For reference, 10 AU is the distance of Saturn's orbit, that's why so dim, it's really not coming near the sun at all.

For those more familiar with photography than astronomy, 200mm referrers to the aperture of the telescope, not the focal length. This is a telescope roughly 8 inches in diameter.

If you're looking to see it, Orion's XT8 would be a great starting telescope with aperture enough to see the comet

I would emphasize that 8 inches is the point at which it becomes possible to see a 14th magnitude object. This requires a very dark sky, excellent weather, and possibly averted viewing.[1] Pluto is mag 14.4 right now and Celestron describes observing it as "the ultimate challenge". https://www.celestron.com/blogs/knowledgebase/the-ultimate-g... They recommend a telescope of 11 inches. (Though they do sell telescopes...)

Also note that the XT8 is a manual, non-motorized scope, so you'll need to find Pluto by hand, navigating from neighboring stars. This can be unexpectedly difficult. The sky is big!

And just to be really annoying, to address people who have never looked through a telescope before: an amateur telescope will give you the ability to see the comet, but it won't look like a photograph from Hubble. It'll just be a dim white dot. If you spend $500 and expect to see jaw dropping astronomical vistae, you will be disappointed.

1: https://en.wikipedia.org/wiki/Averted_vision

200mm are 7.9 inches. Are the focal length and the diameter roughly the same?

Not at all, my 9.25” telescope has a focal length of about 2.4 metres - a focal ratio of f/10.

You’ll recognise f/x from camera lenses and such.

The diameter does control how much light the telescope “swallows” though, you’ll need a larger telescope to see less bright objects (or longer exposures, although when you are using your eye, that has a limit of course!)

So in this case, the post about is saying you’ll need something about 200mm diameter to see the comet. Anything smaller, and you’re just not getting enough light to see it.

That said, if you don't care about seeing it in real time you can use a MUCH smaller lens and stack exposures. You'll likely want a star tracker (MASSIVE decrease in effort) to go with your camera, lens, tripod, intervalometer, and Bahtinov mask (cheap, makes focusing MUCH easier). https://www.youtube.com/watch?v=iuMZG-SyDCU is an excellent tutorial on how to do this without the tracker.

Nope. Focal length is how far the light has to travel, diameter is the aperture, or how big the opening is to collect light.

The XT8 telescope I references has an 8 inch aperture, and a 1200mm focal length

GP is trying to point out that "200mm telescope" here means 200mm in diameter, not whatever arbitrary thing "200mm" apparently means in photography. The unit conversion adds more confusion, I don't know why they did that.

In photography, 200mm is the focal length of the lens. f/X is the focal ratio, with X being some number/ So a 600mm f/4 lens means it's got a 600mm focal length and 600/4 = 150mm aperture diameter. The reason for this is that camera lenses have an "iris" that reduces the aperture; that blocks some light but increases the depth of field. This means that unlike a telescope a camera lens's aperture can vary, so it doesn't make much sense to specify the absolute aperture for most situations.

It's also because the focal ratio tends to be a more accurate way to estimate how bright an image will be than the absolute aperture. A 35mm f/4 lens will take an image with just about the same brightness (LV) as a 600mm f/4 lens, even though the 35mm f/4 is only 8.75mm in diameter compared to the 150mm diameter of the 600mm f/4. The shorter focal length means light gets gathered onto the sensor from a wider angle, which exactly compensates for the decreased diameter. Since photographers typically can't take hours-long exposures (or stack hundreds of photos to get the same effect) the way astronomers can, this system works better for photography.

Sounds close enough in distance and far enough away in time that we could muster a robot intercept mission; would that be likely to be useful enough to warrant the cost?

Yes, and there have been (unofficial) proposals. With SLS or Starship as launch vehicle a fast intercept mission is feasible within 10 years and no corners cut on mission design.