Question

due date: 12/4/2025 11:59:00 pm end date: 12/7/2025 11:59:00 pm
problem 13. (5% of assignment value)
one way to derive the rough age of the universe is to use the value of the hubble constant and a reliable distance to a far - away galaxy (with the assumption that the value of the hubble constant has not changed since the big bang).

part (a)
consider a galaxy at a distance of 760 million light - years receding from us at velocity, v. if the hubble constant is 22 km/s per million light - years, what is its velocity in km/s?
v = km/s

Explanation:

Step1: Recall Hubble's Law

Hubble's Law is given by \( v = H_0 \times d \), where \( v \) is the recessional velocity, \( H_0 \) is the Hubble constant, and \( d \) is the distance to the galaxy.

Step2: Identify given values

We are given \( H_0 = 22 \, \text{km/s per million light - years} \) and \( d = 760 \, \text{million light - years} \).

Step3: Calculate velocity

Substitute the given values into Hubble's Law: \( v=22\,\text{km/s per million light - years}\times760\,\text{million light - years} \).
The "million light - years" units cancel out, and we calculate \( 22\times760 = 16720 \).

Answer:

\( 16720 \)