|
ASTRONOMY - Summer 1999
Dr. Robert Gardner Chapters 1-5 Homework Solutions |
Chapter 1 - Observing the Sky: The Birth of Astronomy.
1. Where on Earth could you observe all of the stars during the
course of a year? Answer: From any location on the equator.
What fraction of the sky can be seen from the North Pole?
Answer:
1/2 (that part above the celestial equator).
5. Explain why we see retrograde motion of the planets, according to
both geocentric and heliocentric cosmologies. Answer
(geocentric):
The planets
move on epicycles which lie on the deferents. As the planets are on the
part of their epicycle closest to the Earth, they are moving in a direction
opposite to that of their larger motion on the deferent. This "opposite
direction" motion makes them appear to move backwards. (See Figure 1.12.)
Answer (heliocentric): The Earth moves faster than the outer planets
in its orbit around the Sun. Therefore the Earth overtakes and passes the
outer planets and this makes them appear to go backwards in their orbits.
(See Figure 1.11.)
7. In what ways did the work of Copernicus and Galileo differ from
the traditional views of the ancient Greeks and of the Catholic
Church?
Answer: The traditional view was one of a geocentric universe with
planetary motion as described by Ptolemy and the Earth stationary.
Copernicus theorized a
Sun-centered universe with the Earth as simply another planet which rotated
on its axis and orbited the Sun. Galileo found craters and mountains on
the Moon, contradicting the traditional view that it is a perfect sphere.
Galileo observed four moons orbiting Jupiter, in contradiction to the
traditional view that everything orbits the Earth. In a nutshell,
Copernicus and Galileo moved the Earth from the center of the universe!
8. Show with a simple diagram how the lower parts of a ship
dissappear first as it sails away from you on a spherical Earth. Use the
same diagram to show why lookouts on old sailing ships could see farther
from the masthead than from the deck. Would there be any advantage to
posting lookouts on the mast if the Earth were flat? (Note that these
nautical arguments for a spherical Earth were quite familiar to Columbus
and other mariners of this time.) Answer: The lines in the diagram
show the lines of site of two observers, one with low elevation and one
with high elevation. Notice that the one with a higher elevation can see
farther and that in both cases, the bottom of the ship disappears over the
horizon before the top of the ship does. If the Earth were flat, an
observer at ground level could see forever (barring obstructions).
Chapter 2 - Orbits and Gravity.
18. Look up the revolution periods and distances from the Sun for
Venus, Earth, Mars, and Jupiter. Calculate D3 and
P2 (in units
specified in the text) and verify that they obey Kepler's third Law.
Answer: Consider the data in Appendix 7:
| Planet | Period (P) | Distance from Sun (D) | D3 | P2 |
| Venus | 0.61521 | 0.7233 | 0.3784 | 0.3909 |
| Earth | 1.000039 | 1.0000 | 1.0000 | 1.0001 |
| Mars | 1.88089 | 1.5237 | 3.5375 | 3.5377 |
| Jupiter | 11.86 | 5.2028 | 140.84 | 140.66 |
Chapter 3 - Earth, Moon, and Sky. 3. Make a table showing each main phase of the Moon and roughly when the Moon rises and sets for each phase. During which phase can you see the Moon in the middle of the morning? In the middle of the afternoon? Answer:
| Phase | Rise | Set |
| New | 6 am | 6 pm |
| Waxing Crescent | between 6 am and noon | between 6 pm and midnight |
| 1st Quarter | noon | midnight |
| Waxing Gibbous | between noon and 6 pm | between midnight and 6 am |
| Full | 6 pm | 6 am |
| Waning Gibbous | between 6 pm and midnight | between 6 am and noon |
| 3rd Quarter | midnight | noon |
| Waning Crescent | between midnight and 6 am | between noon and 6 pm |
Chapter 4 - Radiation and Spectra.
4. Where in an atom would you expect to find electrons? Protons?
Neutrons? Answer: The electrons are in a cloud around the nucleus,
the protons and neutrons are in the nucleus.
Chapter 5 - Astronomical Instruments.
7. Why do astronomers place telescopes in Earth orbit? What
are the advantages for different spectral regions? Answer:
Being in
orbit puts a telescope outside of Earth's atmosphere. This has a number of
advantages including: there are no "cloudy days" in space, there is no
twinkling of starlight and there is therefore better resolution, we can see
fainter stars, there is no sky glow, and we can see wavelengths that do not
penetrate the Earth's atmosphere (like gamma, X-ray, and ultraviolet
wavelengths).
20. The HST cost about $1.7 billion for constuction and
$300
million for its Shuttle launch, and it costs $250 million per year
to operate. If the telescope lasts a total of ten years, what is the cost
per year? Per day? If the telscope can be used just 30 percent of the time
for actual observations, what is the cost per hour and per minute for the
astonomer's observing time on this instrument? Answer: With a 10
year lifetime, the total cost would be
Return to Bob Gardner's NSTCC astronomy homepage.