Quiz 1: Answers
Physics 55: Introduction to Astronomy
Professor Henry Greenside
Friday, September 9, 2005
True or False Questions (1 point each)
Please circle “T” for true or “F” for false to indicate the truth of the following statements.
1. T / F All the moons in our solar system are smaller than the smallest planet Pluto.
Answer: F. See Figure 12.16 on page 345 of the text which I also showed and discussed in lecture. The
solar system has several moons, including Ganymede of Jupiter, Titan of Saturn, and our own Moon,
which are larger than Pluto. Ganymede and Titan are even bigger than Mercury and so would make
respectable planets if they weren’t already orbiting a planet.
2. T / F Because galaxies have so many stars, when two galaxies collide, many of their stars will bump
into each other.
Answer: F. Although galaxies have many stars, the stars are so tiny (.01 AU) compared to the typical
distances between stars (300,000 AU) that two galaxies could collide with few if any of their stars
coming close enough to physically contact one another.
3. T / F Experiments indicate that the universe is about 1.4 billion years old.
Answer: F. Various independent measurements such as the rate of expansion of the universe and the
lifetime of stars, together with supplementary information based on measuring rocks on Earth and on
the Moon suggest that the universe is about 14 billion years old.
4. T / F A news article about the composition of comets was mentioned this week in the Announcements
part of the Physics 55 webpage.
Answer: T. Please continue to check the announcements frequently each week for interesting science
articles as well as administrative notices.
5. T / F If, through a telescope, you see two glowing objects such that one object is further away than
the other, then the closer object is younger in age than the further object.
Answer: F. It is true that the closer an object, the more recently you see the object since it takes
less time for light to travel from the object to Earth. But whether an object is close or faraway says
nothing about the age of the object, only that it existed at some time into the past when it emitted the
light that you see. As an example, it would be easy with a modern telescope to see a human spacecraft
beyond Moon’s orbit, but the spacecraft is obviously younger than the Moon despite being further
away.
6. T / F The total mass of the nine planets, millions of asteroids, billions of Kuiper belt objects, and
trillions of Oort cloud objects exceeds the mass of the Sun.
Answer: F. The Sun contains more than 99.9% of the mass of the solar system so is more than a
thousand times more massive than the mass of all of the many objects orbiting the Sun. You should
think of space as dominated by stars, at least in terms of amount of stuff out there in space.
7. T / F In the mathematical expression,
1
2
=1−
,
3
ψ
3+η
if the positive quantity ψ (lower case Greek psi) becomes bigger, the positive quantity η (lower case
Greek eta) becomes smaller.
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Answer: T. If the quantity ψ becomes bigger, then its cube ψ 3 also becomes bigger since the cubing
function f (x) = x3 is monotonically increasing for all numbers. (You can see this graphically but also
from calculus, since the derivative of the function x3 is 3x2 which is always positive and a function
increases where its derivative is positive.) Since ψ 3 becomes bigger, its reciprocal 1/ψ 3 become smaller.
So the right hand side 1 − 2/(3 + η) must become smaller. But an expression of the form 1 − y becomes
smaller for positive y only if the quantity y becomes bigger (subtracting a bigger number from 1 gives
you less left over) so the expression 2/(3 + η) must become bigger. But this can happen only if the
denominator becomes smaller, which in turn can happen only if the positive quantity η itself becomes
smaller.
Multiple Choice Questions (4 points each)
Circle the letter that best answers each of the following questions.
1. The typical number of stars in a galaxy, the approximate number of galaxies in the observable universe,
and the approximate number of neurons in the human brain all have similar values equal to about
(a) 106 .
(b) 1010 .
(c) 1024 .
(d) 1040 .
Answer: (b). This was a memorization question but an important one since the same number 10 10
shows up in several places. We do not know, however, why the number of stars in a galaxy ends up
being about this big, nor why the total number of galaxies also has this value. So there are further
discoveries to be made...
2. The astronomer Carl Sagan, creator of an immensely popular 1980 television series called Cosmos, told
his TV audience that “we are star stuff” because the elements in our bodies
(a) are similar in composition to the elements found in stars.
(b) were created by chemical reactions in the space between the stars.
(c) were made by nuclear fusion in our Sun.
(d) were produced by nuclear fusion in stars other than the Sun.
(e) are the same as those in famous television stars like himself.
Answer: (d). Our star is a third-generation star. The elements other than hydrogen and helium in
the Sun and elsewhere in our solar system came from stars that existed before our Sun, that fused
hydrogen into more massive elements and then “died,” usually violently is such a way that the star’s
contents were blown out into space, to become part of another star system.
3. Galaxies are important to the human species because
(a) without galaxies, there would not have been a Big Bang.
(b) galaxies provide the gravity that prevents us from falling off the Earth,
(c) galaxies collide frequently which allows material from different parts of the universe to be exchanged.
(d) galaxies recycle elements produced in stars into future generations of stars so that the amount of
elements besides hydrogen and helium increases over time.
Answer: (d). The recycling of nuclei produced by stars within a galaxy is an important part of the
way elements other than H and He arise in the universe. By the way, the amount of hydrogen is finite
in the universe (it was produced by the tremendous energies associated with the birth of the universe
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at the Big Bang as we will discuss toward the end of the course when we get to the Big Bang) so the
recycling can not continue forever. At some point in the far future (millions of billions of years in the
future so need to panic), there will not be enough H left for stars to produce fusion reactions and the
stars will go out one by one. The universe will then become an extremely boring graveyard consisting
of light, neutrinos, blackholes (which themselves are believed to evaporate over enough time into light
because of quantum effects), planets, and corpses of stars like neutron stars that do not generate any
energy. Life as we know it could not survive in such a future environment.
4. Sound travels with a speed of about 300 m/s in air at room temperature. By analogy to a light-year,
which of the following lengths is closest to the value of a “sound-hour”?
(a) 10 km
(b) 100 km
(c) 1,000 km
(d) 10,000 km
Answer: (c). A sound-hour is the distance sound travels after one hour of time so the formula to use
is d = vt, distance is speed v times the travel time t. Simplest is to convert the speed units of m/s
directly to the units km/hr in which case you can multiply the new speed directly by the given travel
time of one hour to get the answer directly in the desired units of kilometers. The calculation is best
set up in terms of “cancelling units” (multiplying by successive conversion factors) and can be done
without a calculator by repeatedly rounding numbers to a single significant digit:
d = vt
m 10−3 km
60 s
60 minute
= 300 ×
×
×
× 1 hour
s
1m
1 minute
1 hour
= 3 × 102 × 10−3 × 6 × 101 × 6 × 101 km
= (3 × 6) × 6 × 102−3+1+1 km
≈ 20 × 6 × 101 km
= 120 × 101 km
≈ 102 × 101 km
= 103 km.
The quantity in parenthesis in the second line is the speed v converted to units of km/hr. Notice how
in the 5th line I approximated the number 18 as 20 to one significant digit, and then approximated the
number 120 in the 7th line as 100, again to one digit. The exact answer would have been 1,080 km so
the error from rounding is less than ten percent and we have easily obtained the important scientific
point that a sound-hour is about a 1000 km in magnitude.
An aside: the Earth has a half-circumference at the equator of πr ≈ 3 × 6, 000 km ≈ 20, 000 km, a
distance of about 20 sound-hours. So a tremendous blast of noise like the 1883 volcanic eruption of
the island Krakatoa would take about 20 hours to be heard at all possible points around the Earth.
I strongly recommend that you follow the above style of calculation in which you write down the
complete chain of unit cancellations as a single step so that you don’t calculate and write down
intermediate numbers that are never actually needed in the problem such as the speed in units of
meters per hour or km per second. Arranging the numbers as shown in the second line makes clear
what data need to be combined to get the answer and it is also much easier to just input successive
numbers into your calculator (or manipulate them as above without a calculator). You also don’t
introduce the possibility of an error by writing down an intermediate number incorrectly or by copying
such an intermediate number incorrectly.
Open Questions
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( 10 points) List the following distances in
the appropriate order on the line below.
increasing size by writing their corresponding numbers in
1. The radius of the Milky Way.
2. One light-month.
3. The radius of the sun.
4. The average earth-moon distance.
5. The typical distance between stars.
6. 1 AU.
7. The radius of the star Deneb.
8. The typical distance between galaxies.
9. The size of the solar system (as defined by its outermost planet Pluto).
10. The typical distance of an object in the Oort cloud to the Sun.
Answer: 4, 3, 7, 6, 9, 2, 10, 5, 1, 8.
Some comments: You needed to know that Deneb was bigger than the Sun (which was mentioned in lecture)
and that Deneb was smaller than the distance between stars, but you didn’t need to know that Deneb is
smaller than 1 AU. Deneb is in fact about 150 times bigger than the Sun. Since one astronomical unit is
about 100 solar diameters (200 solar radii), Deneb has a radius .75 AU that would lie just beyond the orbit
of Venus (0.72 AU) but within the radius of Earth’s orbit. Other stars are bigger still, with Antares (which
some of you saw at the observation session, in the constellation Scorpio) being about 500 times the size of the
Sun (with a radius that would extend well beyond the orbit of Mars). Betelgeuse in the shoulder of Orion
is about 900 times the size of the Sun (it is not called a super red giant for nothing) and its surface would
extend almost out to Jupiter (4.5 vs 5.2 AU). Note also that a light-month is one twelfth of a light year so
must be about 1/48th the distance (4.4 ly) to the nearest star system of Alpha Centauri. So a light-month
is well beyond the orbit of Pluto (about 6 light-hours) but much smaller than the Oort cloud, which extends
almost half-way to the nearest star.
Extra credit (3 points): Name one of the women that I mentioned in class as making an outstanding
contribution to astronomy and describe in a few words what her contribution was.
The three women I mentioned in class were Cecelia Payne-Gaposchkin (who discovered that stars were
made mainly of H and He), Sandra Faber (who mapped out the patterns of galaxies over the universe and
discovered that galaxies reside on the surfaces of bubbles—like a froth—with giant empty voids between
groups of galaxies), and Vera Rubin (whose studies of galaxy rotation helped to prove that a majority of
the mass of the universe was an unknown “dark matter”). But I gave you extra credit if you mentioned any
woman astronomer and something of what she was known for.
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