AST 301
Spring 2003
Exam #1
1. The Sun and Moon have about the same apparent angular size, about 1/2
degree. The Sun is about 350 times bigger in diameter than the Moon.
a) How do the distances to the Sun and Moon compare? That is, which is
greater, and how many times greater? Explain your logic briefly.
If they appear the same even though the Sun is actually 350 times bigger,
the Sun must be 350 times farther away. (angular size ~ size / distance)
b) If the Moon were as far away as the Sun is, what would its angular
size be? (You can leave your answer as a fraction.)
If they were the same distance away, the ratio of their angular sizes would
be the same as the ratio of their sizes, or 1:350.
2. Consider a satellite orbiting the Earth in a circular orbit 200 miles
above the surface of the Earth.
a) Is the speed of the satellite changing during its orbit?
No. Not if the orbit is circular. Its direction of motion is changing, but
its speed is not.
b) Is the satellite accelerating? Explain briefly.
Yes. It is accelerating because its direction of motion is changing.
c) How does the force of the Earth's gravity on the satellite compare to
what it was before the satellite was launched?
It is only slightly smaller. It is a bit farther from the center of the
Earth, and gravity depends on the distance between the centers of the
objects.
d) If the satellite has a booster rocket and uses it to propel itself into
a higher orbit, will its speed be different when it is in a higher orbit?
If so, will it be bigger or smaller? What rule did you use to figure this
out?
It will be smaller. We are comparing speeds in two orbits, and Kepler's
3rd law says the speed is smaller in a bigger orbit.
3. My calendar says the Moon will be full on Sunday.
a) At about what time will the Moon rise on Sunday?
Around sunset. The full Moon must be opposite the Sun.
b) If there is an eclipse on Sunday, which type will it be, solar or lunar?
Explain why this type of eclipse might occur during a full Moon.
Lunar. That's when the Moon is in the Earth's shadow, which could occur
during a full moon.
c) In fact, there won't be an eclipse on Sunday. The next one won't be
until May. Why isn't there an eclipse this month?
The Moon's orbit is tipped so it might pass above or below the Earth's
shadow.
4. Describe one of the observations Galileo made that supported the
Copernican model of the universe, and explain how this observation supported
the Copernican model.
Three options:
1) He saw that Venus shows the phases expected if it orbits the Sun.
2) He saw the moons of Jupiter orbiting Jupiter (not the Earth).
3) He saw mountians on the Moon, so it is similar to the Earth.
5. The Sun has a surface temperature of about 6000 K, and emits visible
light with a typical wavelength of about 500 nm. Filaments in light bulbs
have temperatures of about 3000 K.
a) What is the typical wavelength of light emitted by light bulbs?
About 1000 nm. Wavelength goes as 1/temperature, so 2 times cooler means 2
times longer wavelength.
b) How does the energy of a typical photon from the Sun compare to the
energy of a typical photon from a light bulb? (Which is larger and how
many times larger?)
The Sun's photons typically have twice as much energy. Photon energy goes
as 1/wavelength.
6. Describe the spectrum from one of the gas lamps (tubes containing hot
gas) you saw in class. In particular, say how it differed from the
spectrum of the light bulb.
The light came out only at certain wavelengths. That is, it was in emission
lines, not a continuous spectrum like the light bulb.
7. Describe how the wave properties of electrons cause electrons in
atoms to have only certain allowed orbits. (The electrons can't be in
orbits of just any size, but only certain sized orbits occur.)
The circumference of the electrons' orbits must be right so that an integral
number of electron waves fit around an orbit.
8.a) Describe the path of the Sun across the Austin sky in December, and
compare that path to the path it follows in June. (Specifically, tell me
in what directions to look to see it rise and set, and how close it comes
to passing overhead.)
In December, the Sun rises in the southeast, passes across the southern sky,
and sets in the southwest.
In June it rises in the northeast, passes near overhead (just south of
overhead), and sets in the northwest.
b) Give the Copernican explanation for the different path of the Sun
across the sky in June and December.
The Sun appears to move with the stars during a day because of the rotation
of the Earth. As the Earth orbits around the Sun it is seen in front of
different stars at different times of year. In the summer it is in front of
stars that are north of the equator. In December it is in front of stars
south of the equator because the Earth's equator is tipped relative to the
plane of the Earth's orbit.
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