Lecture 1 (September 22):
What is Science? What is Astronomy?
Chapter 1: Sections 1, 2, 6, 8.
Science must describe natural phenomena in
the universe based on rational, mathematical reasoning. Quantitative
explanations are subject to test by experiment and observation.
Astronomy is about every object or event we
observe on the sky.
What are the conditions for any body of
knowledge to be science?
What part of science is astronomy?
Why does science oppose authority?
Lecture 2 (September 23):
The Celestial Sphere: Stars, Angles on the Sky, Daily Motion.
Sections 1.5, 2.1, 2.2, 2.3.
The celestial sphere is the map of angular
positions of all stars on an imaginary sphere around the Earth. It tells
us the direction to each star, but it does not tell the distance.
Separations between stars or sizes of objects
on the sky are measured in angles.
The North Celestial Pole is the projection of
the North Pole onto the celestial sphere. The celestial Equator is the
projection of the Earth's equator onto the celestial sphere.
The rotation of the Earth causes the apparent
daily motion of the stars.
How do stars move on the sky relative to the
horizon of an observer on Earth?
Why do they move that way?
How is the separation between two stars on the
celestial sphere measured?
What is the zenith?
What is the North Celestial Pole?
Lecture 3 (September 24):
Apparent Motion of the Sun. The Seasons. Sidereal day.
Section 2.5, Box 2.2
The seasons are caused by the tilt of the
axis of the Earth. Winter: days are shorter and the Sun is lower over the
The Sun is seen to move over the sky in one
year relative to the stars. This is why we see different stars at night at
The Earth spins 366.25 times in a year relative
to the distant stars. The sidereal day is one spin relative to the distant
stars. The solar day is the time between two successive passes of the Sun
across the Meridian, and is slightly longer than the sidereal day.
What is the reason for the seasons?
Why do we see different stars at night in
the different seasons?
What time of the year does the Sun reach its
maximum height over the horizon in South Africa?
How many times does the Earth spin around its
own axis during a year?
Week 2 (September 27 - October 1) :
Lecture 4 (September 27):
Measuring the Earth: the Eratosthenes Method.
Section 1.5, Box 1.1, Section 3.6.
Eratosthenes measured the latitude difference
between two cities by noticing the maximum height the Sun reached in each
city. With the small-angle formula he derived the size of the Earth.
We use the small-angle formula to derive
the size of an object once we know its angular size and its distance.
The latitude determines the angular height above
the horizon at which we see the North Celestial Pole.
If the North Pole star is on the zenith,
where are you on the Earth?
If the Sun reaches the zenith exactly on
the Summer solstice, what is your latitude?
How did Eratosthenes calculate the size of
If we know the angular size of an object
seen on the sky, what else do we need to know its real size?
Lecture 5 (September 28):
The Celestial Sphere and Celestial Coordinates. Precession.
Sections 2.4 and 2.6, Box 2.1.
Star positions are specified by two coordinates,
declination and right ascension.
Declination is the angle from the celestial
equator to the star.
Right ascension is the angle that a great circle
fixed on the poles needs to rotate to go from the Vernal equinox to the star.
The Earth axis precesses once every 26000 years,
due to the tides from the Moon and the Sun. This causes the precession of the
What coordinates do we use to specify the
position of a star?
What is the declination of a star on the
What is the declination of a star that is
halfway between the celestial equator and the South pole?
Has the star Polaris always been close to
the North pole?
Galileo's discoveries with the telescope:
mountains on the Moon, phases of Venus, sunspots, Jupiter's satellites,
Milky Way made of many stars.
Galileo also worked on the laws of motion.
He understood that in the absence of forces, objects will continue moving
with a constant velocity along a straight line. He figured out that
gravity on the Earth's surface makes all objects fall with the same
acceleration, and that the trajectory of falling objects is a parabola.
Galileo followed the scientific method and
defended the heliocentric model. But he was also still prejudiced and obstinate
on certain things: he believed planets must move on circular orbits.
What did Galileo find out about the Moon, Venus,
Jupiter, and the Sun?
Why was Galileo the first to know about all this?
How did this influence his views on the
Did Galileo relate his principle of inertia to
the motions of the planets?
Newton formulated three laws that govern all
motion. Learn the three laws!
First Newton's law: A body remains at rest, or
moves in a straight line at constant speed, unless acted upon by a net outside
Second Newton's law: The net outside force that
must act on a body that accelerates is equal to its mass times its
Third Newton's law: Whenever one body exerts a
force on a second body, the second body exerts an equal and opposite force
on the first body, which we call the reaction to the first force.
If you are at rest and not accelerating,
does this imply that no force may be applied on you?
If we could turn off the force of gravity at
some instant of time, what would all the planets do?
If a big boulder and a leaf fall down in a
room where we have made a vacuum, which one is subject to the greatest
acceleration? Which one is subject to the greatest force?
The Sun exerts a force on the Earth that
keeps it on its orbit. Which is the reaction to that force?
Week 4 (October 11-15) :
Lecture 14 (October 11):
Newton's Law of Gravity and the Motion of the Moon.
The law of universal gravitation: any two
objects, whatever their nature or composition, attract each other with a
force proportional to the product of the masses and inversely proportional
to the distance squared.
Earth's force of gravity is responsible for
the fall of objects on Earth's surface and for the orbit of the Moon.
What is the force that makes the Moon go
around the Earth?
If you stand next to a big truck, why don't
you feel the gravitational attraction towards it?
If you move out to space to a distance from
the center of the Earth equal to twice its radius, how much smaller will the
gravitational acceleration be compared to the value at the surface?
What will happen if you put two rocks in space
at rest close to each other? Will they remain at rest?
Lecture 15 (October 12):
Newton's Explanation of Planetary Motion.
Newton proved that his three laws of motion and
the law of universal gravitation imply that a body moving under the
gravitational force of another body must move over a trajectory that is a
circle, an ellipse, a parabola or a hyperbola, obeying all of Kepler's laws.
What are the possible trajectories that an
object moving under the gravity of another object can follow?
Why do we feel the gravity of the Earth but
not the gravity of the Sun?
Do comets obey Kepler's laws?
If a spacecraft is sent to Mars and it
passes by it without using its jet engines, subject only to the force
of gravity, what is the shape of its trajectory around Mars?
Lecture 16 (October 13):
How we Know the Mass of the Sun, the Earth, and the Planets.
Section 4.7, Box 4.4, review boxes 1.2 and 1.3.
Newton's generalization of the third Kepler's
law allows one to measure the mass of any object with a satellite moving
The planets also attract each other, causing
perturbations on their orbits. The perturbations from Kepler's laws were
observed to be precisely as predicted.
Binary stars were also found to orbit around
each other following Kepler's laws.
How do we know the mass of the Sun?
How do we know the mass of Jupiter?
Do planets in the Solar System obey Kepler's
laws exactly, or only approximately?
Venus has no satellites. How do we know
Lecture 17 (October 14):
More Triumphs of Newton's Laws: Tides and Neptune's Discovery.
Sections 4.8, 16.1. Box 9-1.
Newton's theory of gravity makes many successful,
quantitative predictions. Planetary perturbations were so accurately tested
that the presence of a new planet was required and its position predicted,
leading to the discovery of Neptune in 1846.
Other successful predictions: the tides due
to the Moon and the Sun, the oblateness of the Earth, the period of
precession of the equinoxes.
How were Uranus and Neptune discovered?
What causes ocean tides?
If the Earth rotated slower, how would its
Refracting telescopes work with lenses, and
reflecting ones with mirrors with a shape that focuses the light rays.
Large telescopes collect more light
and increase the image resolution. Atmospheric turbulence puts a limit to
the resolution of large optical telescopes.
The development of sensitive electronic
cameras and spectrographs has allowed taking images and spectra of much
fainter objects than it was possible with photographic plates in the past.
Telescopes in space can take images with much
better resolution, in the absence of the blurring from the atmosphere. They
can also detect radiation at wavelengths at which it is blocked by the
Radio telescopes can be used on the ground and
they are big reflecting dishes with radio receivers at the focus.
Why is the size of a telescope related to
its observing power?
Why are today's visual telescopes reflecting?
Why are they built in high mountains?
Why is it useful to have telescopes in space?
How is the light behind the telescope detected
in present observatories?
The Earth is special by the presence of liquid
water and life. Water implies oceans, clouds, ice, rain, erosion.
The Earth interior is hot from its radioactivity,
which causes convection movements in the mantle. These movements make new ocean
crust and subduct old one, while continents float and drift on the mantle.
The plate motions cause the formation of new
Why is the mean density of the Earth higher
than the density of the crust?
How do we know the size of the solid, inner
Why is the Earth's interior so hot?
What are the place where we usually have
earthquakes and volcanos on Earth?
The Earth temperature remains constant if a
balance is maintained between incoming solar light and outgoing infrared
radiation. When this balance is broken we have a radiative forcing that changes
The increase in greenhouse gases due to human
emissions results in a radiative forcing that today is at 2.4 W/m^2.
What is the Earth's albedo?
Why does temperature decrease with altitude in
the troposphere, and increase with altitude in the stratosphere?
What is radiative forcing?
If greenhouse gases are increased and the solar
flux stays constant, how will the infrared luminosity of the Earth change?
How will the Earth surface temperature change?
Lecture 28 (November 2):
The Earth Carbon Cycle and the Ice Ages.
Check out the
Byrd Polar Research Center ,
an institution at The Ohio State University dedicated to glaciology research
where many studies of present and past climate using glaciers are being done.
The greenhouse effect in the Earth has increased
due to anthropogenic emissions of carbon dioxide, methane and other gases.
Most carbon dioxide is in the ocean, and its
atmospheric concentration was in equilibrium with the ocean until human
emissions started. The ocean has absorbed carbon dioxide from the atmosphere
since then, but too slowly to prevent it from increasing.
The ice ages are thought to be related to
variations of the Earth orbit that alter the average solar energy received
by Earth, but the temperature variation must be highly magnified by feedback
effects (among them, lower greenhouse gases in ice ages) that are poorly
Key Questions :
How long ago did the last ice age end? How
long before that was the last interglacial period?
What does the Milankovich theory say?
Where is most of the carbon dioxide on Earth?
Why was carbon dioxide lower during the ice
age than at present?
We are now emitting 6 Gigatons of carbon every
year. Why is the atmospheric carbon increasing by only 3 Gigatons every year?
Lecture 29 (November 3):
Global Warming and Future Climate Change.
Homework 3 handed out.
The mean temperature of the Earth has increased
by 1 F over the last 100 yars. The increase in temperature is consistent with
the modeled response to the radiative forcing of greenhouse gases, plus
smaller effects of solar variation, volcanoes, ozone losses, and aerosols.
The same climate models predict a much larger
temperature increase of 3 to 11 F in the 21st century, which can be partly
mitigated if we reduce greenhouse emissions.
How much carbon dioxide does each human being
release to the atmosphere, on average?
Why does sea level rise when temperature
Why do aerosols affect global warming?
What are the consequences of greenhouse gases
that we can be certain of? What consequences are more uncertain?
Mars' surface is heavily cratered in the
South and resurfaced in the North, has large volcanoes, a huge canyon,
two polar ice caps of carbon dioxide and water ice that vary seasonally,
and a lot of features indicating past water flows.
The Martian atmosphere is very thin and made
mostly of carbon dioxide. Liquid water probably existed in the past and
is in the form of permafrost today. Most of the carbon dioxide was trapped in
carbonate rocks by weathering through rain, which was not returned to the
atmosphere after volcanic activity ceased. Mars has also lost some atmospheric
gases to space.
Why did Mars come closer to Earth in the
2003 opposition than at most other times?
Why does Mars have volcanoes much higher than
any found on Earth?
Jupiter's atmosphere shows bands and zones
resulting from convecitve motions, which generate storms like the Great
Red Spot and other ovals. Clouds of ammonia, ammonium hydrosulfide, and
water vapor appear at three levels of different temperature.
Jupiter emits twice as much radiation as it
receives from the Sun, because of its internal heat, which also drives
The interior of Jupiter is liquid metallic
hydrogen. It probably has a small rocky core in the center.
Why is Jupiter a much less spherical planet
What is the most abundant element in Jupiter?
Is the energy of infrared radiation emitted
by Jupiter the same as the energy of sunlight that it receives?
What do the colors of Jupiter's clouds
correspond to? What causes these colors?
Lecture 35 (November 12):
The Galilean Satellites of Jupiter.
The four Galilean satellites were formed as
a miniature Solar System, with rocks close to Jupiter and ice farther away.
Their rotations are tidally locked up to Jupiter,
and the orbital periods of the first three are trapped in resonances.
The slight orbital eccentricities induced by
satellite perturbations cause huge tide variations from Jupiter.
Io has constant volcanic eruptions and sulfur
geysers. Europa has a cracked icy surface and an underlying liquid ocean.
Ganymede and Callisto have cratered surfaces, grooved terrain, and more
What is peculiar about the orbital periods of
the Galilean satellites?
Why does Io have so much volcanic activity?
What is similar in the way the mean densities of
planets in the Solar System and the Galilean satellites vary with the size
of their orbits?
Pluto was discovered in 1930 by Tombaugh. It is
the smallest planet with a diameter of 2300 km, and a highly inclined and
eccentric orbit. The only details from its surface are very blurry, from
Hubble Space Telescope images.
Pluto has the moon Charon, very large in relation
to its planet (1200 km diameter), and is tidally locked up to Pluto.
Pluto and Charon form part of the Kuiper Belt,
a large number of icy, small objects orbiting beyond Neptune.
Are there craters in Pluto?
How has Pluto been affected by Neptune?
What does the average density of Pluto of
2 grams per cubic centimetre suggest?
What class of objects does Pluto belong to?
Lecture 39 (November 18):
Asteroids, Meteorites, and Meteors.
Homework 5 due.
Sections 17-1 to 17-6.
Check out the
Near-Shoemaker website, on the spaceship that orbited asteroid EROS and
landed on it in 2001.
Asteroids were discovered starting in 1801,
today there are more than 10000 known, most of them orbit between Mars and
Jupiter's gravitational tugs cause gaps in the
distribution of asteriod periods, called Kirkwood gaps.
Several spacecraft have taken images of
asteroids. They are irregularly shaped, some of them are made of various
pieces and may have moons.
Asteroid sometimes collide with Earth, one
collision 65 million years ago caused a major extinction and left a layer of
iridium all over the planet. Asteroids are also the origin of meteorites.
How were asteroids discovered?
What is different in the composition of
asteroids and Kuiper Belt objects?
Comets are small objects made of ice and dirt.
They are in very eccentric orbits. When they reach perihelion and are
close to the Sun, the ices sublimate and generate bright and extended tails.
Comets come from the outskirts of the Solar
System, in the Oort cloud or the Kuiper Belt. They have spent billions of
years in that region, and they become visible when some gravitational
perturbation reduces their perihelion, making them pass close to the Sun. As
their ices evaporate, they generally do not last for many orbital periods
before they break into pieces.
What is a comet nucleus made of?
Why is a comet nucleus so dark?
How are comets and meteor showers related?
In which direction does the ion tail of a comet
127 exoplanets have been discovered. For most of
them, we have only measured the velocity of their parent star through the
Doppler effect, and the way the velocity changes owing to the
gravitational tug of the planet moving around it. For a few cases, we have
observed a slight dimming of the star caused by the transit of the planet
over the star. Some of these are in systems of two or three planets.
Most of the detected planets are very massive
(similar to Jupiter), because our measurements are not accurate enough to
detect less massive planets. As technology for very precise Doppler
measurements of velocity has progressed, we have recently been able to
find planets of the mass of Neptune, but only when they are very close to
Most planetary systems seem very different from
the Solar System: some giant planets are very close to their star, most others
are in highly eccentric orbits. But a few are in orbits similar to Jupiter in
the Solar System.
In the future, we expect to find Earth-like
planets using more sensitive methods. How many there will be, and how many
will have orbits adequate to sustain life, is a big unknown.
How many planets outside the Solar System have
been discovered so far?
What methods have been used to discover these
How are these planets different from the ones
in the Solar System?
Why are all known exoplanets about as massive
as Jupiter, and none are like the Earth?