For this particular evening’s Moon Game, resolution would be the “game.” I decided to try to hunt for the smallest crater my telescope and the atmosphere would resolve. I have found this to be both challenging and rewarding activity. Challenging because you need to know what details are where before you try to find them – so that means a time with the charts, atlases, and the computer, often running back and forth between the scope and the computer. Rewarding because you are noticing small details on the surface you never knew existed, you are inadvertently learning more about the Moon (it’s always fun to learn without trying), and you are “playing” by stretching your telescope’s optics and eyepieces, and your own observing techniques, to explore their limits. It’s also enjoyable because all evening you are parked one object instead of jumping all over the sky, sort of like playing ball with the Moon!
So just how small of a detail can you see? If you look at your telescope’s manual or the marketing materials, you’ll find a maximum resolution given typically in arcseconds, with an arcsecond being 1/3600 of a degree. Simply put, it is the smallest angle of view your telescope can resolve. The basic formula, called Dawes Limit, is R= 4.56/D where R is the resolution in arcseconds and D is the diameter of your telescope’s main objective measured in inches. So if your telescope’s specifications are a 6” objective, then its resolution capability is 4.56/6 which equals 0.76 arcseconds.
At this point I image you may be thinking something along the lines of, “OK. Great. My telescope can resolve 0.75 arcseconds. Tell me something that means something!” So here’s how we make this mean something in terms of observing the Moon. To determine what 0.75 arcseconds resolution is when looking at the Moon, we need to know how far away the Moon is, then we apply the formula S=D*(R/(3600*180/Pi)) or S=D*(R/206,265) where S is the size or diameter of what you can resolve, where D is the distance to the object you are looking at, and where R is your telescope’s resolution in arcseconds. With this formula, whatever unit of measure you use for D, is the unit of measure that S will be in. So if you plug in the distance to the Moon in miles, then S will be in miles also.
On average, the distance from the surface of the Earth to the surface of the Moon is 247,545 miles. Using the above formula then have the smallest object we can observe using the Dawes Limit criterion is 247,545*(0.76/206,265) or 0.9 miles. So, theoretically, if you go to your Moon atlases and find yourself some 2, 1.5, and 1 mile diameter craters, you should easily spot the 2 mile and 1.5 mile ones, then be challenged with the 1 mile craters. But before we go on, let me fill you in a little about the Dawes Limit. First of all, don’t believe that this is the resolution limit of your telescope! Dawes Limit is a criteria which was derived by trial and error by an amateur astronomer during the 1800’s, it is not a law of physics or optics. Further, it was derived by observing bright point sources of light (i.e., stars), so it is a resolution limit which only really applies to observing point light sources which produce a series of concentric circles of light in a telescope -- called an airy disc (See Picture 1).
Of course, this airy disc size changes with both the seeing and transparency of the atmosphere, which I imagine was quite different in 1800’s vs. today. Our Moon of course is not a star, so it produces no airy disc pattern. That being the case, you will note with this Moon Game, the Dawes Limit still works reasonably well in terms of round craters when the contrast is high between the crater’s wall or interior, and the surrounding terrain. However, other features, such as crater walls, rilles, rays, and wrinkle ridges, which may be much thinner than the Dawes Limit predicts for your telescope to achieve, are still spectacularly resolved! So be aware, that you may be able to beat this limit, depending on the atmosphere, the quality of your optics, image brightness, image contrast, color or light wavelength, how well your telescope is collimated, how good your own eye’s physiology is (e.g., some people have better than 20/20 vision, more cones and rods in their eyes, etc.), and your observing technique.
So where should you begin if you want to play this Moon Game? First, start with a good Moon atlas like the “Sky Publishing Atlas Of The Lunar Terminator.” There is also a great program called Virtual Atlas of the Moon -- and best of all it is free! See http://www.astrosurf.com/avl/UK_index.html for details. The beauty of this program, is that you can add many databases of images from the myriad of NASA probes and Apollo missions – so once you zoom in on a crater or area, you can have quite a selection of photographs of the area from a variety of light angles. I have found this program invaluable, easy to us, and fun.
Once you have this program installed and all the supporting Lunar photo files, the next step is to find an easy target area near the Moon’s Terminator for the evening you will be viewing, then hunt through the Atlas for craters of the size you desire. Most atlases won’t have size details on these small craters, so to determine their size you’ll need to measure the diameter of a nearby known crater with a ruler, then compare that to the size of your target crater to determine its approximate diameter. For instance, let’s say you have a large known crater near your observation area that is listed as 50 miles in diameter. On your atlas, or computer screen, you measure this crater as 2 inches across or 50.8mm. In this convenient case, every millimeter is approximately 1 mile, so you find the craters on the atlas photo that are 1mm across and these are your 1 mile craters. The Virtual Atlas of the Moon software is great for this because it lets you enlarge the picture size ridiculously large, making it easier to measure those smaller craters.
For a real-life example, here’s my notes from a recent Moon Game resolution-expedition:
OBSERVATION LOG ENTRY
DATE: April 09, 2006; 7:30-10:30pm EST; Vienna, VA.
CONDITIONS: Seeing – Undetermined (Having too much fun to care); Transparency – Not noted; Sky – Clear with 3/4 Moon; Max Resolving – 56x/inch without softening.
INSTRUMENT: 10” f4.7 Newtonian (Orion 10XTi) w/2hrs Thermal Adjustment.
OBJECTIVE: Lunar maximum resolution test and pattern hunt.
Began observation with intent to hunt for new patterns to add to my collection for the Moon. Quickly this went by the wayside as the detail and resolution I was attaining of the surface grabbed all of my attention.
Originally spent the initial time with Crater Keppler, but the details in Gassendi (See Picture 2) drew me for the balance of the evening. The pattern of Rilles was clearly visible in the crater making for a fantastic observation. While the seeing was shifting very slowly to in and out of focus for the finest details, it was curious that I could attain the most resolution with my right eye, and pulling my head further away from the eyepiece so that I could not see the entire field of view. So this technique was extremely valuable for detecting the finest details within Gassendi.
Structures referenced in the Gassendi picture as A through D were clearly visible all the time even at low magnifications 151x (8mm Edmund RKE), 171x ( 7mm TeleVue Nagler), 200x (5.9mm Siebert Star Splitter and 6mm University Optics HD Ortho). The Rille structures were also fairly clear through these eyepieces. The RKE, Nagler, and Star Splitter all took the 2.8x Klee Barlow exceptionally well with little softening and no loss of details, so I stayed at the higher powers using just the Star Splitter and the University Optics HD which yielded 561x under Barlow (56x/inch). With this combination all the other listed details in the Gassendi picture (E through H) maintained a steady view as the seeing slowly shifted. H was not resolved as two craterlets, but only as one. I estimate craterl C to be approximately 1 mile in diameter. Crater’s E and G are both sub-1 mile, perhaps 0.6 so they were near the Dawes Limit for the telescope and the atmosphere.
As you can see from my Observation Log notes, it was an interesting and fun evening with the Moon, all the time spent on only two major craters. And while I exceeded my goal of observing a 1 mile diameter crater, the real thrill of the evening was being able to catch the incredibly intricate details of the rilles within the crater – I literally felt like I was peeking into forbidden detail of the crater floor, taking my “one small step” from a quarter million miles away and still feeling like I was close enough to almost touch. This was quite unexpected, and just goes to show how the celestial object we often most neglect, the Moon, can often be the most memorable and rewarding.
So the evening was done and I stretched my scope to the limit, and proud of it! Like this little Man in the Moon (See Picture 3) I found doing another Moon Game, I was also left with a surprised look on my face, and a much happier and better smile for sure! So, what’s the smallest crater you can see?
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