Final answer:
It takes approximately 229 million years for light to travel from one side of the local supercluster to the other.
Step-by-step explanation:
To calculate the time it takes for light to travel from one side of the local supercluster to the other, we need to use the speed of light and the diameter of the supercluster.
The speed of light is approximately 299,792 kilometers per second.
Since the diameter of the local supercluster is given in megaparsecs (Mpc), we first need to convert it to kilometers
. 1 megaparsec is equivalent to approximately 3.09 x 10^19 kilometers.
Therefore, the diameter of the supercluster in kilometers is 70 Mpc x 3.09 x 10^19 kilometers/Mpc = 2.16 x 10^21 kilometers.
To calculate the time it takes for light to travel this distance, we divide the distance by the speed of light:
2.16 x 10^21 kilometers / 2.99 x 10^5 kilometers/second = 7.22 x 10^15 seconds.
To express this time in millions of years, we divide by the number of seconds in a year (60 seconds/minute x 60 minutes/hour x 24 hours/day x 365.25 days/year) and then divide by 10^6:
7.22 x 10^15 seconds / (60 x 60 x 24 x 365.25 x 10^6) = 229 million years.
Therefore, it takes approximately 229 million years for light to travel from one side of the local supercluster to the other.