Hubble's Law Measurements

Question

In measurements concerning distances, luminosity, etc. to evaluate the Hubble's parameter, do scientists take into considerations the fact that the light, emitted from a star, and received by a detector, is actually not representing the actual distance of the star? Thus when we say the current value of the Hubble's parameter is wrong, in a sense, it reflects measurements obtained from past events.

For example, if we denote (D), (O) for detector and object respectively,

(D)----$d_0$-----(O) -perceived

(D)-----$d$---------(O) -actual

then the actual distance $d=d_0(1+v/c)$.

Answer 1

The answer is yes. Hubble's law relates the "velocity of recession" to the proper distance - which is the distance to the other galaxy now.

That is not usually the distance we measure, as you have identified.

The difference between the two is very small at low redshifts, but becomes larger at higher redshifts, and depends on the expansion history of the universe and hence the cosmological parameters like $\Omega_M$, $\Omega_\Lambda$ as well as $H_0$.