Final answer:
Using Hubble's Law and given data, the approximate speed of a galaxy 10 Gly away is 2×105 km/s, or 71.6% the speed of light. This correlates with observations of galaxies moving away at speeds exceeding 0.9 times the speed of light.
Step-by-step explanation:
To determine the approximate speed relative to us of a galaxy near the edge of the known universe, we need to use Hubble's Law, which states that the speed at which a galaxy is moving away from us (v) is directly proportional to its distance from us (d). The Hubble constant (H0) is the proportionality constant in this law and has an average value of about 70 km/s/Mpc. Given that 1 Mpc is approximately 3.26 million light-years (Mly), we can calculate the speed for a galaxy that is 10 billion light-years (10 Gly) away.
First, convert the distance from Gly to Mpc:
- 10 Gly = 10,000 Mly = 10,000 / 3.26 Mpc = 3067.48 Mpc
Next, we apply Hubble's Law:
- v = H0 × d
- v = 70 km/s/Mpc × 3067.48 Mpc
- v = 214,723.6 km/s
This speed (v) corresponds to the answer choice (a) 2×105 km/s, as it is approximately 214,724 km/s, which is close to 2×105 km/s.
To find the fraction of the speed of light (c) this is, we use the fact that the speed of light is about 3×105 km/s:
- Fraction of c = speed of galaxy / speed of light
- Fraction of c = 214,724 km/s / 3×105 km/s
- Fraction of c = 0.71575
Therefore, the galaxy is moving away from us at approximately 71.6% of the speed of light. This is consistent with the fact that we have observed galaxies having red shifts corresponding to speeds greater than 0.9c.