Why do we see the lines in a star spectra displaced from the wavelength they belong to and so we need to calibrate the spectra ? Is it only because the relative motion of star and earth ?
Yes, the relative motion will cause a doppler shift in the wavelengths observed. Also if your space is expanding, i.e the objects are not changing position in space, just the space between points is expanding, you also get a red shift in the light as the light traverses space which you can think of as space stretching the wave out if you like. Furthermore, you might also get a shift in the wavelength if your light has passed through a strong gravitational field due to relativitic effects.
So in short the following contribute to the shifting of the wavelength:
- Doppler Effect
- Space expansion
- Gravitational red shift
You can find more info at: https://en.m.wikipedia.org/wiki/Redshift
If a star was moving toward Earth, its light waves will appear to be pushed together. This decreasing distance between Earth and the star in effect, shortens the wavelength of the light received by Earth. This is called the Doppler effect. The star's spectral lines move toward the blue end of the spectrum.
Now consider the complete opposite, where a star is moving away from the Earth. Due to the Doppler effect, the spectral lines will now appear to be red shifted.