# Hubble’s law distance and time dependence

Hubble’s law states that the recessional velocity is proportional to the distance. The further the observed distance, the further back in time one is observing. I want to know (generally) how this time dependence of observed light sources at different distances is accounted for in the law? Thx

From the non relativistic Doppler effect $$\lambda_o=\lambda_e(1+\frac{v}{c})$$$$\frac{\Delta \lambda}{\lambda_e}=\frac{v}{c}$$$$z=\frac{v}{c}$$ A plot of redshift($$cz$$) vs. the physical distance $$r(t)(a(t)\chi)$$ is giving a linear relationship(best fit curve) implying $$cz \sim r(t)$$$$cz=v(t)=H(t)r(t)$$
• Yes it is, two photons from two galaxies are emmitted say at $\chi _1$ and $\chi_2$ where $\chi_1\gt \chi_2$ (comoving distance) and if are received today $t_0$ then the physical distance travelled by then would be $a(t)\chi_1$ and $a(t)\chi_2$ where the emmision time would be $t_{e1}$ and $t_{e2}$ where $t_{e1} \lt t_{e2}$ – Apashanka Das Mar 21 at 10:56