>>68882The most common type of telescope, and possibly the one that brings the most frustration (because they are usually purchased without much thought or a specific goal in mind), is the refractor telescope. I'm guessing you had something like the one in the picture. That's a 70mm aperture refractor telescope. The 70mm refers to the size of its primary lens, which is located at the end of the tube. This type is often chosen for children or as a first telescope because they are inexpensive and most brands offer one for sale. They are also incredibly easy to use. You simply point it at your astronomical object of choice, look through the eyepiece, and that's it, minimal adjustments are required.
Still, you can fall in love with a 70mm refractor IF you are aware of its capabilities and limitations. As I mentioned in the original post, if you try to punch above your weight when equipment is concerned, frustration will usually ensue. Even with excellent lenses, 70mm refractors are not all that suited for observing stars and deep-sky objects. They will improve your visibility significantly, but stars, nebulae, and deep-sky objects are quite far from Earth, so they will still appear as bright points in the sky.
70mm refractors are primarily for objects within the solar system. If you know how to use them and have some patience while waiting for a clear night, you can, for example, see the rings of Saturn, the moons of Jupiter, comets, and so on. Of course, you can have a lot of fun observing the Moon; many features of its surface will be visible. Again, you can use it for objects farther away, but keep in mind that they won't look like the pictures from NASA. Still, there's a lot of enjoyment to be had with a 70mm telescope.
In fact, I'm currently shopping around for one. They are perfect for what I want to do. The key is to purchase one from a reputable brand like Celestron. Having a very good 70mm telescope is far better than having a poor-quality 130mm one. The quality of the lens is crucial. There are many issues that can arise with inferior lenses, such as chromatic aberration and fuzziness caused by poorly adjusted components inside the telescope. So, opt for a small aperture with good quality.
Now, you are correct that astronomy is mostly about geometry. Actually SEEING objects is a relatively small part of the overall experience, and I'm afraid not many people realize this. However, since you mentioned your calculator, so you know what's up. There's a VERY good book I recommend: Celestial Calculations: A Gentle Introduction to Computational Astronomy. It's a beautiful book and incredibly enjoyable. You don't need more than high school math to appreciate it, and it includes many exercises.
I've mostly been going through some lunar atlases and studying geometry on the side while I wait for clear skies in my area. That's why I haven't updated this thread; clouds are currently making any observation impossible. I'm checking weather predictions, and it seems this will continue until the end of the month. Let's hope for better conditions soon.