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I found two telescopes that i'd like to buy, but one has 900mm focal length ((Skywatcher Newton 114/900 EQ1)) and the other has 500mm focal length ((National Geographic Dobson N 114/500)).

My questions are:

  1. What is the "recommended" focal length for observing deep sky?
  2. Are there better telescopes in the same price range?
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I don't think there is a "recommended" FL for DSO observation. If you only observe visually, the eyepieces you use are just as important und the magnification depends on them. If you are concerned about the field-of-view you will get from these telescopes, I recommend checking out FOV calculator tools such as astronomy.tools. There you can enter your telescope and eyepiece information and show the FOV compared to a deep sky object of your choice.

I personally have been very happy with Skywatcher telescopes (I own an Esprit 100ED Triplet and a 200/1000 Newtonian), however I never really tested them visually as I only use them for imaging.

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There isn't really a "best" focal length because it depends on the object you might want to observe.

Angular Size

The Ring Nebula (Messier 57) is only about 1.4' across. Meanwhile there are larger objects such as the Andromeda Galaxy (Messier 31) -- that's about 3° across (and a pair of binoculars may work better than a telescope because too much focal length means the whole object wont fit into the field of view.

Consider that a telescope that an instrument that can take in the entire Andromeda Galaxy wold render the Ring Nebula as a very tiny dot ... while an instrument that can nicely resolve the Ring Nebula would only be able to view a tiny piece of the Andromeda Galaxy.

Aperture

In the "What telescope should I get?" category, consider that the larger the aperture, the better the ability to resolve detail. An 8" Dobsonian mounted telescope would resolve more detail than a 4" refractor. A 16" Schmidt Cassegrain Telescope (aka SCT or "Cat" because an SCT is a "Catadioptric" telescope so they get the nickname "Cat") would resolve significantly more detail... but be so heavy that it really needs a permanent pier in an observatory (the largest telescope I use as a "portable" telescope is a 14" Cat ... but absolutely requires two people to set it up because it is too heavy and unbalanced for just one person to lift it onto the tripod.) The point here is that there is such a thing as "too big" in that you have to consider if you can transport it or set it up without requiring assistance.

Dobsonian reflector telescopes are very easy to setup and use and provide surprisingly good views. They often have short-ish focal ratios (e.g. f/5-f/6 or something near that range). An 8" (200mm) aperture model would have a focal length of around 1000-1200mm. That tends to be pretty good as an all-around instrument... it's not particularly short but also not particularly long for a telescope.

You can find them made by brands such as (and in no particular order) Orion, Zhumell, Apertura, Sky-Watcher, Explore-Scientific, Celestron, or Meade. There are other brands that I left off the list such as Obsession -- they make great telescopes but their smallest instrument is a 12.5" Dob with sizes up to 25".

These telescopes typically do not include electronics or motors ... but there are variations that do have those options. They are typically not well-suited for imaging (but you did not ask about imaging).

Mount

If the telescope is perched atop a tripod, place strong consideration on the stability of the mount. My first telescope came with a tripod that had aluminum extruded legs. Merely touching the focus knob resulted in the telescope vibrating enough that viewing through the telescope and trying to focus was a real test of patience because the object would shake so violently that it was difficult to determine if the focus was improving or getting worse.

This is one of the reasons why, when asked for a suggestion on a first telescope, I typically suggest a Dobsonian mounted reflector ... because the mount doesn't have legs and tends to be very stable. Focusing is usually not a problem.

This is not to suggest that tripod-mounted telescopes are inferior... it's just to suggest that if a tripod-mount will be used, you want a very sturdy tripod.

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When this type of question is asked it seems to be almost universally accepted that the poster is looking at equipment that is at the maximum price range they can afford.

The bottom line is you will get what you pay for and that applies to viewing Deep Sky Objects in a very big way.

No traditional eyepiece will give you a view with the color and detail of an electronic eyepiece.

If you think you will eventually have the resources to get into the electronic side of viewing it would be worth your while to look into it now. Better to know what direction you want to go before you start. :)

A Google with "electronic eyepiece for telescope" will yield pages of adds for the products. I use Mallincams which are not readily available on line. You can see what users are doing with those cameras at the Mallincam iO website

https://groups.io/g/MallinCam

They have a photo section with thousands of Deep Sky Object images made with the various cameras. Some are snapshots of live video, some have been processed.

You can also view live broadcasts of Electronic viewing sessions at

https://www.liveskies.org/

There are no schedules at Live Skies. People from all over the world come on line with a broadcast whenever they want to. Generally most broadcasts originate in North America. If it is dark and clear somewhere, someone might be broadcasting on line.

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