Okay so if I'm correct, Hubbles red-shift relationship was first established via expecting a doppler shift - a change in the observed wavelength (perspective of reciever at the time of reception) with respect to that emitted (perspective of the emitter), caused solely due to the respective motion between the two bodies. However the cosmological red-shift was then dedcuded via the fact that a correlation between the distant of the galaxy and the recession velocity was sufficiently significant. My questions are: - Is it correct that if the red-shift was solely down to the doppler shift, such a correlation would not be expected following the cosmological principle - all red-shifts observed, if data is collected on a wide enough scale would cancel due to the isotropy and homogenity tof the universe? -However, I also thought that Ho was determined via taylor expansion, and so assuming sufficiently small distances/redshifts , such that all terms can be neglected expect the first one giving arise to the linear relationship. But these two seem to contradict one another? Thanks very much anyone who can shed some light on this.