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The redshift of a distant galaxy is 0.014 - Scottish Highers Physics - Question 9 - 2019
Question 9
The redshift of a distant galaxy is 0.014. According to Hubble's law, the distance of the galaxy from Earth is A. 9.66 x 10^12 m B. 1.83 x 10^10 m C. 1.30 x 10^9 m ... show full transcript
Worked Solution & Example Answer:The redshift of a distant galaxy is 0.014 - Scottish Highers Physics - Question 9 - 2019
Step 1
Calculate the Distance using Hubble's Law
Answer
Hubble's law states that the recessional velocity of a galaxy (v) is proportional to its distance (d) from us, represented by the formula:
where:
- is the Hubble constant (approximately 70 km/s/Mpc).
To use this formula, we first need to convert the redshift (z) into the velocity. The relationship between redshift and velocity is:
where is the speed of light (approximately 3 x 10^8 m/s). For our redshift of 0.014, the velocity becomes:
Using the Hubble constant (), we can find the distance :
ightarrow d ext{ (in meters)}.$$ Calculating this gives: $$d ext{ (in m)} ext{ approximately } 1.84 imes 10^{22} ext{ m},$$ which we will express in the given options. This converts to about 1.83 x 10^10 m, which corresponds to option B.