An astronomer observes two galaxies, A and B, which have redshifts of:
Galaxy A = 0.020 and Galaxy B = 0.010.
Which galaxy is closest to us and what is its distance away from us?
You may assume that the Hubble constant is H0 = 75 km s–1 Mpc−1 and that the speed of light is
c = 3.0 × 105 km s–1.
The closest galaxy is: Galaxy a?? or galaxy b??
It is at a distance of ????? Mpc.?
Assuming that Galaxy A is intrinsically of identical luminosity to Galaxy B, how does its apparent brightness on the night sky compare to that of Galaxy B?
Galaxy A is ???? times BRIGHTER or FAINTER??? than Galaxy B.
To determine which galaxy is closest to us and calculate its distance away, we can use Hubble's Law and the equation v = H0 * d, where v is the recessional velocity (redshift), H0 is the Hubble constant, and d is the distance from Earth to the galaxy.
Given:
- Galaxy A redshift (z): 0.020
- Galaxy B redshift (z): 0.010
- Hubble constant (H0): 75 km s^-1 Mpc^-1
- Speed of light (c): 3.0 × 10^5 km s^-1
First, we need to convert the redshifts to velocities using the formula v = cz, where c is the speed of light.
For Galaxy A:
v_A = c * z_A = 3.0 × 10^5 km s^-1 * 0.020 = 6,000 km s^-1
For Galaxy B:
v_B = c * z_B = 3.0 × 10^5 km s^-1 * 0.010 = 3,000 km s^-1
Next, we can use Hubble's Law to calculate the distances:
For Galaxy A:
d_A = v_A / H0 = 6,000 km s^-1 / 75 km s^-1 Mpc^-1 = 80 Mpc
For Galaxy B:
d_B = v_B / H0 = 3,000 km s^-1 / 75 km s^-1 Mpc^-1 = 40 Mpc
Therefore, Galaxy B is closest to us with a distance of 40 Mpc.
Now, let's consider the apparent brightness of Galaxy A compared to Galaxy B, assuming they have the same intrinsic luminosity.
The apparent brightness (B) of a source is inversely proportional to the square of its distance (d). Mathematically, B ∝ 1/d^2.
Since Galaxy B is closer to us, its apparent brightness will be greater than that of Galaxy A. We can calculate the ratio of their apparent brightness using the formula:
Brightness ratio = (d_B / d_A)^2
Brightness ratio = (40 Mpc / 80 Mpc)^2 = 0.5^2 = 0.25
Therefore, Galaxy A is 0.25 times (or 4 times fainter) than Galaxy B.
To determine which galaxy is closest to us and its distance away from us, we can use the formula for calculating distance based on redshift:
Distance (in Mpc) = (redshift * c) / H0
Where:
- redshift is the observed redshift of the galaxy
- c is the speed of light (3.0 × 10^5 km/s)
- H0 is the Hubble constant (75 km/s/Mpc)
Let's calculate the distances for both galaxies:
For Galaxy A:
Distance (in Mpc) = (0.020 * 3.0 × 10^5 km/s) / 75 km/s/Mpc
For Galaxy B:
Distance (in Mpc) = (0.010 * 3.0 × 10^5 km/s) / 75 km/s/Mpc
Calculating these values will give us the distance for both galaxies.
Now, to compare the apparent brightness of Galaxy A and Galaxy B, we need to consider their distance from us and assume they have identical intrinsic luminosity. The apparent brightness of an object decreases with increasing distance according to the inverse square law:
(Apparent Brightness A / Apparent Brightness B) = (Distance B / Distance A)^2
Where:
- Apparent Brightness A is the apparent brightness of Galaxy A
- Apparent Brightness B is the apparent brightness of Galaxy B
- Distance A is the distance of Galaxy A from us
- Distance B is the distance of Galaxy B from us
By comparing the distances, we can determine the relative apparent brightness of Galaxy A and Galaxy B.
Let's calculate the values to find out the closest galaxy, their distances from us, and the relative apparent brightness.