If you have setting circles (round scales on the Declination and Right Ascension axes) on an inexpensive telescope mount, forget them. The setting circles on inexpensive amateur-level telescopes are just decorations to give the gear a “scientific-looking” appearance. They are nowhere near accurate enough to be used for locating things in the sky, and often don’t even have the necessary adjustment capabilities.
What you might have expected
Beginners are often given the impression that they can use these setting circles to point the telescope to the location of an object (looked up in a catalog) and it will then be in the eyepiece ready for viewing.
Sorry, that is just misleading advertising. Large, expensive mechanical telescope systems with carefully-engraved and calibrated setting circles, such as what used to be standard in astronomical observatories, were used that way, but that is not how modern telescope pointing is done. A well-aligned electronic system (a go-to mount or digital setting circles) does work that way, as do carefully built and engraved setting circles on mid-range mounts costing many thousands of dollars.
On entry-level mounts, and even on more expensive mounts having accurate mechanical setting circles, you will find things by Star Hopping — moving in planned hops from better-known objects to lesser known ones, not by setting the telescope position to the mechanical marks on the mount.
Setting circles on inexpensive mounts
There are two reasons that the “setting circles” on inexpensive mounts won’t work for you: they aren’t accurate enough, and they lack appropriate adjustments for calibration.
Accuracy of setting circles
Let’s look more closely at the “setting circle” on this inexpensive telescope mount. This circle is attached to the Right-Ascension shaft, which is calibrated like a clock: One revolution of the shaft is called “24 hours”, and the hours are subdivided into 60 minutes of 60 seconds each.
The numbers on the setting circle to the right are “hours” of right ascension. There are 6 subdivisions for each hour, so each “tick” on the dial is 60 / 6 = 10 minutes of right ascension, or 10 / 60 * 24 = 4 degrees out of the 360-degree rotation of the axis. The lines are fairly fat, and the arrow painted next to them isn’t particularly pointy. Let’s assume you could accurately read the position of the arrow to the nearest halfway point between two tick marks. So, assuming the dial was somehow calibrated (which it isn’t, as we’ll discuss below), you could use this scale to measure positions to an accuracy of about 2 degrees in the sky.
2 degrees error in pointing a telescope is a lot of error. The full moon, for example, is about 1/2-degree in diameter — so the error in those setting circles is about 4 times the apparent size of the full moon. Of course, you can see the moon, so you wouldn’t use setting circles to find it; you’d use them to find something smaller and dimmer.
Suppose, for example, we wanted to find Messier 57, the Ring Nebula. It is located at Right Ascension 18h, 53m, 35.079s, Declination 33°01’45.03″. That’s a very precise location — ‘way more precise than the dials can represent. So, if the RA dial was calibrated properly (and it isn’t), we’d have to set the RA dial to “just above” 1 tick below 19 hours — that would be the best approximation to the location we could get. Furthermore, M57 is quite small — only about 1.5 arc-minutes in diameter. Our pointing error of 2 degrees is 2 * 60 = 120 arc-minutes. So we would be pointing the telescope using a dial with an error 80 times larger than the object we are trying to find.
Imagine you’re kind of shaky while shooting with a bow and arrow, and you have 50-50 success hitting a 6-foot-wide garage door. But you’re aiming for a 1-inch-wide circular target. That’s the magnitude of error we’re talking about. The chances an object would be visible in our telescope when the dials were set to the approximate location are not good. It just won’t work.
With the low accuracy of the dials on the setting circles, their other shortcoming doesn’t really matter. But just for completeness: the setting circles on the mount shown here are fixed in place, and that’s another problem.
There needs to be a way to move the dials without moving the mount, then to easily lock down the dials so they move with the mount. The idea is that you point the telescope at some known object, that you can find visually, and that is near the thing you’re trying to find; then you adjust the setting circles so they read the correct known coordinates of the known object at which you are now pointing, then you move the telescope and circles to the coordinates of the object you’re trying to find. Non-adjustable setting circles can’t be calibrated to a known object, and are truly just decorations.
Actually, that’s not entirely fair. You could use a nearby known object, and use the non-adjustable circles to measure the distance in RA and Dec between it and your target. However, this requires that you do subtraction in base-60 (what’s the difference, in units of 5 arc-minutes, between 18h, 53m, 35.079s and 19h, 17m, 14.2s?) And the accuracy is still a problem.
Setting circles on higher-end mounts
On this mount (a Losmandy GM8), for example, notice how much finer the lines are on the setting circle and that the pointer is also a fine line. You could probably point this to 1/2 or 1/4-tick accuracy. And there are 10 ticks per hour, so 6 minutes per tick. That’s about 2.4 degrees per tick, and 1/4-tick accuracy means you could probably point to an accuracy of about 1/2 degree. That’s still not accurate enough to find difficult objects, but it’s closer. And, the setting circle dial can be rotated independently of moving the telescope, so it can be calibrated to a known object.
You could successfully point to the moon (1/2-degree diameter) or possibly to larger deep space objects such as M27, the Dumbell Nebula (.1 degrees) with this system.
The hour is divided into 15 segments — 4 minutes per tick. And, you don’t have to guess at the value between ticks, because there is a vernier scale — that scale of numbers on the “pointer side”, with zero in the centre. A vernier scale is used to measure the next value “in-between” the ticks on a scale, by seeing which tick on the big scale lines up most perfectly with one of the ticks on the vernier. In this case there are 4 verner ticks in each direction (zero and 3 ticks above it or 3 ticks below it).
In this particular example the pointer (marked by zero) is just a little past the 20-minute tick mark. How much past? The 2nd vernier line to the right of zero lines up most perfectly with one of the tick marks on the setting circle, indicating that we are 2/4 of the way to the next tick, or 2 minutes more. So, this scale is reading “zero hours, 22 minutes”, and that’s quite accurate. Again assuming we can judge halfway points visually, we should be able to measure to 1/2-minute accuracy with this system: which is about 0.2 degrees. If we had the patience and no better alternatives, we could find things with these setting circles.
Even then, that’s not how we find things
But we usually don’t.
The G11 shown above is a “go-to” mount, which finds things electronically after a calibration. And the GM8 has “digital setting circles” — electronic encoders which measure the mount’s movement from a known object far more accurately than the mechanical setting circles ever could.
Without the electronic help, and even on the inexpensive M4 mount shown on the top of this page, most interesting objects can also be found by star hopping, much more successfully than trying to use the mechanical setting circles.
That’s why, if you look at expensive, very high-end mounts, such as those by Paramount or Astro-Physics, you’ll find they have done away with the setting circles entirely. That’s just not how astronomers find things in the modern age.