Astro-110 Section-2
Problem Set #2
Homework #2
Due in class on Wed, 20 Feb
Student ID Number
Name (First,Last)
Score (leave blank)
Multiple Choice questions (like those that will appear on the exams). 5 pts each.
1. If you dunk a person into cold water, what happens to the infrared radiation they emit?
(a) It gets brighter and redder (longer λ).
(b) It gets dimmer and redder (longer λ).
(c) It gets dimmer and bluer (shorter λ).
(d) It gets brighter and bluer (shorter λ).
(e) What? Are you nuts? We don’t emit infrared radiation!
2. The wavelength of a photon emitted by an atom depends on
(a) The size of the atom.
(b) The number of protons in the atom.
(c) The energy difference between the initial and final energy states of the electron making a
transition.
(d) The number of electrons in the atom.
(e) The temperature of the atom.
3. An orange spaceship leaves the Earth at 0.1c (a tenth the speed of light [note: we don’t know how
to do this - yet]). Before it disappears from view, what color would it appear to be to an observer
on Earth?
(a) blue
(b) green
(c) yellow
(d) red
(e) purple
4. Police radar and laser guns that detect speeders are an application of
(a) Blackbody radiation
(b) Atomic line emission
(c) The Doppler effect
(d) Quantum mechanics
(e) The Stefan-Boltzmann law
5. Which of the following is NOT light?
(a) Gamma rays
Astro-110 Section-2
Problem Set #2
(b) X-rays
(c) Radio waves
(d) Heat you feel standing some distance from a fire.
(e) Sound you hear from a guitar amplifier.
6. What is the main advantage in putting an optical/infrared telescope, like the Hubble Space Telescope, into orbit around the Earth?
(a) A space telescope’s images are sharper because the telescope is above the blurring effects of
the turbulent atmosphere.
(b) In space, a telescope is closer to the stars, giving us a closer look.
(c) Space telescopes are less expensive to build than ground-based telescopes.
(d) A space telescope’s images are sharper because it is not attached to the spinning planet.
(e) All of the above.
—– Somewhat more challenging problems —–
Remember - we can’t give partial credit for answers where you don’t show your work. If you need
to attach an additional page, do so.
7. You have a normal incandescent light bulb with a tungsten filament. When turned on, current flows
through the filament and heats it up to a temperature of about 3000 K. You may find Wien’s law
λmax = 2.9 × 106 /T and the Stefan-Boltzmann law Power = ²AσT 4 useful. The Stefan-Boltzmann
constant σ = 5.67 × 10−8 W/m2 K 4 .
What is the wavelength where most of the light is emitted from this light bulb?
(a) 10 pts
(units! don’t just write a number)
(b) 10 pts
If the area of the glowing part of the filament is about 1 cm2 (10−4 m2 ), how much
power is radiated by this light bulb? (assume the filament is an ideal blackbody. Again, units!
don’t just write a number).
8. Several years ago, in another example of “fair and balanced” reporting, FOX TV aired a documentary claiming that the moon landings were a hoax. This show was a travesty of conspiracy theory,
sensationalism, pseudoscience and stupidity. One recurring question posed was “if we really landed
on the moon, why doesn’t NASA prove it by pointing the Hubble Space Telescope at the moon
and showing us the evidence of the landings? Shouldn’t we be able to see the bottom half of the
Lunar Modules (LMs) left behind, and the other items (lunar rovers, etc.) left around the landing
sites? Clearly NASA can’t show us these sites because we never landed on the moon! It was all
a hoax!” Well, as intelligent and critical thinking Astro-110 students, you should easily be able to
answer this challenge. Should the Hubble Space Telescope (HST) be able to see the remains of the
Apollo landing sites?
Astro-110 Section-2
Problem Set #2
The answer is easy to calculate, and illustrates the power of quantitative argument. Consider that
the Hubble Space Telescope has a primary mirror diameter of only 2.4 meters. It is located in
low Earth orbit (a few 100 km above the Earth’s surface), and the moon orbits the Earth at a
an average distance of 384,000 km. Recall from class that the minimum resolvable angle for an
optical system is given by the diffraction limit: θmin ' λ/D. (Recall this equation gives the angle
in radians - and if you like, you can convert this to degrees by using the fact that there are 2π
radians in a circle of 360o or 57.3o = 1 radian.)
(a) 10 pts
For a mirror with D = 2.4m (e.g. HST), what is the diffraction limit angle (Note:
units are important! Be sure to specify whether your answer is in radians or degrees)?
(b) 20 pts
What feature size does this angle correspond to at the distance of the moon?
(c) 20 pts
Approximately what mirror diameter would be needed to see the bottom half of a
Lunar Module (Obviously, to do this you need to know the size of the LM. You won’t find it
in your book, so you can try Google or simply make an educated guess on which to base your
calculations - JUST BE SURE TO STATE YOUR ASSUMPTIONS!)?
Side Note (for your information)
There are many problems with the assertions made in the FOX show and by other moon
hoax conspiracy theorists. Just one example (of many) to show we WERE really there:
The 2nd lunar landing team on Apollo 12 setup and left behind an instrument called a
retroreflector on the surface of the moon. From that time in the early 70’s until quite
recently (2002), we were bouncing a laser beam off of this retroreflector from a facility on
Haleakala on Maui. This “lunar ranging” experiment allowed us to measure the precise
distance to the moon and enabled us to study subtle variations in the moons orbit. If
this instrument wasn’t there, we would never have been able to get the return signal on
the laser beam. I suppose the nitwits who produced this show are more interested in
conspiracy theories than facts. Who do they suppose left this apparatus on the moon
(aliens? Elvis?)?