinkers believed that the heavens must be
perfect and unchanging.
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Since the most perfect shape is a circle (obviously…),
stars and planets must move on circular orbits and
must also have perfectly spherical shapes.
The ancient Greek understanding of the universe
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Geocentric, and the planets are embedded in spheres
made of a transparent “fifth element”
The ancient Greek understanding of the universe
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The answer is that the planets were thought to move in
epicycles, or circles-on-circles
Claudius Ptolemy (c. 100-170 A.D.)
Ancient Green astronomy culminated in the Ptolemaic
model after Claudius Ptolemy
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This model required the planets to move in epicycles,
and the main circular orbits had to be slightly offcenter from the Earth. So this model got
mathematically complicated and was difficult to use.
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Nonetheless, it could make pretty accurate
predictions for planetary positions, and was used for
the next 1500 years.
Nicolaus Copernicus (1473-1543)
Copernicus made a heliocentric model. But his ultimate
model was still pretty complicated (required epicycles)
and not completely accurate, in part because he still
required that all orbits be circular.
Tycho Brahe (1546-1601)
Brahe brought scientific precision to measurements of the
positions of stars and planets.
Johannes Kepler, 1571-1630
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Worked briefly as Tycho’s assistant
before his death; afterwards he took
Tycho’s measurements back to
Germany, and used them to update
Copernicus’ heliocentric model
Johannes Kepler, 1571-1630
He concluded that the planets obey three “laws”
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The orbit of a planet is an ellipse, with the Sun at one
focus
Johannes Kepler, 1571-1630
He concluded that the planets obey three “laws”
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The orbit of a planet is an ellipse, with the Sun at one
focus
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A line segment joining a planet and the Sun sweeps
out equal areas during equal intervals of time
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The square of the orbital period of a planet is
proportional to the cube of the semi-major axis of its
orbit: p2=a3
Galileo Galilei, 1562-1642
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Constructed the first (useful)
telescopes, which he used to
make several crucial
discoveries
Galileo Galilei, 1562-1642
Galileo used telescopes to find that:
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Jupiter has moons orbiting around it
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Venus has phases, just like the Moon — suggesting
that Venus orbits the Sun
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The Moon has craters and mountains; it isn’t
“perfect”
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The Milky Way is just a collection of stars
He used these arguments, along with Newton’s first law,
to argue in favor of heliocentrism
Two major questions in early 20th century
astronomy
In 1700s and 1800s it became universally accepted that the
planets orbit the Sun, and that the Sun is just one of many
stars in the Milky Way galaxy. But what about the rest of
the Universe?
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Is the Milky Way galaxy all that there is?
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Does the Universe evolve, or is it eternal and
unchanging?
Two major questions in early 20th century
astronomy
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Edwin Hubble then used
Cepheid variable stars to estimate
the distances to the “spiral
nebulae” — finding that they are
very far away indeed, and hence
that they are actually separate
galaxies!
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He also showed (as did others)
that these other galaxies are
receding from us, and so the
Universe is not unchanging.
(1889-1953)
What is science?
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Seek explanations for observed phenomena that rely
solely on natural causes
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The creation and testing of models of nature that
explain phenomena as simply as possible
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A scientific model must make testable predictions about
natural phenomena that would force us to revise or
abandon the model if the predictions do not agree with
observations
The progress of science has been largely about
learning not to impose our pre-conceived notions on
nature; you go where the evidence takes you
Occam’s razor
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Given two competing — and equally
successful — explanations for an
observed phenomenon, the simpler one
is preferred
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This idea has really been taken to heart
by scientists. The development of
physics has largely been driven by the
search for a small number of principles
or equations that describe a huge range
of phenomena
William of Occam
1285-1347
Classical mechanics
The theory of classical mechanics (also often called
“Newtonian mechanics”) is concerned with the motion of
objects.
Basic concepts in movement
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speed — the distance travelled in a certain amount of
time. (For example, a car driving at 60mph.)
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velocity — this refers to both the speed and the
direction. (For example, a car driving north at 60mph
has a different velocity than a car driving east at
60mph.)
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acceleration — a change in velocity. (So a car that is
turning but maintaining a constant speed is
accelerating. So is a car that is going in a straight line
but is slowing down; this is negative acceleration)
Acceleration
Newton’s first law (originally due to Galileo)
“A body at rest remains at rest and a body in motion
continues to move at constant velocity along a straight
line unless acted upon by an external force” (this is
Galileo’s formulation)
This law may seem contrary to our everyday experience. But
that’s because in our everyday experience, there are always the
forces of gravity, friction, and air resistance at work
Newton’s second law
Force = mass x acceleration
F=ma
A force is just a push or a pull that causes something to
accelerate, i.e. to change its velocity
Newton’s third law
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For every force, there is an equal and opposite force
Newton’s third law
Momentum
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An object at rest will remain at rest, and an object in
motion will remain in motion with constant velocity
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Why is this? Because of momentum!
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momentum = mass x velocity
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So we can re-state Newton’s first law as: an object’s
momentum will not change unless a force is applied to
it
Angular momentum
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There is also a “circling momentum”, or angular
momentum
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A version of Newton’s first law also applies to angular
momentum — an object’s angular momentum will not
change unless some external force is applied. Angular
momentum is conserved.
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This is why the Earth continues to orbit around the
Sun, even though nothing is pushing it. And it’s why
the Earth continues to spin.
Angular momentum
angular momentum = mass x velocity x distance
So, at fixed angular momentum, an object that is further
away will move slower
Angular momentum
angular momentum = mass x velocity x distance
So, at fixed angular momentum, an object that is further
away will move slower
Energy
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Energy is usually defined as “the ability to do work” or
“the ability to make things move”
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There are different kinds of energy
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kinetic energy — the energy of movement
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thermal energy — heat is a kind of energy
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potential energy — energy that is being stored
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radiative energy — this is just light
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mass-energy — this is how nuclear reactions work
Potential energy
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This is energy that is being stored up, and can be
converted into a different kind of energy
This is an example of gravitational
potential energy, which is a particularly
important concept in astronomy
Conservation laws in physics
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Energy is conserved
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Momentum is conserved
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Angular moment is conserved
Conservation laws — angular momentum
angular momentum = mass x velocity x radius
The orbital
radius is large,
so the velocity
is small
The orbital
radius is small,
so the velocity
is large
Conservation laws — energy
orbital energy = kinetic energy + potential energy
The gravitational
potential energy
is large, so the
kinetic energy is
small
The gravitational
potential energy
is small, so the
kinetic energy is
large
Gravity — an inverse square law
Gravity follows an “inverse-square” law:
This means that if the distance between two objects
doubles, the force between them is reduced by a factor of
4. If the distance triples, the force is reduced by a factor of
9.
The gravitational constant:
Gravity — tides
It is a common misconception that the high tide is caused
by the Moon “pulling” the oceans toward it. But this can’t
be quite true — if it were, how come there’s a high tide on
Earth both in the direction of the Moon, but also in the
opposite direction?
Gravity — tides
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Gravity from the Moon pulls harder on the near side of
the Earth than on the far side, squishing the Earth and
creating a bulge on both sides. This causes high tides.
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The Earth rotates, but the locations of the bulges are
always approximately in-line with the Moon.
The Sun
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•
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Over 99.8% of solar system's mass
Made mostly of hydrogen and helium
Converts 4 million tons of mass into energy each second
(E=mc2)
Some basic facts about the solar system:
similar spin and orbital rotation among the planets
All of the major planets:
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lie approximately in the same plane
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follow ~circular orbits
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orbit in the same direction, and in the same direction as
the Sun’s rotation
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rotate in the same direction and have axes of rotation
that are ~perpendicular to the orbital plane (with the
exceptions of Venus and Uranus)
Some basic facts about the solar system:
similar spin and orbital rotation among the planets
All of the major planets:
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lie approximately in the same plane
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follow ~circular orbits
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orbit in the same direction, and in the same direction as
the Sun’s rotation
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rotate in the same direction and have axes of rotation
that are ~perpendicular to the orbital plane (with the
exceptions of Venus and Uranus)
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have moons that also orbit in the same direction (with
the exceptions of Mercury and Venus which don’t have
moons, and Neptune that has a moon orbiting in the
opposite direction)
Some basic facts about the solar system:
two kinds of (major) planets
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The four inner planets (Mercury, Venus, Earth, and
Mars) are relatively small, and are rocky. These are the
terrestrial planets
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The four outer planets — Jupiter, Saturn, Uranus, and
Neptune — are larger, more massive, and made
primarily of hydrogen and helium gas. These are the
jovian planets (aka gas giants)
Some basic facts about the solar system:
asteroids
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Asteroids are small rocky objects, and most are orbiting
in the asteroid belt between Jupiter and Mars.
Some basic facts about the solar system:
comets
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Comets are small objects of rock and ice (dirty snowballs)
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1000s exist out in the Kuiper belt beyond Neptune, and
many more than that exist out in the spherical Oort cloud
surrounding our solar system.
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Some have highly elliptical orbits, and come into the inner
regions of the solar system and heat up. Then we can see
their tails of melted material.
How did the solar system form?
06_CollapseSolarNebula
The nebular theory of solar system formation
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A nebula becomes dense and massive enough to start
self-gravitating. It begins collapsing.
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But because it has some net angular momentum, it
begins rotating very rapidly. So there is a limit to how
much it can collapse in the plane of rotation, but it can
fully collapse in the vertical direction, leaving a
spinning protoplanetary disk with a dense protostellar
core
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The gas heats up as it contracts; gravitational potential
energy -> thermal energy
The nebular theory of solar system formation
Planets condense out of the protoplanetary disk
Inside of the frost line, only rocks and metals can condense
into planetesimals, and hydrogen compounds (including
water) remain in a gaseous state. But beyond the frost line
hydrogen compounds can also condense into ices.
The nebular theory of solar system formation
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But there simply isn’t much rocky material and metals
around, so the planetesimals inside the frost line never
become very big -> so the inner terrestrial planets are
relatively small and rocky
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However the outer planetesimals have a lot more
hydrogen, helium, and hydrogen compounds that can
condense. So they can become much more massive, and
due to their gravitational force can start attracting even
more material -> so the outer jovian planets are large and
contain mostly hydrogen, helium, and hydrogen compounds
The nebular theory of solar system formation
Eventually the protostellar core becomes so hot, and so
dense, that it begins to undergo nuclear reactions. It
becomes a star.
The nebular theory of solar system formation
The protoplanetary disk begins to clear out because:
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The planets accrete the material around them
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The planets eject material that they don’t accrete by
gravitational perturbations
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After the star begins to shine brightly it eject winds,
blowing out remaining diffuse material
How does this theory explain the asteroids and
comets?
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The remaining planetesimals within the frost line are
asteroids in the asteroid belt.
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The remaining planetesimals outside of the frost line
are comets in the Kuiper belt
How do planets get their moons? Three ways…
The moons of the jovian planets probably formed out of
disks in the same way that the planets formed out of the
protoplanetary disk
How do planets get their moons? Three ways…
There may not have been enough rocks/metals around
for the terrestrial planets to form significant disks, and
therefore moons. Mercury and Venus don’t have moons.
However Mars has two moons which may have been
asteroids that were gravitationally captured
How do planets get their moons? Three ways…
There may not have been enough rocks/metals around
for the terrestrial planets to form significant disks, and
therefore moons. Mercury and Venus don’t have moons.
However Mars has two moons which may have been
asteroids that were gravitationally captured
Neptune also has a moon that orbits in the “wrong”
direction, so that may also have been gravitationally
captured.
How do planets get their moons? Three ways…
So then how do we explain our Moon? It is too large for
gravitational capture. It also has a significantly lower
density than the Earth, suggesting that it did not form in a
disk of the same material…
How do planets get their moons? Three ways…
The giant impact hypothesis — when the Earth was
young it may have collided with another smaller (Marssized) planet, spewing debris out into a ring which
eventually condensed into the Moon
Age of the solar system
The most accurate way to determine the age of the solar
system is through radiometric dating (also called
radioactive dating)
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The atoms of certain elements can spontaneously
decay into other kinds of elements
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Example: potassium-40 (19 protons and 21 neutrons)
decays into argon-40 (18 protons and 22 neutrons)
with a half-life of 1.25 billion years. This means that
after 1.25 billion years, half of the potassium has
become argon. After another 1.25 billion years, half
the remaining potassium also becomes argon. And so
on.
Age of the solar system