A100 - Dan Swearingen
Homework 3
Due Tuesday, October 8, 1996 at the beginning of class.

Chapter 3:

Page 104, Questions for review:

1. Why is light called electromagnetic radiation?

Light is known as electromagnetic radiation because it has two complementary components which were found to be a magnetic field wave in synchronous motion with an electric field wave.

6. What is the Doppler shift?

A Doppler shift is the change in a wave's wavelegnth caused by the motion of the source relative to that of the observer. The Doppler shift can be easily detected in sound by the ear. An example is when a car honks its horn while approaching you. While approaching the tone will be higher than the actual tone. When the car is opposite you the tone will be its actual value. As the car moves away the tone will be lower (see figure 3-18 in text). The Doppler shift can be calculated using this formula:

7. What gases in the atmosphere absorb infrared radiation? Which gases absorb ultraviolet?

Some of the gases found in our atmosphere which absorb infrared light are: carbon dioxide, methane, and water vapor. Gases found in our atmosphere which absorb ultraviolet light are ozone (O3) and oxygen gas (O2).

Page 105, Thought questions and problems:

2. Suppose you are operating a remote-controlled spacecraft on Mars from a station here on Earth. How long will it take the craft to respond to your command if Mars is at its nearest point to the Earth?

First you must figure out how close Mars can get to the earth. This is easily seen by drawing a picture:

Now that we have the distance, 0.5 AU, we convert it to km so that we can see how long it will take radio commands to reach Mars.

If it takes 4.2 minutes for the control signals to reach Earth, it could be difficult to stop or turn the remote-control vehicle before it hits an something.

3. Sketch an atom emitting light. Does the electron end up in a higher or lower orbit? Repeat for an atom absorbing light.

When an atom emits light an electron has fallen from a higher orbit to a lower orbit. The amount of energy the emitted photon has will equal the energy difference between the initial and final orbits.

When an atom absorbs light the electron moves from a lower orbit to a higher orbit. The incoming photon must be equal to the energy difference between the initial and final orbits or it will not be absorbed.

7. If you added more water or carbon dioxide to our atmosphere, how would it alter the loss of heat from our planet? Would you expect the Earth to get warmer or cooler? Why?

The situation for carbon dioxide is different from the situation for water. If we add CO2 to our atmosphere it will make it harder to lose heat (infrared radiation) back to space so it would probably increase the equalibrium temperature of the Earth. This is because the Sun pumps energy onto the Earth in the form of visible light photons. These photons heat the objects which absorb the visible light. These objects in turn radiate infrared radiation. The more infrared light gets absorbed in the atmosphere, the less gets radiated back to space, causing the energy to be retained, hence the temperature rises.

Water is more complicated because it dependes on whether the water vapor is invisible or in a visible form like a cloud. Water vapor in the atmosphere in a transpearent way is just like CO2, it absorbs infrared light. However, water in the form of pools on the ground, ice, snow, or clouds, reflect a large percentage of the sunlight shining on them directly back to space (something like 20% to 90%). So it is impossible to say, without more study, whether adding water to the atmosphere will make it hotter by blocking infrared light or cooler by reflecting more of the Sun's energy away.

9. You body temperature is about 300 degrees Kelvin. At what wavelength do you radiate most strongly? What is the region of the electromagnetic spectrum is this? Do you understand now how a rattlesnake can bite you in the dark?

10,000 nanometers is infrared light. Rattlesnakes can sense infrared quite well with their tongues. Humans can sense infrared light with the nerves in our skin but we can't make out shapes or judge distances this way.

10. A light bulb radiates most strongly at a wavelength of about 3000 nanometers. How hot is its filament?

Wein's law again:

10b. If the light bulb from number 10 radiates 100 watts ( = 100 joules/sec) of photons, how many photons per second are radiated?

This one was easy!!!!!!! Given the wavelength of the photons from above, 3000 nm you just calculate how many joules each photon has and divide that into 100 joules per second.

13. Can you explain why the atmospheric layer containing ozone is much warmer than the layers above and below it?

Ozone (O3+) absorbs ultraviolet light. Light is energy. So the ozone layer is hot because of the energy it absorbs.

Essay 2:

1. Explain why the sky is blue during the day.

The sky is blue because air scatters blue light more than it scatters red light. So, when you look up at the sky (the sky, not the sun) you are looking at a portion of air. That air has scattered blue light so blue light is what enters your eyes.

2. Explain why the sky is red when looking towards the rising or setting sun.

Remember the blue light we talked about? That blue light was scattered OUT of the light from the sun. So when we look towards the Sun when it is at a low angle so its light is passing through a lot of air (like around sunset or sunrise) we are seeing "blue depleted" light -- which leaves RED light.

Chapter 4:

Page 140, Questions for review:

1. Why is the Earth not perfectly round?

The Earth is not perfectly round for at least three reasons. The first reason is that the Earth is somewhat flexible so it bulges outwards at the equator because of its rotation. The second reason is that the land masses are not distributed evenly and their weight presses down on the Earth, "dimpling" it slightly. The third reason is because geologic processes keep thrusting up mountains and erosion keeps digging out valleys so the Earth cannot be perfectly smooth.

5. What is the relation between rising and sinking material in the Earth's interior and subduction and rifting?

Subduction and rifting are the sinking and rising, respectively, of land masses at plate boudaries. These slow motions are caused by the convective motion of the underlying material driving the crust material above because it just floats on the lower layers.

6. When it is winter in Australia, what season is it in New York? Is it April in Paris?

When it is winter in Australia the south pole of the Earth is pointed away from the Sun so the north pole must be pointed towards the Sun making it summer in the Northern hemisphere where New York is located. Since Paris is also in the Northern hemisphere it must be summer there too.

7. What is precession? What are some of its possible consequences?

Precession is the slow wobble of the Earth due to the fact that the Earth is not perfectly round and therefore the Sun and the Moon's gravitational pull is somewhat stronger on the equator of the Earth than elsewhere. A "torque" like this will cause any rotating object to wobble. The period of one complete precesssion cycle is almost 26,000 years.

A consequences of the precession cycle is that the position on the Earth's orbit around the Sun where winter (in the North) is now will be where summer occurs in 13,000 years. This slow drift of the seasons prompted the Catholic church to call for the implementation of a new calendar called the Gregorian calendar which accounts for precession.

15. If the Earth rotated more slowly would you expect it to have as strong a magnetic field?

No it would probably weaken. The Earth's magnetic field is due to a combination of two factors: Earth's relatively high iron content and Earth's relatively high rotation speed. If you reduced either factor you should expect the magnetic field's strength to be reduced.

Page 141, Thought questions and problems

1. Given that Pluto's mass is 1.3 x 1025 grams and its radius is 1.1 X 108 centimeters, what is its average density? Does this indicate that Pluto has a large iron core like the Earth? Why?

With a density of only 2.5 gm/cc compared to Earth's 5.5 gm/cc, Pluto must have much less iron in its core, as a percentage of all material, than Earth has.

6. How does the eventual acceptance of the plate tectonic theory illustrate some aspects of the scientific method?

Over time the plate tectonic theory had to survive scientific tests. As we learned more about the Earth's interior and more bits of the fossil record were discovered it was found that the plate tectonic theory was consistent with all the new data. Identical land animal fossils on several continents implied that these continents were once closer together which implies that the continents move. The discovery of the mid ocean rifts showed that new material is flowing up towards the surface while the discovery of the subduction zones shows where the material sinks below. As more data supports a theory and less contradicts it, the theory becomes "accepted."

7. Astronomers are still uncertain about how the Earth's atmosphere formed. How does this illustrate the workings of the scientific method?

The problem with our current models is that there is not enough data to allow us to determine which of the popular models are best. A model may come to be accepted if new data supports it, while at the same time contradicting other models.

Essay 3:

Page E3-16, Questions for review:

1. What is meant by collecting area? How does it affect the ability to see faint objects?

Collecting area is the area over which a telescope focuses and collects light from a particular object. Generally this is the size of the opening of the telescope. The greater the collecting area, the more photons per second the telescope can collect from the area of interest. Having more collecting area reduces the amount of time for any exposure to be made. For really faint objects having more collecting area can bring the object above the observing threshold of the equipment you have, making it possible to detect it.

2. What is resolution of a telescope? What physical process limits it?

The resolution of a telescope is the telescope's ability to determine if two points are seen as two points or one smudgy point. Resolution, or resolving power is measured as an angle below which differentiation cannot be made.

The resolution of a telescope is a consequence of the wave nature of light. Because waves can add to each other, or cancel each other, in a process called diffraction, the aperature of the telescope must be as large as possible compared to the distance to the objects and the wavelength of the light to give the best performance. An equation which describes the resolution of a telescope is

Note that for a particular size of telescope resolution gets better if you look at shorter wavelengths. At a particular wavelegnth resolution improves if you increase the diameter of your telescope.

4. What is the difference between a reflecting and a refracting telescope?

A reflecting telescope uses the reflection of light as it's method of focus.

A refracting telescope uses the refraction (or bending) of light as its method of focus.

5. What are some reasons for using mirrors rather than lenses in telescopes?

To improve resolving power you want your telescope as wide as possible. Lenses larger than one meter are not really feasable while 10 meter mirrors have been built successfully. Lenses focus different colors (wavelengths) of light different places (chromatic abberation) making good imagery difficult. Mirrors don't care about the wavelegth.

8. What is meant by active optics?

Active optics are where you manipulate the mirrors and lenses in your telescope to compensate for the swimming effects in your images caused by the motions of the gases in the atmosphere. These techniques have become possible with the advent of cheap high speed computers.

Page E3-16, Thought questions and problems:

5. Compare the collecting power of a telescope with a 10-centimeter (about 4-inch) diameter mirror to that of the human eye. (Take the diameter of the pupil of the eye to be about 5 millimeters.).

So the 10 cm telescope has 400 times more collecting power than the human eye.

6. Estimate your eye's resolving power by drawing two lines 1 millimeter apart on a piece of paper. Put the paper on the wall and then step back until the two lines appear as one, measuring that distance. From the distance and the separation of the lines (1 millimeter), estimate their angular separation. How does your result for the eye's resolving-power compare with that calculated from the resolving power formula, using a pupil diameter of 5 millimeters and a wavelength of 500 nanometers?

I found that I could see the lines as two out to about 2 meters. To find the angular resolution you think of the 2 meters and the 1 mm separation of the lines as making a long, skinny triangle.

So the resolution of my eye is about 100 arc-seconds. If we use the resolution formula:

We find that the theoretical resolution of the human eye is

This is much better than I had achieved. So I was seeing at only one-fifth of the eye's theoretical capability.

7. Can the unaided eye resolve a crater on the moon whose angular diameter is 1 arc-minute (= 60 arc seconds)? (take the pupil diameter to be 5 millimeters and the wavelength of the light to be 500 nanometers)

I can resolve 100 arc seconds. If craters are 60 arc seconds I'd bet that there are people whose eyes are good enough. 60 arc seconds is certainly within the 20 arc second maximum capability of the eye.