Mapping the Orbit and Phases of the Moon
Summary: Track the phases of the Moon, observe it's orbit around the Earth, measure its orbital period, and measure the angle between the plane of the moon's orbit and the ecliptic plane.
Needed Supplies: Observing log, pencil, star map SC001, crossbow, phase of the Moon template.
Start Date: You will have the greatest success with this lab if you follow the moon through 5-6 weeks. This means that you must start this lab by September 23, but stand a better chance of succesfully completing it if you start right away.
Due Date: October 31. Note, however, that it will be impossible to complete this lab if you don't start at least 5 weeks earlier– and you may need even more time if the weather does not cooperate.
General Description:
Look up! Observe the moon. Hints: if the moon is near 1st quarter or full moon phase, you will be able to make your observations in the early or late evening. If the moon is past full moon or near 3rd quarter, you will have to make your observations either very late at night or in the early morning. This lab requires only simple observations that take only about 10-15 minutes each night but reveals a surprising number of effects. To do this lab, you need to become familiar with the constellations and the use of star maps, a skill also developed in the Constellations and Bright Stars lab.
Frequency of observations: The Moon takes about 1 month to orbit the Earth. The goal is to observe the Moon during one full cycle. You may have to extend this by 1-2 weeks if bad weather prevented you from getting good coverage. You will need 8-12 well-spaced observations during the cycle (that's observing every 3-4 days or almost on every clear night), to get good coverage. Also, for the period after the full Moon, the Moon is visible only late at night or early in the morning. A bit of effort will be necessary to observe the later part of the cycle. It really isn't as much work as it may sound. Remember that each observation takes no more than 15 minutes! This is one of the most interesting labs in Introductory Astronomy.
Curious about why the Full Moon appears so large when it is rising? This is the famous Moon illusion, a well understood phenomenon.
Procedure
Go out and determine the position of the Moon with respect to the stars and constellations you can identify. Do this as accurately as you can. You can do this by careful "eyeballing" (to the nearest 1o or better) of the position if there are stars visible near the Moon or better still, using the crossbow to measure its angular separation from two stars. You should use the crossbow when observing during scheduled labs and "eyeball" when observing on your own time.
When using the crossbow: You need to choose 2 stars that are good, fixed references for measuring the position of the Moon on that particular night. Measure the separation 1) between the Moon and each of the two stars and 2) between the two stars (or another pair of stars in that same area of the sky). This latter measurement will allow you to figure out the scale of the star chart (i.e. how many mm correspond to 1o). You need to know this to plot the position of the Moon from your measurements.
Note: Star charts are like geographical maps. They are obtained by projecting a curved surface (a portion of a sphere) on a flat surface (sheet of paper). This inevitably leads to distortions, where the scale is not uniform across the entire map. This is why on many maps of the Earth (planispheres) Greenland appears much larger than South America, while in fact it is much smaller, as can be verified with a globe. For this reason, you should not assume that the same scale applies everywhere on the SC001 star map and you need to determine the scale near the observed position of the Moon for each crossbow observation. As you will see, this requires little additional work.
When "eyeballing" the position: It is difficult to do this when the Moon is rising or setting (i.e. low in the sky) as fewer stars are visible low in the sky and all the stars are on the same side of the Moon (the others being blocked by the horizon). As much as possible, make the observation when the Moon is well above the horizon.
Plot this position on your star chart (SC001) by sketching a small moon in its approximate phase at the correct location relative to the stars. If you used the crossbow, check your work by comparing your plotted position with what you see in the sky. Label the position with the date. See the binder of examples kept in the storage shed.
Using the templates provided for the phases of the Moon, draw the phase of the Moon precisely as well as the surface features you can see with your naked eye. Indicate the date and time next to your sketch. See the binder of examples in the storage shed.
In your observing log, record the date and time, weather conditions, phase of the moon, and the constellation in which the Moon appears. If you used the crossbow, record the names of your reference stars and all measurements. Add notes (including personal comments) as appropriate.
Outside of lab, use the star chart (SC001) to find the position of the Moon and of the Sun along the ecliptic (both in degrees) on the date of your observation. This is known as the ecliptic longitude. This is done by simply reading off the degree scale along the ecliptic (wavy curve on the map). The position of the Sun in the sky throughout the year is also shown along that curve. Example: Suppose that you observe the Moon very near the star Spica (in Virgo) on November 21. The Moon's ecliptic longitude would be 204o and the Sun's would be 238o.
Make a table of your observations. For each entry, give the date and time, the ecliptic longitude of the Moon and Sun and the angle between the Moon and the Sun in the sky, obtained from the values you got in 5). In the above example, the Sun-Earth-Moon angle would be (204o-238o) + 360o=326o. This angle is 0o at the new Moon (Sun and Moon are lined up in the sky), 180o at the Full Moon and grows during the cycle to 360o.
Once you have completed your observations, use your table of Sun-Earth-Moon angles, your plotted positions on the star chart, and your sketches of the phase of the Moon during the cycle to answer the following questions (based on your observations!):
a) Write a brief summary describing the changes you observed in the phase of the moon. Your summary should include the times of the day (or night) when you would now expect to observe a first quarter moon, full moon, last quarter moon, and new moon.
b) Why does the moon go through phases? How does the phase relate to the Sun-Earth-Moon angle?
c) Do your observations indicate that we are indeed always seeing the same face of the Moon at all times? What does this mean?
d) What is the period for the completion of one cycle of lunar phases, as determined from your measurements? There are some subtleties here. To find when one cycle is completed, you need some point of reference (i.e. where is the statring line of the lap?). There are two fairly obvious choices: 1) the Sun and 2) the stars. The synodic period of the Moon (cycle of phases) is measured with respect to the Sun. The synodic cycle is completed when the Sun-Earth-Moon angle has changed by 360o. The sidereal period is measured with respect to the stars and is completed when the Moon has returned to the same ecliptic longitude. Determine each period based on your tabulated angles. You can do this by making a plot of the angle measured vs. the time in days, drawing a smooth curve through your data and seeing where it crosses the point of completion of the cycle. Make a separate graph for each of the synodic and sidereal periods and determine the period to the nearest 0.1 day. Are the synodic and sidereal periods different? Why or why not? Finally, compare your values with those given in your textbook and comment.
e) Describe the orbital path of the moon through the stars. What constellations does it pass through? How does the path of the Moon in the sky compare with that of the Sun (i.e. the ecliptic)? If you find a deviation between the ecliptic and the path of the Moon, what does it reveal?