We can analyze distant stars by investigating the spectrum of their light. But we have billions of stars in the sky, and I wonder how it is possible to isolate the light of one particular star from the other stars.
How is that possible to isolate one particular star light from the others
astronomyspectroscopy
Related Solutions
Telescopes and any other optics that look at objects in space are set so that the focus is at infinity as defined by the equations of optics.
Resolving power has to do with the size of the primary mirror and the wavelength of light that you are interested in. The smaller the mirror, the less angular size you can resolve (so you can only separate two objects that are far apart). The bigger the mirror, the closer two objects can be and you can see them as separate features. Similarly with wavelength, the longer (redder) the wavelength of light that you're interested in, the bigger the mirror you need, whereas the shorter (bluer) the wavelength, the smaller the mirror can be. This is known as the diffraction limit.
But there's another factor to consider, and that's the resolution of the actual detector. Let's say that your diffraction limit for 500 nm light (green) on a 2.4 m mirror (Hubble) is roughly 0.05 arcseconds. But, if your detector only records 1.00 arcseconds per pixel, then that is your limit. Usually detectors are designed to be at or a little better than the diffraction limit of the optics, though.
In terms of time needed, that has to do with how bright the object is per angular unit. For example, the Andromeda galaxy is very bright as a whole, but that brightness is spread over a large portion of the sky. So the brighter the object is and the more concentrated that light source is, the shorter time is needed to properly photograph it. And this also has to do with the "speed" of your optics -- a larger f/number is "slower" and requires more exposure time than a smaller f/number.
But every detector is different in terms of how sensitive it is and how long you actually need to record the same amount of light. This gets into issues of quantum efficiency that I think are beyond your question. Suffice to say, there is no set equation to know how long you need to expose an object to properly capture it.
As you point out, this is a difficult task. Nonetheless, it can be done. Key to the process is having on hand the absorption line spectra (Fraunhofer lines) for as many of the (pure, unmixed) elements as possible in advance; this then lets the investigator determine if (in your example) the combined spectra for A+B is 1) actually another element C, or 2) just a mixture of A+B.
Also note that the spectrum for (for example) iron and other "heavy" elements is complex, with many lines at unique wavelengths. As such, the "fingerprint" for iron has many distinguishing features in it, all of which must be present to positively identify the presence of iron. So, one by one, the different elements in the spectrum can be picked out, and the process of looking for line matches between the "archived" reference standards and the actual spectrum proceeds until all the lines are accounted for.
Best Answer
Good question! The basic idea is to use a telescope to image some region of space, place an aperture that passes just the light from the star you wish to study, and then couple that light into a spectrometer. There is a good video demonstration of this process that you can watch here.