According to Hubble, the color of stars can tell us whether the stars are receding from us and the speed of their acceleration. Now I read an article that says that the color of stars denote whether they are "new" stars or "old" stars. What is right?
Both are right, sort of. Basically, the color of light that a star emits is somewhat related to its age, whereas the color of light that we actually observe from a star is related to the speed at which it's moving with respect to us.
Stars emit colors of many different wavelengths, but the wavelength of light where a star's emission is concentrated is related to the star's temperature - the hotter the star, the more blue it is; the cooler the star, the more red it is.
There are a couple of ways in which this relates to a star's age: For most of a star's life, it is on the "main sequence", which means that it is undergoing nuclear burning of hydrogen in its center and the energy produced from that process balances it against the force of gravity. When it runs out of hydrogen to burn, the star becomes unbalanced, and its size and temperature can change. For some stars, particularly those that start off very hot, the temperature at this point in the star's life will tend to decrease and therefore the star will become red. So that is one way in which older stars are redder than young stars.
Often, though, when we talk about stars' ages being related to their color we are talking about stars which are still on the "main sequence", since that's where they spend most of their lives. Basically, it turns out that the hotter (and therefore bluer) a star is while it's on the main sequence, the faster it burns its hydrogen and the quicker it dies. So if you see a blue star on the main sequence, you know it must be relatively young - otherewise it would have burnt out already. But the converse isn't true - that is, just because you see a red star doesn't mean that it's old! Where this becomes useful is when you look at a bunch of stars (for example, all the stars in a faraway galaxy). If you see that all the stars are red, then you can infer that there hasn't been much star formation going on in this galaxy recently - otherwise, you'd expect to see some young blue stars just by chance. So you can figure out that the stars in the galaxy must be relatively old.
All the above has to do with the color of light that a star emits. However, we also have to take into account what happens to a star's light between when it is emitted and when we observe it. In that case, there is something called the "Doppler effect" which changes the frequency of the light waves - and since the frequency of light is directly related to its color, it changes the color as well. This is very similar to the effect you get when a train passes, and its whistle goes from high to low pitch as it goes past you. When this effect is applied to light waves as opposed to sound waves, it makes light that is emitted by something moving away from us appear more red, and light emitted by something moving towards us appear more blue.
This page updated on June 27, 2015