Notice that the lines are banded or thickened. You might fall slightly above or below these bands based on the factors discussed earlier. Beware of anyone or any calculator that states overly precise limiting magnitudes. These are at best guides and give a false impression that an object is either perfectly visible or perfectly invisible. Objects on the edge of visibility come in and out of view over a period of time. One night that object might be visible three times in a half hour (my standard for detectability). On another night it simply is completely invisible. On rare perfect nights not only can I detect it much of the time but there is detail too. Also if the galaxy or cluster or planetary is unusually large, then the detection limit will suffer. Note that as aperture increases, minor differences (say between a 20 inch and a 22 inch telescope) become insignificant, even undetectable except for rare edge cases.
At first aperture is everything, then it is nothing; eventually it simply is. At first we can't get enough aperture. Then almost like a boomerang we trim way back in aperture. Notice how many experienced amateurs own not only their big scope but also a smaller scope? Finally, aperture takes its place in the pantheon of factors, being traded for field of view and for convenience of viewing. A 6 inch [15cm] is a perfect aperture to learn how to observe. With it you can see thousands of objects from a dark sky. A 12 inch [30cm] will resolve almost all clusters and show galaxy groupings. If you think that you “need” large aperture to see the skies, that small aperture won’t work, then something has seriously gone amiss. Large aperture makes it more difficult to learn the art of observing. Do yourself a favor and spend a lot of time observing with smaller scopes too.
What magnifications should be used? I favor three strategies both based on exit pupil (the eyepiece's focal length in mm divided by the telescope's overall focal ratio [e.g., 24mm eyepiece on a F/6 scope produces a 4mm exit pupil]):
The first is based on Richard Berry's advice. Arrange your eyepieces so that they give exit pupils as following:
5-7mm Richest Field observing
3-5mm best deep sky observing
1-2mm best detailed observing (globulars, planetaries, lunar and planetary)
second is based on Stephen O'Meara's comments (e.g., his Herschel 400
Observing Guide). He uses modest aperture (4 inches [10cm]) at low,
medium and high powers. He takes his time studying the object carefully
at each power. His low, medium and high exit pupils are:
If you are wondering who to look to for observing advice, pay attention to the top observers who use smaller scopes, like O'Meara.
The third is a strategy that I've
developed in response to the super wide angle eyepieces available
today. It allows me to see large scale objects otherwise too big for a
given scope. I call this strategy “framing” or
the view where the object is magnified to fill the eyepiece’s field of
as much as possible with a nice border around it for contrast.
Increasing the apparent object size
beyond this 'cut-off' results in a less pleasing more difficult view.
widest possible field of view is important, even at the cost of more
glass for the light to pass through. In this approach, I smoothly
decrement the exit pupil. I use a set of exit pupils as
follows (note that the typical set of eyepieces does not fit
5-6mm for largest scale objects
3-4mm for medium scale objects
1-2mm for small scale objects
Finally, poor seeing conditions especially with larger apertures will limit magnifications to 200-300x or 2-3mm exit pupil.
It helps to have an observing program and plan your evening's viewing. The Astronomical League has a number of observing plans. Or create your own, i.e., comparing the shapes of globular clusters in the Sagittarius region or colorful double stars in Bootes. Use a table for your eyepieces, tools, charts and texts or for your tablet and lightshield. Plan on 20 minutes per object. I strongly encourage you to sketch what you see. This hones your observing skills and brings out details in the object. Observe at all three ranges of power: low, medium and high.For observing large scale regions of the Milky Way and more on organizing observing and sketching sessions, see my dark nebulae observing comments at http://www.bbastrodesigns.com/dneb/Observing%20Dark%20Nebulae.html
Counting the Pleiades, an exercise into extended limiting magnitude
Averted vision works best if you know where to aim your eyes
in the field of view. Here's a chart to help.
This leads to the interesting conclusion that the brightness of the sky glow as seen in the eyepiece is entirely dependent on exit pupil. At a given location on a given night, no matter the size of scopes, if they are giving the same exit pupil, then the sky glow brightness will be very similar.
So why then is aperture the dominant factor? If exit pupil or sky background brightness is kept constant, then as aperture increases so must the magnification. The object appears larger and is easier to see. It’s like moving in closer. If magnification is kept constant then the object and background brightness increase, also making the object easier to see.
What is sky glow brightness? The night sky, even at very dark sites, glows faintly due to zodiacal light and airglow. See Brian Skiff's discussion at http://www.astropix.com/HTML/L_STORY/SKYBRITE.HTM. You can measure the darkness (or brightness) of your night using a sky glow meter available at http://unihedron.com/projects/darksky/. Dark sky sites have readings close to 21.5 magnitudes per square arcsecond. Observing through a telescope with your eye's pupil fully opened results in a sky glow in the field of view equal to that of the night sky. Magnifying the image results in smaller exit pupils, the useful maximum magnification or smallest exit pupil being close to 1mm. The sky glow brightness drops more than 4 magnitudes to close to 26 magnitude as exit pupil shrinks to 1mm.
So how can we see the object in the scope? The eye is a marvelous detector of low contrast faint objects, but the light must fall on large numbers of rod cells so that the eye-brain can detect the slight contrast difference between object and background. The slighter the contrast, the more rod cells that the object's light must fall on in order to generate a signal difference between object and background. By increasing the telescope magnification, the object is magnified so that its light falls on many rod cells. There are two points to consider when an object is in the field of view of an eyepiece. The first is the object combined with the sky glow from the atmosphere that is directly between us and the object, and the second is a point away from the object, which is the sky glow only. The ratio of brightness between these two points is sometimes called the object contrast. This contrast value stays constant despite any increase in magnification because both points are equally dimmed.
The seminal reference on visual astronomy is Clark's book, "Visual Astronomy of the Deep Sky". In it Clark explains and quantifies the visual detection of objects. Clark has added additional comments since the book's publication, at http://clarkvision.com/visastro/omva1/index.html Clark uses data from a World War II study by Blackwell.
Here a brief presentation of the Blackwell data. The eye's detection ability with sky background brightness values from 21 to 26 is:
From the chart we can see that large exit pupils result in the best ability to detect objects over a wide range of apparent sizes. As the exit pupil shrinks, the ability to detect objects declines and becomes concentrated on apparent sizes of about a degree. We can see this by plotting best apparent detection size against declining sky background brightness. Here are two visualizations of the data:
The data and its interpretation has been the subject of intensive discussions between Prof Clark, Nils Olaf Carlin, Harold Lang and myself.
For Nils Olof Carlin's analysis of Blackwell's original data, see blackwel.html. Here, Nils shows that the best contrast comes when the background is dimmed below visual detection and the object is about one degree in apparent size.
Bill Ferris has generated a series of ODM matrices that compare the variables with each other: http://members.aol.com/billferris/odm.htm
I wrote a visual detection calculator that presents the data by aperture and exit pupil. I believe that the whole issue of visual detection needs more observations and possibly a new model. The detector that I wrote uses the Blackwell data. Like any ground breaking study, there remains much to be done. The study was done with two eyes - how does a single eye do? Objects in with complex isophotes need to be studied, distractions of other objects in the field of view needs to be investigated and variations in the color of the objects need to be checked. Also needing observations is variation in the ages of the observers and especially telescope construction features like baffling and cleanliness of optics.
Greg Crinklaw has invested a great deal of time into improving his visual detection calculator based on empirical results at the eyepiece. See his SkyTools software and in particular his comet chasing page.