An object has a lookback time of 1 billion years. Assuming it is nonrelativistic, and that the Hubble constant is 22.4 km/s/Mly, what is its cosmological redshift?
A)0.074
B)0.126
C)0.546
D)1.89

Question

Quizplus · Accepted Answer

The cosmological redshift, $z$, can be approximated for nonrelativistic distances by $z \approx v/c$, where $v$ is the recessional velocity and $c$ is the speed of light. Given the Hubble constant, $H_0 = 22.4$ km/s/Mly, and a lookback time of 1 billion years (1 Gyr), we first convert the lookback time to megaparsecs (Mpc) to use with the Hubble constant. Knowing that 1 Mly ≈ 1.029 Mpc and the age corresponds to a distance (since the lookback time essentially tells us how far away in time and space the object is), we can calculate the recessional velocity ($v = H_0 \times d$). With $c \approx 3 \times 10^5$ km/s, we can find $z$. However, since the calculation steps are not shown in detail here, the correct answer is chosen based on the provided options, which is A) 0.074, indicating a relatively small redshift corresponding to the nonrelativistic nature of the object's motion and the given parameters.

An Object Has a Lookback Time of 1 Billion Years