Download Due Date: Thursday, September 21, 2006

Homework, September 14, 2006
AST110-6
Due Date: Thursday, September 21, 2006
1. Chapter 3, Problem 8. Clearly state each of Kepler’s laws of planetary motion. For
each law, describe in you own words what it means in a way that could be understood
by almost anyone. (15pt)
2. Chapter 4, Review Questions 1, 2, and 3:
a. How does speed differ from velocity? Give an example in which you can be
traveling at constant speed but not at constant velocity. (5pt)
b. What do we mean by acceleration? Explain what we mean when we state an
acceleration in units of m/s 2. (5pt)
c. What is the acceleration of gravity? If you drop a rock from very high up,
approximately how fast will it be falling after 4 seconds? (5pt)
3. Chapter 4, Review Questions 7. State each of Newton’s three laws of motion. For
each law, give an example of its application. (15pt)
4. Stellar Parallax: One of the reasons that Sun-centered model of the solar system was
not accepted before Galileo’s time was that stellar parallax was not detected. Galileo
was not able to measure any appreciable stellar parallax either. The changes in the
position of near-by stars (with respect to very distant stars) can be calculated from a
formula similar to the one we used to calculate the angular size of the Sun and the
Moon in homework#3.
S [deg] = 57.29  D  d,
where S is the change in the angular position of the star in six months, d is the
distance between Earth and the star, and D is the diameter of Earth’s orbit around the
Sun. That is, D = 2 AU, or approximately 300 million km. Calculate the stellar
parallax of the nearest star, Alpha Centauri in degree to see for yourself how
difficult it is to measure stellar parallax. The distance d from the Sun to Alpha
Centauri is about 4.5 light-years. Make sure you use the same unit of distances for d
and D when you do you calculation. (15pt)
5. Phases of Planets: Planets (as viewed from Earth) can go through phases just like our
Moon. However, not all the planets show changing phases. A graphical method to
determine if you can see difference phases of satellites and planets is the following.
We will use the phases of the Moon to illustrate this method.
1. Make a drawing of the three object involved. Since the distance between the Earth
and the Moon is much smaller than the distance between the Sun and the Earth,
we will put the Sun far away from Earth, and put Earth and Moon relatively close
together in the drawing.
2. Put the Moon at the position where you want to determine its phase. Draw the
illuminated side of the Moon. It should be the side facing the Sun.
3. Draw a line M-E from the Moon to the Earth.
4. Draw a line M-S from the Moon toward the Sun.
5. Repeat steps 2 to 4 for the Moon at different positions.
The figure below shows the situations for full and quarter Moon. After you have done
this excise for a few positions, you should be able to make the following conclusions:
1. If the angles A between M-E and M-S is large (say, more than 45 degrees), then
we can expect to see a Moon that’s not completely illuminated.
2. When A is small, we have a full Moon.
3. When A is about 180 degrees, we have a new Moon.
4. If the angle A changes substantially as you move it around your observing
position (the Earth), then we can see the phase changes.
Problems:
a) Show how Galileo could observe the phase of Venus changes from Earth with his
telescope. Make a drawing to show the three positions of Venus when it is in
a. Full phase, (5pt)
b. Quarter phase, and (5pt)
c. New phase. (5pt)
The distance between the Sun and Venus is about 0.7 AU.
b) Use this method to show that from Earth, we always see a ‘full’ Jupiter. Make a
drawing to show Jupiter at three different positions in the Sun-Earth-Jupiter
system:
a. when Jupiter is in the line connecting Sun and Earth, with the Earth in
between Sun and Jupiter, (5pt)
b. when the Sun-Jupiter line makes an angle of 45 degrees with the SunEarth line, (5pt) and
c. when the Sun-Jupiter line makes an angle of 90 degrees with the SunEarth line. (5pt),
and show that in these cases, we always see the fully illuminated side of Jupiter.
The distance between Jupiter and the Sun is about 5AU.
c) Can you go to another planet in the solar system and see the phase of Jupiter
changes from full to quarter to new? Which planet or planets (use the old
definition of planets)? (10pt)
Quarter Moon
M-S
A
E-M
M-S
A
Sun
E-M
Earth
Full Moon