AST 3043 HOMEWORK PROJECT

Fall 2008

Almost all the parts of the project involve the use of the calendar pages for the twelve months of 2008, which are found on pages 118 through 141 of the Old Farmer's Almanac 2008. The left-hand pages are explained on pages 110 and 111. Note that on the left-hand page for each month there's a table giving the dates and times of the Moon's phases. Also, the leftmost column of the main table on the left-hand page gives the number of each day in the year starting from 1 on January 1. To find the interval between two dates, simply subtract the smaller day number from the larger one. For example, between June 25 (day number 177, see p. 128) and February 27 (day number 58 on p. 120) there are 177 - 58 = 119 days. Additionally, the next-to-last column in the main table on the left-hand page gives the Moon's place for each day in the form of a three-letter abbreviation for the constellation (star grouping) that it is located in. The right-hand calendar pages are explained on pages 112 and 113. On page 113 there's a table identifying the symbols used for the Sun, Moon, and planets as well as the configurations: conjunction, opposition, ascending node, and descending node. There's a glossary on pages 106 and 107 which defines these terms, but we'll cover them more fully in lecture. The data on eclipses are to be found on p. 98. (Some of the odder things in the right-hand calendar pages are defined on pp. 142 and 143.)

For this project you'll look up various dates and calculate the intervals between them. The idea is that if you were looking at the sky without a telescope or any accurate timekeeping device you would only be able to tell when things happened to within a day. For example, with the naked eye it's hard to tell exactly when the Moon is full even to the nearest day; I've chosen a quarter phase instead because in reality it should be easier to time. Naturally in the real world weather would interfere, resulting in some of the dates being missed. Furthermore, only over periods of time much longer than a year would you be able to reckon the lengths of some astronomical cycles. Most of the cycles I've chosen are easy to follow over a year. In addition you'll estimate the uncertainty in your value for the synodic month.

The project consists of six parts. The detailed instructions for each are given below. Remember that I'm not interested in fancy presentations; handwritten is fine so long as I can read everything and it's clear what each number is. Be sure to use labels in tables.

The due date for this project is Thursday, Nov. 13 by the end of the class period. There's a late penalty of 10 (ten) percentage points for every day or part thereof that the project is turned in after the deadline. I recommend that you not start on it until after I've lectured on eclipses, which is the last part of the material covered in this project. That will happen well into the term. The project shouldn't take more than a couple of hours at most to complete, but don't put it off until the day before it's due; you might have questions.

1. Look up the dates (but not the times) of third or last quarter Moon for each month from January 2008 through December 2008 in the appropriate table. Note that there can be more than one for a given month since the synodic month is less than 30 days, whereas the typical calendar months are 30 or 31 days long. List the dates in a column, and next to each put the day number so that there are two columns. Then subtract the day numbers to find the intervals between the successive dates of third or last quarter, and list those to the right of the day numbers in a third column. Draw a horizontal line below the columns. Then average the intervals and write the average rounded off to exactly two (2) decimal places under the horizontal line. There's a link here to a sample to show how it's done. You don't need to write anything else, but you should notice how your value compares with the (average) true synodic month of 29.53059 days. You should also observe how there's no obvious pattern in the intervals; for instance, they don't necessarily simply alternate between two values. After the projects have been turned in I plan to show the true behavior of the intervals. By the way, if you have an interval that's about twice as large as the others it means that you've missed a date and need to go back and find it.
2. In the next-to-last column on the left-hand calendar page look for the first appearance of the abbreviation TAU (for the constellation of Taurus) in each group of two or three. Note the date and day number for that appearance. Keep in mind that it is possible for the Moon to pass into a given constellation two rather different times in a given calendar month since the sidereal month is 27 days, substantially shorter than a calendar month. Also, watch out for those times when the constellation appears at the beginning or end of a month -- it may connect with the end of the previous month or the beginning of the next month. You always want to pick the first of a group (if there is one). List those dates in one column and the day numbers in the next column. Then find the intervals between them. Again draw a horizontal line under the columns. Then average the intervals and write the average, again to two decimal places, under the line. Notice how your value compares with the sidereal month of 27.32166 days.
3. Look up the dates when the Moon is at its descending node in the tables on the right-hand calendar pages. (Remember, the symbols are given on page 113. Be sure not to get the symbols for the ascending and descending nodes mixed up.) As before, list the dates in a column with the corresponding day numbers in the next column. Find the time intervals between successive occurrences of this node by subtracting the day numbers and place those in the third column. Then draw a horizontal line under the columns, calculate the average of the intervals to two decimal places, and write it under the line. Notice how the average compares to the nodical (draconitic) month of 27.21220 days.
4. Look up the dates at which Mercury is at greatest western elongation in the tables on the right-hand calendar pages. Be sure to include only the western elongation ("greatest elongation W." but not "greatest elongation E."). List those dates in a column and the corresponding day numbers next to them. Then find the intervals between the dates and write those in a third column. Draw a horizontal line under the columns. Calculate the average of the intervals to one decimal place this time and write it below the line. Notice how the average compares with the synodic period of Mercury, which is 115.88 days.
5. Find the dates and day numbers for the two lunar eclipses in 2008 using the table on page 98. List them in a column, and next to them write the corresponding day numbers. Find the interval between them, and write it next to the other two columns. Then find the dates of the two solar eclipses, and list those beneath the dates of the lunar eclipses. List the day numbers for the solar eclipses next to the dates, find the interval between them, and write that beneath the intervals for the lunar eclipses. Notice how these values compare with the eclipse intervals we see in the Dresden Codex of the Maya, namely 148 and 177 days. (HINT: You don't necessarily have both intervals represented. Remember the lecture on the saros cycle.)
6. An important part of estimating parameters from observations in modern science is finding the uncertainty of the estimate. I want you to estimate the uncertainty of the value you found for the nodical month in part (3). You do this by first subtracting the mean value you found from each value in the third column; the differences are what we call residuals. Square each residual, and add the squares together to get the sum of squares. Take the number of residuals you have -- call it N -- and multiply it by (N - 1). Then divide the sum of squares by that product and take the square root of what you got. That number is a measure of the uncertainty in your estimate of the sidereal month. Subtract the true nodical month from your estimate and divide the difference by the uncertainty; the ratio would be expected to be between -2 and +2. There's an example using the data from the sample page in part (1) for you to go by. You should be sure to use the true value for the nodical month rather than that for the sidereal month that is used in the example. Also, the number of residuals N for the nodical month may not necessarily be the same as in the example, which is for the sidereal month. Again the answers should be to two decimal places, rounded.

NOTE: You are not on your honor to do your own work on this project with absolutely no help from anyone else. However, I encourage you to at least try to do it on your own before you seek someone else's help. Then, if you need to or just want to check your work, you can get together with someone or a group of classmates. You should be aware that I'm glad to help you with it or glance over it on any day before the due date. All I ask is that you not simply copy someone else's results. I want you to root around in the almanac on your own to find these dates, and I hope you'll notice some other things therein. You may even find it amusing, as I do. Check out "Anecdotes & Pleasantries" on p. 252. Or there's "The Wonders of Blunders" on p. 180. You'll find some things you may not know about how to wash your hands on p. 150 and an article about Pennsylvania Dutch hex signs on p. 152. There's an article by Bob Berman on getting and using a telescope for amateur astronomy, "Through the Looking Glass." Just don't put any stock in the astrology you find in the almanac!