STILL FRAMES
Prime Focus Photography
Attach a camera (with its lens removed) to a telecope (with its eyepiece removed). The telescope needs to be able to focus directly onto the camera's detector chip, so suitable spacing is needed. In this simple example using common parts, I show a small Maksutov telescope with an old Canon EOS 1000D camera connected with an EOS-compatible T-mount (where the camera's lens would have been), screwed into a small extension tube (not really needed in this case), screwed into the back of the Maksutov. With a set-up like this you must focus the telescope while looking through the camera's view finder.
The resulting picture of the moon is not in very good focus, neither is it highly magnified. A camera with a smaller detector chip (e.g. Altair GPCAM 1 or 2, which is a good value astro cam but needs a computer) would give higher magnification.
Note that you can screw a 'T2 nose-piece 1.25 inch adapter' onto the T-mount instead, which allows you to put the camera where an eyepiece would normally go.
Eyepiece Projection Photography
A different method is to use eyepiece projection rather than prime focus. These pictures show that, but include an 'imaging flip mirror' to aid focussing. The 1st of the 3 pictures shows (L to R): the camera, the projector tube beside the eyepiece which is to be inserted and locked into the projector tube, the flip mirror with an eyepiece in it as focus aid. The 2nd picture shows the kit assembled. The 3rd picture shows the whole gangling assembly. When tightened up this is fairly stable but there is some sag, causing the eyepiece and the camera to be a lttle misaligned. So you would adjust the telescope's direction just before taking the picture. If all the components screw together then you don't need the T2 nose-piece and sag is reduced.
Here is an eyepiece projection of the moon, which is now slightly too big to fit in a frame. The projector tube was set at its shortest giving its lowest magnification. To increase magnification you can lengthen the projector tube (on this particular version) or you can use a shorter focal length eyepiece.
An optically shorter telescope than the f12 Maksutov shown here may not cope well with the long path of the eyepiece projector and flip mirror, leading to darkening around the edges of photos ('vignetting') or failure to focus.
I used the super, free program GIMP to stitch my demo moon pictures together by using the 'layers' features. You may see that there is a slightly bright doughnut in the middle of the lower frame. I suspect that is caused by the 1.25inch nosepiece at the telescope end of the flip mirror. I'm still experimenting with this in order to pin down the cause. It is likely that the Maksutov's internal baffle tube contributes most of the reflection seen in that 'doughnut'. If I thought it mattered enough I could line the tube with a black velvet or similar. A little too drastic for me. If you examine the stitched photo closely enough at the top and bottom of the crescent you may see that there are coloured fringes - red at the bottom and blue at the top. This is due to the refractive index of air being different for different wavelengths. It's an atmospheric effect and not due to the Maksutov's 'corrector plate' or the eyepiece being merely achromatic. Well, that's where the assymetry in the optical path must lie, surely. If it were the telescope then the fringe would be around the whole image and would all be one colour, dependent on focus. Surely? Wanting to make life easy, rather than getting more involved with practical detail, I use colour cameras. An alternative would be monochrome cameras and RGB filters - taking a picture in each colour. With filters, images would then be combined by processing three images as separate (GIMP) layers, colouring each and shifting so that they coincide despite the time delay between each shot. That would naturally lose most of this differential refraction. The colour fringe effect is larger the closer the subject is to the horizon. Corrector devices are available, if you must. Monochrome cameras without colour filters are especially badly affected by differential refraction. If you can get 'raw' pictures from your camera (e.g. stored with the .cr2 extension on a Canon EOS) then you can try the open source and multi-platform program 'RawTherapee' which does a very good job of reducing the red and blue fringes. It also allows dark frame processing and more.
You can do better than that sample!
VIDEO
Prime Focus Photography