Homework #1 Solutions

Astronomy 100

Due 17 September 2002

1. (Review #5, page 8) Which is the outermost planet in our solar system? Why does that change?
   

   Currently, Pluto is the outermost planet in our solar system. The outermost planet alternates between Neptune and Pluto due to the eccentric nature of Pluto's orbit. Because of this eccentricity, for a short period during Pluto's orbit it is closer to the sun than Neptune.

2. (Review #5, page 37) If Earth did not rotate, could we define the celestial poles and celestial equator? The ecliptic?
   

   We could not define the terms for the celestial poles or the celestial equator. Since the North and South celestial poles are defined as extensions of Earth's rotation axis, without rotation, it would not be possible to define these. Since the celestial equator is halfway between the celestial poles, we could not define this either. However, the definition of the ecliptic would not change. This is the apparent path of the sun due to the Earth's orbit around it. Even if the earth did not rotate, it would still orbit the sun.

3. (Problem #7, page 37) Identify the phases of the moon if on March 21 the moon were located at (a) the vernal equinox, (b) the autumnal equinox, (c) the summer solstice, (d) the winter solstice.
   

   The key point to notice is that March 21 is the vernal equinox. This means the sun will be at a specific point, in relation to the heavens.
   a) If the moon is also at the vernal equinox, this means the Sun will be behind the moon. The phase of the moon in this case is New Moon.
   b) If the moon is at the autumnal equinox, it is directly opposite the Sun. This means that from Earth, we will see a Full Moon.
   c) If the moon is at the summer solstice, it is at right angles to the Sun. The phase of the moon will be First Quarter.
   d) If the moon is at the winter solstice, it is again at right angles to the Sun, but this time on the opposite side of the Earth. The phase of the moon will be Third Quarter.

4. (Review #2, page 62) Why did classical astronomers conclude that Earth had to be motionless?
   

   Classical astronomers argued that the Earth must be motionless for two main reasons. The first reason was because they could not observe parallax in the stars. They concluded that if the Earth moved, the stars should have a parallax. Secondly, if the Earth moved, we should feel it, like being on a merry-go-round. Additionally, we should feel a constant wind as the Earth moved.

5. (Problem #4, page 63) If a planet had an average distance from the sun of 10 AU, what would its orbital period be?
   

   To solve this problem, we need to use Kepler's Third Law: $P^2=a^3$, where $P$ is the period in years, and $a$ is the semi-major axis (essentially the distance) in AU.
   

   P² = (10 AU)³
   P² = 1000
   P = 31.6 years