Galaxy A is 600 million light years from earth. Galaxy B is moving away from the earth at a speed that is 80% as large as that of Galaxy A. How far from earth is Galaxy B?

A. 750 million light years.
B. 640 million light years.
C. 540 million light years.
D. 480 million light years

0.8*600,000,000 = ?

To determine the distance of Galaxy B from Earth, we can use the concept of redshift. Redshift occurs when objects in space move away from each other, causing the wavelengths of light they emit to stretch, resulting in a shift towards longer wavelengths (red light).

Given that Galaxy A is 600 million light years away from Earth, we need to find the distance of Galaxy B. We know that the speed of Galaxy B is 80% of the speed of Galaxy A. Redshift is directly proportional to the recessional velocity (speed at which an object is moving away from us). So, if Galaxy B is moving at 80% of Galaxy A's speed, it means it will have a lower redshift compared to Galaxy A.

Using the formula for redshift, we have:

z = (Δλ / λ)

Where:
z is the redshift,
Δλ is the observed change in wavelength,
λ is the rest wavelength of the object.

Since we are comparing two galaxies, the rest wavelengths are the same. Therefore, we can simplify the equation to:

z(B) = (v(B) / c)

Where:
z(B) is the redshift of Galaxy B,
v(B) is the velocity of Galaxy B,
c is the speed of light.

Now, we know that Galaxy A is 600 million light years away, and based on Hubble's law, the recessional velocity (v(A)) is directly proportional to the distance (d) of the galaxy:

v(A) = H₀ * d(A)

Where:
H₀ is the Hubble constant.

Since Galaxy B is moving at 80% of Galaxy A's speed, we can write the equation for Galaxy B as:

v(B) = 0.8 * v(A) = 0.8 * H₀ * d(A)

Now, we can substitute this into the equation for redshift to find the redshift of Galaxy B:

z(B) = (0.8 * H₀ * d(A)) / c

Given that the speed of light is approximately 300,000 km/s, we need to convert it to light years by multiplying it by the number of seconds in a year and dividing by the number of kilometers in a light year:

c ≈ 300,000 km/s * (60 s/min * 60 min/hr * 24 hr/day * 365.25 days/yr) / (9.461 x 10^12 km/ly) ≈ 9.461 x 10^12 ly/yr

Now, we can substitute this value into the equation for redshift:

z(B) = (0.8 * H₀ * d(A)) / (9.461 x 10^12)

Since d(A) is given as 600 million light years, we can plug in these values to find the redshift of Galaxy B.

After finding the redshift, we can use the equation for redshift-distance relation:

z = H₀ * d

Where:
z is the redshift,
H₀ is the Hubble constant,
d is the distance.

Rearranging the equation, we can solve for the distance:

d = z / H₀

Substituting the redshift of Galaxy B into this equation, we can determine its distance from Earth.

So, now let's calculate the distance of Galaxy B from Earth:

z(B) = (0.8 * H₀ * d(A)) / (9.461 x 10^12)
d(B) = z(B) / H₀

Unfortunately, we don't have the value of the Hubble constant or the units provided in the possible answer choices, so we cannot determine the exact distance of Galaxy B from the given options.