If doing spectroscopy the target's brightness and the resolution play major roles. I heard that compared to normal imaging, the limiting magnitude for a given exposure time is reduced by approximately 6 magnitudes - I guess this is for low resolution. If wanting to do spectroscopy on faint magnitudes the total exposure time needs to be increased. The purpose of spectroscopy is to find out about chemical elements, which can vary by region on any celestial object and this distribution can be studied. Let's take some small solar system object with a rotation period of two hours as an example. There are several elements distributed on it's surface and revealed to the observer through it's rotation. But reaching a high enough SNR means a total exposure time of e.g. five hours. So this means that each individually gathered low SNR spectrum would carry the chemical traces of the current region facing the observer at that time. Stacking dozens of individual spectra - or averaging? - would result in a collection of all geochemical elements on the object's surface. Does this make sense and are such observations scientifically useful at all?
Yes for the same SNR you need much more light for spectroscopy compared with imaging. (Very roughly R times more where R is the resolving power (reciprocal of resolution), plus one or two magnitudes more to allow for losses in the spectrograph) You can certainly combine spectra to improve SNR though and if you synchronised the exposures with the rotation it should be possible to build up spectra of fainter objects at the various phases. Note that at the optical wavengths the reflectance spectrum, once corrected for the solar spectrum only contains broad features indicative of the material and certainly not a full analysis of the elements present. Working in the IR gives more information but it is still just the characteristics of the mineral composition rather than an elemental analysis. You might find this article "Visible-Wavelength Spectroscopy of Asteroids" of interest
Would it be that simple as to put a low resolution grating like the RSpec's SA-100 filter inside a filter wheel and image faint point sources with it? Or do you need more than just such a grating?
The SA-100 is a great way to start in spectroscopy: it’s inexpensive, and using it will give you experience at the procedures for wavelength-calibration, instrumental response, and SNR versus exposure vs target brightness. As you have already recognized, you will only get good spectra from “point” sources, but there are plenty of educational and research projects that are within its capabilities.
Probably everyone’s first project with the SA-100 is to examine the range of stellar spectral types, to see the change in the continuum (from hot to cool stars) and the sequence of the prominent absorption lines. A few years ago I helped a high school student do this project for the County science fair, with good results (i.e. he learned quite a bit, and he received an “honorable mention” from the judges). His equipment was amazingly simple: the SA-100 grating mounted in front of the standard lens on a DSLR camera (similar to the old-time aperture prism arrangement).
The setup that you ask about – put the SA-10 into your filter wheel – does work nicely. The only pifall relates to how the spectrum is spread out on the focal plane of your CCD. Since the spectrum spans a fixed angle, the “spread” of the spectrum on your image is relatd to the span-angle times the distance from the SA-100 to the focal plane. In many setups (e.g. mine...) the distance is shorter than you’d like. I found it better to put the SA-100 on an extension tube that set it about 3-4 inches in front of the focal plane. There is useful information and a spacing-calculator on the RSpec website: http://www.rspec-astro.com/star-analyser/, and a wealth of useful info on Robin’s website (http://www.threehillsobservatory.co.uk/astro/spectroscopy.htm)
The SA-100 is a remarkable device: with it, your CCD, and a modest telescope, you can observe the red shift of quasar 3C-273. And it has been used for assessing supernovae types and “imposters”.
Yes it is possible to take low resolution spectra of asteroids this way. (You would probably need the SA200 for a filter wheel, not an SA100) Note the Star Analyser is manufactured by Paton Hawksley in the UK. Tom field who wrote the RSpec software sells them in the US. You can see an example of 2012 DA14 which I recorded as it passed close to earth here
https://www.youtube.com/watch?v=KXFmDSCA8OM (real time spectrum images)
http://www.spectro-aras.com/forum/viewtopic.php?f=6&t=550 (The analysis of the spectrum)
Here is another reference (Vesta, Ceres, 2004 BL86 reflectance using an SA200 by Lorenzo Franco)