Astronomy

Homework

# Scholars Online Astronomy - Chapter 3: The Motions of the Moon

## Homework

Reading: Astronomy, Chapter 3: Eclipses and the Motion of the Moon

##### Study Notes: notes on your assigned reading from the text
• Section 3.1 — Lunar Phases. Be sure that you know the difference between emitted light and reflected light. Technically, anything that puts out more energy than it can absorb and redirect from external sources emits light. Jupiter is the only object in the solar system that does this besides the Sun, so astronomers might consider it a protostar. You should understand the terms for the lunar phases and when and where the Moon is for each phase. Spend some time with a light for the Sun, a partner for the Moon, and yourself as the Earth and practice predicting where the Moon will be relative to the Sun, and the times of day that you can see it, for each of the major phases.

Remember that you have two motions to worry about: the observer's position on the Earth as the Earth rotates on its axis, and the Moon's position relative to its source of light, the Sun, and to the Earth. Be sure that you understand the difference between the synodic month and the sidereal month and why it occurs.

• Section 3.2 — Lunar Orientation to Earth. Again you may want to use an accomplice to visualize this properly. The Moon keeps a face to Earth, so it has to rotate once on its axis as it moves around the Earth. One of the very difficult things about astronomy is that it demands that we visualize our position in space even as we move, so these exercises, the SN planetarium, and actual observations will help you get more comfortable envisioning the actual motions. Even if it means you have to bribe siblings with cookies, take the time to go through modeling the lunar motions!
• Section 3.3 — Eclipses occur when the Moon is on the nodes of its orbit. The "nodes" are the points where the Moon's orbit crosses the solar ecliptic. When the Moon is on a straight line to the Sun, its position in its orbit intersects with the Sun's position on the ecliptic. If the Moon is in another part of its orbit relative to the nodes, it will cross above or below the Sun's position, and no eclipse can occur. Study figure 3-6 and make sure that you understand how the Moon's position in its orbits relative to its nodes.
• Section 3.4 — Lunar eclipses occur when the Moon passes through the Earth's shadow, which has two parts. From the umbra, no part of the Sun can be seen; the Earth blocks it out entirely. From the penumbra, some part of the Sun can be seen; the Moon experiences a "partial solar eclipse". Because of the Earth's atmosphere, some red wavelength Sunlight is bent into the umbra, and the Moon receives this filtered red light.
• Section 3.5 — Solar eclipses occur when the Moon passes between the Sun and the Earth, so that from some part of the Earth, at least part of the Sun's light is blocked by the Moon. If the entire face is blocked, the eclipse is total; if only part of the face is blocked, the eclipse is partial. If the Moon is at apogee (far from the Earth), its disk is too small to cover the entire solar disk, and we get an annular eclipse.
• Section 3.6 — Distances based on Eclipses. The pattern of eclipses is driven by the periods of the Moon's orbit about the Earth, the rotation of the nodes, and the rotation of the apsides (the points of apogee and perigee). If you put the three periods together, they repeat every 18 years, 11 days, and 8 hours. This means that the same type of eclipse occurs during with that period -- other eclipses occur within the period, obviously. Can you find pairs of eclipses with the Saros cycle period in figure 3-13 that have the same pattern, shifted 1/3 of the globe west? A second point for this section: how did Aristarchus figure the distances to the Moon and Sun? Why was he incorrect?

### Key Formulae to Know

• The Saros Cycle

Eclipses repeat when the nodes and phases of the moon line up. The type of eclispe (annular vs full) and eclipse length will depend on the Moon's position relative to perigee or apogee.

The synodic month (phase to same phase) is 29.53 days (the lunar month).

The line of nodes shifts all the way around the lunar orbit in 346.6 days (the eclipse year.)

We need a situation where X lunar months = Y eclipse years. At that time, the eclipse cycle will restart. From observation, ancient astronomers determined the Saros cycle as 223 lunar months = 19 eclipse years = 6485.3 days, or 18 years, 11 days, and 8 hours.

If an eclipse occured on August 11, 1999 over Europe, a similar eclipse should have occured 18 years, 11 days, and 8 hours later.
1999 + 18 = 2017
August 11 + 11 days = August 21 (adjusted for 2000 not being a leap year)
8 hours means the eclipse will occur 1/3 of the way around Earth to the west, i.e., over the US.

### Web Lecture

Read the following weblecture before chat: Lunar Eclipses

### Study Activity

These tasks should be possible on any computer-based planetarium program. You will need to review the user guide for your program to identify exactly how to do each one.

Set your planetarium program to look down on the Earth-Moon system from above the Earth's North Pole. Allow the program to run so that the Moon orbits the Earth at least once and try to stop it when the Moon is at New, First Quarter, Full, and Third Quarter phases. What time of day is it visible in first quarter? in third quarter? Which direction must you look to see it?

Now set your location for your home, and run the planetarium program through the same period. How does the moon appear to move against the background sky over the course of a month? Where does it rise (or set)? Does this point change? How does rising or setting time correspond to the phases of the Moon?

Use the NASA eclipse site (below) to identify the date and time of a solar eclipse and a lunar eclipse. Set your planetarium program to observe the Moon from two hours before he start of the eclipse until two hours after it is over. Which direction does the Moon move across the face of the sun in a solar eclipse? Which direction does it move through the Earth's shadow in a lunar eclipse?

Optional websites: Visit NASA's Eclipse site.

• Will there be any solar eclipses during our course this year (September to June)? Where will the eclipse(s) [if any] be visible? HINT: look at the map of the moon's shadow. Which direction does the shadow move (based on the times of totality)? Will it be a total eclipse, or annular?
• Check out the time for the total lunar eclipse on 10 December 2011 for your location. Will you be able to observe a complete eclipse? The beginning or end of the eclipse?
• If the ecipse will not be visible from your location, check out the possibility of following the eclipse online.

### Chat Preparation Activities

• Essay question: The Moodle forum for the session will assign a specific study question for you to prepare for chat. You need to read this question and post your answer before chat starts for this session.
• Go over the list of Key Words and Key Ideas at the end of the chapter. If you don't remember the definition of the key word, review its use (the page number on which it is explained is given).
• Read through the Review Questions and be prepared to discuss them in class. If any of them confuses you, ask about it!
• Mastery Exercise: The Moodle Mastery exercise for the chapter will contain sections related to our chat topic. Try to complete these before the chat starts, so that you can ask questions.

### Chapter Quiz

• Required: Complete the Mastery exercise with a passing score of 85% or better.
• Go to the Moodle and take the quiz for this chat session to see how much you already know about astronomy!

### Lab Work

Read through the lab for this week; bring questions to chat on any aspect of the lab, whether you intend not perform it or not. If you decide to perform the lab, be sure to submit your report by the posted due date.