Final answer:
The correct option for the speed at which two galaxies 2.00×10² Mly apart are separating due to space expansion is option (b) 2×10´km/s, which is equivalent to 4,000 km/s, as calculated using Hubble's Law with a simplified Hubble constant of 20 km/s/Mly.
Step-by-step explanation:
A student asked how fast two galaxies, separated by 2.00×10² Mly, are moving apart due to the expansion of space. This question delves into the realms of astrophysics and cosmology and can be understood by applying Hubble's Law.
Hubble's Law states that the recessional velocity of galaxies (V) is directly proportional to their distance from us (d), which can be represented by the equation V = H₀×d. Here, H₀ denotes the Hubble constant. The accepted value of the Hubble constant, although subject to slight variations, is often considered to be around 70 km/s/Mpc. For simplicity, if we take a rounded value of the Hubble constant as 20 km/s/Mly, this can be used for our calculations.
To find the recessional velocity of the two galaxies, we take their distance, 2.00×10² Mly, and apply the Hubble constant in the equation V = 20 km/s/Mly × 2.00×10² Mly, which gives us 4.00×10³ km/s. Hence, the galaxies are moving apart at a speed of 4,000 km/s. Choosing the correct option from the provided list, we deduce that option (b) 2×10´km/s is the best answer since it approximately represents the calculated recessional velocity of 4,000 km/s.