After taking six weeks of data on the Moon, it is now time to begin analyzing the data. For the first part of the analysis, you will estimate the synodic period of the Moon in three different ways. Record all of your answers on the worksheet (Word, PDF).
You recorded the phase of the Moon in your observations. We know that it takes less than six weeks for the Moon to go through all of its phases. The observations started when the Moon was the crescent phase and they ended just after the full phase. You want to estimate the amount of time it took to go from a first quarter Moon to the next first quarter Moon. Choose two dates, one near the start of the observations and one near the end, when the Moon was first quarter. If you don't have observations of this phase, estimate the date based on observations of adjacent phases and by checking Stellarium around those dates. Record these dates on the answer sheet. Count the number of days elapsed from one phase to the next and this will give you the first estimate for the synodic period.
You will now determine the synodic period using the rise times you estimated for each observation. Open this website to see the moonrises for each month of the year.
Note that some dates don't have moonrises because the Moon rose before midnight on the previous day. Daylight Saving Time affects these times, so you will see a jump ahead an hour on the second Sunday in March and a drop of an hour on the first Sunday in November.
Please check the accuracy of your estimates by comparing to the actual rise times. Choose one rise time from each week that you think is the most accurate. Write your chosen dates and the corresponding rise time estimates in the spaces provided on the data sheet.
Once you've chosen your six dates and times, you will need to determine the number of days and minutes between adjacent rise times. To help with this, use the following calculator. The calculator will prompt you if any times appear ambiguous. You need to include AM/PM with 12-hour time and you need to press Cancel if you are using 24-hour time. If you are using Firefox, you must use 24-hour time.
Use the information you get from the calculator to fill in the first two blank columns in the next chart on your data sheet. For the last column, you need to divide the change in rise times in minutes (the second blank column) by the number of days (the first blank column). Here is an example:
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Let's say that you had the following data:
For the first two dates, the time calculator will tell you that the time difference is "8 days, 540 minutes." Fill this information into the first two blank columns of the chart. For the last column, take 540 minutes and divide it by 8 days:
Follow the same procedure for the second and third dates and third and fourth dates. Your table would look like this:
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Find the average of the five values you calculated in the last column. For five numbers, you can find the average by adding the numbers together and dividing the answer by five.
During one synodic period for the Moon, the rise time will change by 24 hours or 1,440 minutes. Take 1,440 minutes and divide it by the average change in rise time per day which you found above to find the synodic period in days.
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Let's finish our example:
Average Change in Rise Time Per Day = (67.5 + 30 + 50 + 45 + 34.3) / 5 = 226.8 / 5 = 45.4 min/day Synodic Period = 1,440 min / 45.4 min/day = 31.7 days |
Before moving on, please perform a self-check. Does your synodic period make sense? Is it close to the length of a month? If not, you should check your work. Ask your classmates or your instructor for advice.
For our final estimate, we are going to use data from Stellarium. Start the Stellarium program.
The shortcuts given the first lab can also be in the PDF found here. You may have to hold "Function" with some of these keys. http://natsci.parkland.edu/ast/101/shortcuts2.pdf
Remove the atmosphere and the ground to view the entire night sky without any interference. Display the equatorial grid of the celestial sphere, showing lines of right ascension and declination. In order to keep the view relatively stable, we need to switch the view from an azimuthal mount to an equatorial mount. This will remove the tilt from the equatorial grid and the two telescopes button next to the Saturn button will stay lit up.
Set the date to the first date you observed the Moon. Use the search window to find the Moon. Make sure you have selected the Moon and it stays in center of the screen. Type "space" if you need to center the Moon. Adjust the time in reverse until the Moon and the Sun are vertically aligned. (Remember the time-changing shortcuts in the table above.) It should be no more than a couple days. The Moon rarely passes directly in front of the Sun, so the new Moon phase is defined by them having the same right ascension (RA). If you select each object, they should have an RA (of date) no more than 1m apart. This marks the beginning of the new synodic period. Record the first date and time on the sheet.
By now, you may have an idea when the Moon will be in the new phase again. Move the time forward so the Moon returns to this configuration with the Sun at the end of the synodic period. Again, make sure the Moon is at the center of the screen. When you've found the Moon at the same right ascension as the Sun again, record the second date and time on the sheet.
Take the dates and times you've just determined and plug them into the calculator above to find the number of days and minutes between your two observations. Record the information on your answer sheet.
Congratulations. You've finished the first page of your analysis. Please check your answers with your lab instructor before moving to the next page.
You just found three different estimates for the synodic period: one using phases, one using rise times, and one using Stellarium. We'll determine how accurate your estimates are by calculating a percent error with the actual synodic period, 29.5306 days. Start by converting each of the previous values into minutes, considering that there are 1,440 minutes in a day. One or more of your estimates will be in terms of both the number of days and minutes. Take the number of days and multiply it by 1,440 and then add the number of minutes to it. Consider the following example:
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Example:
Let's say that your estimate is 14 days, 342 minutes. The estimate in minutes would then be: |
Use the following equation to calculate the percent errors. Note: subtract before dividing, and the vertical bars mean you calculate the absolute value by dropping any negative signs.
We will use Stellarium again to determine the sidereal period. Since the sidereal period is determined by the Moon's position relative to the stars, we will watch it pass through the constellations. We will use the same settings you used for the Stellarium estimate of the synodic period. If you closed Stellarium already, please follow the instructions above, beginning with "First, remove the..."
Set the date and time to the same date and observing time as your first Moon observation. Use the time of your observation, not your estimate for the rise time of the Moon. Find the Moon using the search window. Turn on the constellation boundaries and the constellation labels. Turn off the equatorial gird.
Go through all 42 days of your observations and record any new constellation where you find the Moon on the data sheet under "...constellations traversed by the Moon..." The Moon may spend only a few hours in one constellation, so you may want to change time by hours instead of days.
We will estimate the sidereal period by looking at the time it takes for the Moon to go through the constellations. Start by finding a date near the beginning of the observations during which the Moon was in the constellation Sagittarius. Write down this first date under "Date 1" on the data sheet.
Now, find a second date in which the Moon was in Sagittarius after having made a complete cycle through the constellations. Remember that it takes several weeks for this to occur, so your second date should be at least three weeks later than your first date. Once you have chosen your second date, write it on the data sheet under "Date 2". Determine the number of days elapsed from your first date to your second date to get your first value for the sidereal period.
Repeat the above procedure for the constellations of Capricornus, Aquarius, Pisces, and Aries.
Take your five estimates for the sidereal period of the Moon and calculate the average of them (remember that you get the average of five numbers by adding them together and then dividing the answer by five). The actual sidereal period of the Moon is 27.322 days. Use the equation below to calculate a percent error. Record the answer on the data sheet.
Congratulations! You've now finished all of the analysis. Be sure to turn in your completed data sheet to your lab instructor or in the dropbox on Cobra.