Is it possible to determine the distance between the earth and a star by only studying the light emitted from this star? I was reading about the Doppler shift and how we can measure how fast something is moving through its Doppler shift. This got me thinking is their a way/formula to measure the distance between us and a star by only analysing the light emitted from it.
Thanks in Advance!
 A: Well, the Doppler effect won't do. Redshift only yields a good distance estimate at cosmological distances, and very few individual stars can have a measured Redshift at those distances.
However, there are methods and it depends how laterally you want to think. If you have a sufficiently detailed spectrum of a star, it is possible to measure both the effective temperature and surface gravity of a star (there are myriad temperature- and gravity-sensitive absorption lines in most stellar spectra). This in turn determines the spectral type of the star.
If we know the spectral type and have a measurement of its apparent brightness, then it's distance can be estimated because there is a well-established relationship between spectral type and absolute luminosity.
Note that this estimate will not be really precise (maybe good to 20% at best) and could be biased by interstellar extinction (although that too can be accounted for if you also know the colour of the star).
Worked example: the spectrum of a star tells us it has a solar-like temperature and gravity and it has an apparent visual magnitude of about 9.8.  Since the absolute visual magnitude of a solar-type star is about 4.8 (at a distance of 10 pc), then the 5 magnitude difference corresponds to a factor of 100 in flux, so the star is at distance of 100 pc.
A: 
Is it possible to determine the distance between the earth and a star by only studying the light emitted from this star ?

Not for most stars. Doppler shift only allows us to measure the relative speed of a start along its line of sight, and tells us nothing about its distance. There are, however, some specific types of star for which an analysis of their light and how it varies over time can give us an idea of the star's absolute brightness. Once we know this, a measurement of the star's apparent brightness will tell us the approximate distance to the star.
For more details of how stellar distances are measured, see this Wikipedia article.
A: If the star is not too far away, one can determine the distance by measuring parallax from two different points of Earth's orbit.
