Download PS 224: Astronomy Fall 2014 Midterm (October 16, 2014)

PS 224: Astronomy
Fall 2014
Midterm (October 16, 2014)
Name:
Solutions
Time: 1:15 hrs
Feel free to use equations and figures if you think they would be useful.
Calculators are not needed.
If you use the reverse side of the page, make a note of that.
Neatly written answers will be much appreciated.
The exam is divided into three sections (total: 50 pts):
Section I: True or False. 2 pts x 10 = 20 points
SectionII: The Process of Science (3 questions, attempt any 3 of 4). 6 pts x 3 = 18 pts
Section III: Short-answer (3 questions, attempt #6 and 2 of the other 4). 4 pts x 3 = 12 pts
1/5
1. Section I: True or False? Explain briefly in one or two sentences. (2 pts each)
a. Our Solar System is located at the center of the Milky Way.
False. Our Solar System rotates the Milky Way and is located somewhere in the middle
of the Galaxy’s disk.
b. Astronomers are building a new telescope that will allow us to see 100 million
light-years into the past.
False. Light-year is a unit of distance not time.
c. Patterns of stars in the sky changes year to year.
False. The pattern of stars stays the same year to year as the stars are very far away from
us and move relatively little every year.
d. With my uber-fast spaceship, I can travel to the celestial sphere in 100 years.
False. There is no celestial sphere; it is a mythical sphere that the Greeks thought all
stars were attached to.
e. Scientific theories can never be proved true beyond all doubt.
True. Scientific theories represent our current understanding of the physical or biological
systems. In the future, we might come up with a simpler model or with more data, the
understanding may change.
f. A scientific model must make a testable prediction.
True. The basis of a scientific method is to come up with theories and models that have a
predictions that can be tested with experimental data.
g. When energy is converted from one form to another, a tiny amount is inevitably
lost.
False. Energy can neither be created nor destroyed but only converted from one form or
another.
h. Images taken in X-ray are always displayed in false color.
True. We cannot see X-ray photons with our eye. They have to be rendered in one of the
visible colors for us to be able to see them.
i. The more distance the stars, the smaller its parallax.
True. Parallax is a measure of how much stars move on a year-to-year basis. More
distant stars move less.
j.
Red dwarfs have a higher surface temperature and are brighter than all giants.
False. Red dwarfs can have similar surface temperature as some of the giants but they
are much dimmer due to their smaller surface area.
2/5
Section II: Process of Science (5 pts each, only do three problems)
2) Think of some ways in which you can demonstrate the following by simply looking at the sky:
a) the Sun and stars lie beyond the Earth's atmosphere
— The Sun and stars disappear behind the clouds in our atmosphere.
— The Sun and stars rise/set and move across the sky. If they were nearer than the
atmosphere or were attached to it, they would move along with us.
b) the stars are further away than the Moon
— The Moon can block the stars as it moves through the sky.
— We can resolve surface features on the Moon with the naked eye whereas all stars are
point sources.
3) How could you show that the seasons depend on the tilt of the Earth rather than the distance
the Earth is from the Sun?
If the seasons depended on the distance of the Earth from the Sun, the seasons would be the
same all over the Earth. To verify this, I would jump on a plane and fly across the equator to
the Southern Hemisphere.
4) In order for us to understand how the solar system got to be that way it is, we must identify
the major solar system patterns that our formation theory must explain. Name five patterns of
motion or planetary arrangement/location that our theory should be able to explain.
1. Most planets (all except Venus) orbit the Sun in the same counter-clock-wise direction,
which is the same as the direction of Sun’s rotation.
2. Orbits of all planets are at small inclinations with respect to Solar
3. There are two types of planets with their composition depending on the distance from the
Sun: the small, rocky planets are all nearer to the Sun while the larger, gaseous planets
are further away.
4. There are a large number of steroids and comets although the rest of the space has been
cleared away.
5. Most of the moons also follow these patterns: they rotate in the same direction and have
small inclinations.
6. There are notable exceptions like the relatively large size of Earth's Moon, Venus’s
clockwise orbit, and Uranus’s tilt.
3/5
5) A newspaper article claims astronomers have found a very old star that has rare earth
elements ytterbium and promethium and is moving fast enough that it will escape the Milky Way.
If correct this fundamentally changes our understanding. Do you believe this claim? Explain how
you are going to investigate this fascinating star.
I would not believe this claim because this is a “very old” star with rare-earth elements. Such
heavy elements are only produced in supernovae, so the earliest stars probably do not have
those elements. So it is unlikely that a “very old” star has rare earth elements.
To test this I would conduct spectroscopic observations of this star. I would look for
absorption/emission lines that correspond to ytterbium and promethium to confirm/reject that
the star has those elements. To check its high velocity, I would look for Doppler shift of
absorption/emission lines in the spectrum. Since this stars is apparently moving very fast, the
shift should be easily detectable.
Section III: Short-answer questions (attempt # 6 and two of the other four)
3
6) Newton’s version of Kepler’s Third Law:
4⇡ 2
a
P =
⇥
G
M1 + M2
2
a) Imagine another solar system, with a star of the same mass as the Sun. Suppose there is
a planet in that solar system with a mass of 2 MEarth orbiting at a distance of 1 AU from the
star. What (approximately) is the orbital period of this planet? Explain your answer.
The mass of planet is very small and negligible when compared to the mass of the star. So a
solar system with a 2 MEarth planet would have an orbit very similar to ours. If you want to
be very precise, their year might be slightly shorter because P2 is inversely proportional to
total mass; so it total mass goes up, period goes down.
b) Suppose a solar system has a star that is four times more massive than our Sun. If that
solar system has a planet the same size as Earth, orbiting at a distance of 1 AU, what is the
orbital period of the planet? Explain.
If you increase the mass of the star at the center by 4x, the period will decrease by 2x. Again,
P2 ∝ 1 / M, so if M goes up by 4x, P2 goes up 4x, and P goes up by √4 = 2x.
4/5
7) Briefly explain what we mean by the statement: "The farther away we look in distance, the
further back we look in time.” How far back can we look?
Light travels at a finite speed. So to get from point A to point B, it takes a finite amount of
time. The nearer the object, the sooner we see the light coming from it. The further an object,
the longer it takes for its light to get to us. So by looking further away, we are also looking
into the past of that object and what it was like when it emitted that light.
We can look back to when the first light photons were emitted at the formation of the
Universe. Our best measurements out this at 13.8 billion years.
8) If you lived on the Moon, what would be the shape of Earth when we see new Moon from
Earth? Explain.
Earth
Sun
Moon
A new Moon occurs when the Moon is between the Earth and the Sun when the side of the
Moon facing the Earth cannot see the Sun. So if you were on the Moon at this time, you
would see the full Earth.What four properties of the Sun have we directly measured? What
methods were used?
9) What four properties of the Sun have we directly measured? What methods were used?
We can directly measure the following properties of the Sun:
1. Mass using Kepler’s laws
2. Radius using the angular size and distance from Earth
3. Composition from spectroscopy
4. Rotation rate of its surface by tracking sunspots or with Doppler shift
10) How do we know what is going on in the center of the Sun so well if we cannot see it or
send spacecraft to it?
We rely on measurements of its surface properties and detailed mathematical models to find
out what is going on at the center of the Sun. In addition, we can observe and measure
vibrations on the Solar surface that are similar to those on Earth’s surface. This methods,
helioseismology, tells us a lot about what is happening in the Sun’s interior.
5/5