Homework Assignment 2
Physics 55
Made available: Tuesday, September 6, 2005
Due in class on: Monday, September 12, 2005
Note: All problems in this homework are required. There are no advanced problems but there are some
optional extra credit problems that anyone can try to have some fun and to earn some extra credit. Only
some of these problems will be graded for credit (you don’t know which ones in advance) but I recommend
that you try to do as many as you can to help learn the material. As usual, strive to write clear, readable
answers with good insights (it wouldn’t hurt to read the homework part of the course syllabus one more
time).
Problem 1: Will further intellectual shocks occur?
Over the centuries, astronomical observations have diminished several times what the human race has felt was
its privileged role in the world. For example, most cultures thought for a long time that Earth was the center
of the universe but observations eventually showed that the Earth is in orbit around the Sun, that Earth was
one of the smaller planets in our Solar System, that the Sun itself is a rather undistinguished star among
about 100,000,000,000 stars in the Milky Way, that the Milky Way itself is just one of about 100, 000, 000, 000
galaxies, and that the human civilization itself has been in existence only an incredibly short fraction of the
age of the universe (about 2 seconds worth if the age of the universe is shrunk to a year, see Fig. 1.12 on
page 15 of your text).
Argue whether there will be at least one more intellectual shock (of any kind, although it could be astronomical) to human society of an impact comparable to or exceeding the realization that Earth was not the
center of the universe. If you think there will be, then suggest what that shock will be and justify briefly
why you think its impact will be so strong. If you think not, explain why you think this way. Your answer
should be at least a half-page long but you are welcome to write a longer answer if you find that you have a
lot to say.
I will summarize some of your answers (anonymously) on the Physics 55 webpage for your classmates to
enjoy.
Problem 2: Number of Stars That Have Received Marconi’s Message?
Estimate how many stars have received Marconi’s radio message of 1903 (the first trans-atlantic radio
message, you can read about it at the URL http://www.stormfax.com/wireless.htm). Use the fact that
radio waves are a form of light and so travel outward at the speed of light, and use the fact that the average
distance between stars in the Milky Way is about 4 ly.
For extra credit, estimate the amount of time it will take for Marconi’s message to be received by the 1,000
galaxies nearest to Earth.
Hint: If the average distance between objects in some volume is d then the number of objects per unit volume
(this is called the number density n) is about n = 1/d3 .
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Problem 3: Practice With a Raisin Cake Universe
Do problem 17 on page 24 of the text.
Problem 4: Are Atoms in a Gas Like Stars or Galaxies?
An important point in Chapter 1 of the book and repeated in lecture is the value of creating simple physical
scale models of astronomical phenomena to get some intuition about sizes, time scales, and speeds.
Imagine that you have become the curator of a new science museum in your home city and that you have
decided to help visitors get some intuition about the size of an atom and the way atoms interact in a gas.
Please answer the following questions.
1. A hydrogen atom, the simplest and most abundant atom in the universe, has a diameter of about
0.1 nm (1 nm or one nanometer is 10−9 m where the “m” stands for a meter) and at its center sits a
nucleus consisting of a single proton, whose diameter is about 2 × 10−6 nm.
Invent and discuss a scale model that you could set up in your museum (or on the grounds of your
museum if that is more appropriate) that would allow visitors to appreciate the relative size of the
nucleus to the atom. Figure 1.7 on page 11 of the text might give you some inspiration.
2. In the Bohr model of the hydrogen atom, the electron acts like a planet that goes in a circular orbit
around the proton, which then acts as the Sun (whose diameter is ≈ 109 m) . If the entire hydrogen
atom were now magically magnified in size so that a proton had the same diameter as our Sun, what
would be the distance of the electron to the proton in AU? Which contains a greater fraction of empty
space, an atom or our solar system?
Note: I hope that you know that the Bohr model is fundamentally wrong. Electrons do not orbit
nuclei, they exist as probability clouds in the vicinity of the nucleus and an electron can be found
arbitrarily far away from or even inside the nucleus when an experiment is carried out to locate the
position of an electron.
3. Finally, let’s ask if the motions of atoms in a gas may be similar to stars moving in a galaxy or to
galaxies moving in the universe. From an introductory chemistry course, one learns that one mole
of hydrogen atoms (about 6 × 1023 atoms) at standard temperature and pressure (STP, i.e., at the
temperature of ice which is 0◦ C or 273 K, and at atmospheric pressure) occupies a volume of 22.4 liters
(where a liter is 1000 cubic centimeters or 0.001 m3 ).
(a) From these data, calculate what is the average distance between hydrogen atoms.
(b) By comparing the ratio of the distance between hydrogen atoms to their diameters, explain
whether atoms at STP are like stars in a galaxy or like galaxies in the universe or like something
else.
(c) Based on your calculations, explain whether the hydrogen atoms in a gas at STP are likely to
collide with one another.
Problem 5: Using SkyGazer to Prepare for an Observing Session
Using your SkyGazer software, please answer the following questions:
1. Starting on Saturday, September 24, determine when the planet Mars will rise above the horizon and
when will it set below the horizon. An accuracy of a minute is fine.
From your results, what would you recommend as a good time for the class to be at the Duke observation
site to observe Mars (please justify your answer briefly)?
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For this problem, I recommend zooming out until the entire sky is visible as a circle at the center of
your screen, this makes it easy to see when Mars will rise and set. You can then zoom in when Mars is
close to the horizon to get an accurate estimate. Also make sure that your horizon is clear (a straight
line) by clicking on the menu Control, then selecting the menu option “Define Horizon”, then click on
the button “Clear” in the lower right part of the Define Horizon Profile window, then click “Apply” to
make it happen.
2. Starting on Saturday, September 24, determine at which compass direction Mars will rise and at what
compass direction Mars will set. (You should give a direction to an accuracy of 10 ◦ , e.g., north would
be 0◦ , south west would be 225◦ , and so on.)
3. Discuss briefly how your compass directions for the rising and setting of Mars are related to the compass
directions for where the Sun rises and sets the same day. Are they the same?
4. At what time, if any, on Saturday, September 24, will Mars cross the meridian? Note: You can
visualize the meridian by selecting the menu Display, then the menu option “Reference Markers”, then
the option “Meridian Line”.
Prove your answer by printing out and including with this assignment the SkyGazer screen when Mars
is just crossing the meridian. You should have the Time Panel present on your screen before printing
the screen so that the time of meridian crossing is indicated.
(a) Printing your screen on a Windows XP computer unfortunately takes several steps. While your
SkyGazer program is open, open also Microsoft Word. Then switch to the SkyGazer program
(you can do this by hitting Alt-Tab several times or by clicking on the SkyGazer icon in the
horizontal tray at the bottom of your screen) and make the SkyGazer program full screen (click
on the “Maximize” icon in the upper right corner of the SkyGazer window). With SkyGazer filling
the screen, now press the “Print Screen” key on your keyboard which will save the screen as an
image on the clipboard. Finally, switch to the Microsoft Word program (again by using Alt-Tab
or by clicking on the Word icon in the tray), then in Word click on the menu Edit and select the
option Paste. The SkyGazer screen image will now appear in the Word document and you can
resize it, add comments, and then print it.
(b) Macintosh users have similar options for printing out a copy of the screen, please look at the following web site for advice: www.macdevcenter.com/pub/a/mac/2003/02/28/screenshot.html
(For extra credit, determine precisely what amount of time you will have to wait for Mars to cross your
meridian exactly again the next evening: a solar day? a sidereal day? Some other amount of time?)
5. By zooming in on Mars, predict what phase Mars will have on Saturday evening of September 24. (See
Figure 2.21 of the text regarding how to describe the phases of a moon or planet. Do you understand
why the phase will not change over the evening?)
You can zoom Mars by left-clicking once on Mars to bring up its Data Panel. Then click on the button
“Center” and then on the button “Lock”. You can then zoom in or out by left-clicking on the + and zoom buttons in the lower left part of the SkyGazer window.
6. Use SkyGazer, describe the location and phase of the Moon on Saturday, September 24 at the time
when Mars is crossing the meridian. Based on your results, do you expect the Moon to cause trouble
in observing Mars or the stars during an observation session on Saturday, September 24?
Problem 6: Optional Extra Credit: Thinking Spherically
Assuming that the earth is a sphere, where on the earth’s surface is it possible for a person to walk one
kilometer south, one kilometer east, and one kilometer north and end up in the exact same place?
Note: if you have thought of only one place, you need to think some more.
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Problem 7: Optional Extra Credit: Ultimate Speed of An Indestructible Sphere
An indestructible sphere of mass 100 kg is launched by rocket far into space. What will its speed be after a
sufficiently long time?
It may be useful for you to know that the mass of a star is of order 1030 kg and the relative speed of stars
in a galaxy is of order 10 km/sec.
Problem 8: Comments about the Homework and Course
• About how long did this assignment take to complete?
• Do you feel that you are understanding the course material? If not, can you indicate what topics or
ideas you would like to understand better?
• Other comments or suggestions about the homeworks, lectures, or observation sessions?
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