The most obvious object in the nighttime sky is the Moon. Its surface features and changing phases have fascinated humans for centuries. Much was learned about the Moon once telescopes began to be used to extend what was known from unaided observations. With the advent of the space age, the Moon became an obvious place to visit, first with unmanned probes and then by the men of the Apollo missions between 1969 and 1972. By being able to actually travel to the Moon, we have learned more about it than any other object in the sky. Even with a huge body of knowledge about it, the Moon still holds an attraction for visual observations with the unaided eye, binoculars, or small telescopes. The Moon’s major surface features, its maria and highlands, are visible even to the unaided eye. The maria are the dark, smoother regions that reminded the ancients of seas. (Maria is the plural of the Latin mare, which means “sea.”) The highlands are the lighter regions of the Moon, which are much more rugged and mountainous than the maria. Although they are not noticeable to most people, even the smallest telescopes or binoculars reveal numerous craters all over the surface of the Moon. Virtually all of these craters were formed by meteors striking the Moon. Larger telescopes reveal a huge number of large and small craters peppering the Moon’s surface. Surface relief (low and high regions) is most easily visible near the terminator, the boundary between day and night on the Moon’s surface. Near the terminator the Sun casts long shadows from mountains and valleys, making them stand out.
In this lab you will make a few observations and measurements of the Moon using your telescope. As you make your observations, be aware of how what you see through the telescope compares with what you see with your unaided eye. Make careful and detailed observations. Remember that observations should include the date and time, the weather conditions, and the instrument used (including the eyepiece). In addition, for lunar observations, you should include the phase of the Moon. You can state the phase as what percentage of the whole disk is visible (first quarter would be 50%), or as the number of days since new moon (first quarter would be 7 days past new).
In this lab you will be measuring the size of some craters on the Moon using a technique known as the transit method. This technique uses the fact that the Earth rotates at a constant rate, so any object in the sky appears to move across our sky. This “drift” is very apparent in a telescope with the clock drive turned off. The time it takes a particular object to cross a point (like the edge of your telescope’s eyepiece) depends on its angular size and its declination. Objects near the celestial equator move more quickly than objects near the poles, and it takes larger objects longer to cross a particular point than smaller ones. Here’s what you do. Locate the object you want to measure in your eyepiece. Make sure you know your directions in the eyepiece (N, S, E, W). Remember you can find west by turning off the clock drive momentarily. Objects will drift toward the west in the eyepiece. Move your telescope using the hand controller until the object you want to measure is near the western edge of the field of view. Turn off your clock drive and let the object drift out of view. Start timing (with a stopwatch) the moment the object gets to the edge of the eyepiece, and time until it passes out of view. This time is the transit time, and we’ll call it “T.” Record this time, including the fractions of seconds. You may want to repeat this a couple of times to make sure you’re getting consistent results. To find the angular size from this timing, you will need to know the declination of the object also. (For objects near the celestial equator you don’t have to worry about the declination.) Here’s the formula to calculate the angular size from the transit time and the declination. It will give you the angular size in arc seconds. You can convert to arc minutes by dividing by 60.
Angular size (arc seconds) = T •15• cos(dec).
In the formula cos(dec) is the cosine of the object’s declination. You can get that off your calculator. Your instructor will provide the current value of the Moon’s declination, since it changes from night to night.
It would be nice to be able to calculate the actual size of a crater on the Moon once you have its angular size. This can be done since we know that the Moon is 384,000 km away from us by using a little trigonometry, but we also have to compensate for the fact that the Moon is a ball, and we see many craters more or less “from the side” as we look at the Moon. Sparing you the gory details, it works out to be
Diameter (in km) = Angular size (in arc sec) • 1.86 ÷ cos(long)
where cos(long) is the cosine of the crater’s lunar longitude (found from the Moon Map). The 1.86 comes from converting arc seconds into kilometers for an object at the Moon’s distance.
Materials
Telescope and accessories, Moon Map, stopwatch.
Procedure
Setup
· Before making telescopic observations, record the date, time, etc. on your observing sheet. Make sure to note the Moon’s phase and declination.
· Align your telescope with the North Pole, align your finderscope, and focus on the Moon with your low power (30 mm) eyepiece. Refer to your Telescope Setup Instructions from the previous lab if necessary.
· Make a note of how the orientation of the Moon in your telescope compares with its orientation as seen with your unaided eye.
Crater Counting
· With the low power eyepiece still in place, count the number of craters of all sizes you can see in a region of one of the maria.
· Record this number of craters, along with the approximate latitude and longitude of the region you were observing, on your observing sheet.
· Now count the number of craters of all sizes you can see in a similar-sized region in the highlands.
· Record this number of craters, along with the approximate latitude and longitude of the region you were observing, on your observing sheet.
Sketch of Terminator
· Switch to your high power (10 mm) eyepiece and focus on the terminator. (Note that if the image is blurry or unstable even after focusing, the seeing may be too poor for high powers. If that’s the case, use your medium power eyepiece.)
· Scan the telescope along the terminator until you find an interesting region.
· Make a sketch of this region on your observing sheet. Make note of the directions N, S, E & W on your sketch.
· Use your Moon Map to determine the approximate longitude and latitude of the region you sketched and record this on your sketch. If possible, label craters with their names.
Size of Lunar Craters
· Find a large crater near longitude 0° such as Ptolemaeus, Archimedes, Plato, or Tycho.
· Measure its transit time. Make three timings to get a good value.
· Find a large crater away from longitude 0° such as Gassendi or Petavius and measure its transit times, again by taking three timings. Be sure to record its longitude.
· Once you have finished your timing measurements, pack up your equipment and return it to the Field Station.
· After your equipment is put away, you can calculate the angular sizes of your craters and the actual diameters of the craters. (Note that this can be done on your own at a later date.)
o For each crater, find the average of the three timings.
o Use the average transit time for each crater and the formula given above (along with the Moon’s declination) to calculate the angular size for both craters.
o Calculate the actual diameter (in km) of the crater near 0° longitude. For this crater you can leave out the division by cos(long) since cos(0°) = 1.
o Calculate the actual diameter (in km) of the crater away from 0° longitude. For this one you will need to include the division by cos(long).
Questions
1. Why do you suppose the highlands have so many more craters than the maria?
2. How do the sizes of the craters you measured compare with objects on the Earth? Remember that there are about 1 ½ km in a mile. Sumner County is roughly 50 km across.
Your report should include your crater counts, timings and sizes, along with your original observing sheet. Include answers to the questions in the appropriate section.