If the Hubble constant was measured to be 5% higher than its current value, by what factor would the value of critical density of the universe change? Give your answer as a percentage correct to one significant figure.
Question
If the Hubble constant was measured to be 5% higher than its current value, by what factor would the value of critical density of the universe change? Give your answer as a percentage correct to one significant figure.
Solution
The critical density (ρc) of the universe is given by the equation:
ρc = 3H² / 8πG
where H is the Hubble constant and G is the gravitational constant.
If the Hubble constant H was measured to be 5% higher than its current value, it would be 1.05H.
Substituting this into the equation gives:
ρc' = 3(1.05H)² / 8πG = 1.1025 * (3H² / 8πG) = 1.1025ρc
So the critical density of the universe would increase by 10.25%.
Rounded to one significant figure, this is a 10% increase.
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