Possible equations (choose the correct one): $τ =10^{12}$/H; H=v/d. If gravity is unimportant and H equals 75 km/s/Mpc, then the age of the universe is about

Question

Quizplus · Accepted Answer

First, we need to find the value of H in units of seconds. To do this, we can convert 1 Mpc (megaparsec) to km:

1 Mpc = 3.086 × 10^19 km

So:

H = 75 km/s/Mpc 
  = 75 km/s / (3.086 × 10^19 km/Mpc) 
  = 2.43 × 10^-18 s^-1

Next, we can use the equation H = v/d to solve for the age of the universe (τ), where v is the recessional velocity of distant galaxies and d is the distance to those galaxies. We'll assume v is equal to H times the distance to the galaxies (i.e. v = Hd) due to the expansion of the universe:

τ = 1/H 
  = 1/(2.43 × 10^-18 s^-1) 
  = 4.11 × 10^17 s 
  ≈ 13 billion years

So, the best choice is B, which is 13 billion years.

Possible Equations (Choose the Correct One) τ=1012τ =10^{12}τ=1012 /H; H=v/d If Gravity Is Unimportant and H Equals 75 Km/s/Mpc

Possible Equations (Choose the Correct One) $τ =10^{12}$ /H; H=v/d If Gravity Is Unimportant and H Equals 75 Km/s/Mpc