The farthest object we have seen (in 2011) has a redshift z of about 7.09, which corresponds to a recessional velocity v = 0.970c. What is the light travel time for this object as a percentage of the estimated age of the universe, 13.4 billion years?
A)55.9%
B)64.0%
C)94.0%
D)97.0%

Question

Quizplus · Accepted Answer

The light travel time is the distance to the object divided by the speed of light. The distance to the object is given by the redshift, which is related to the recessional velocity by the equation z = v/c. The recessional velocity is given as 0.970c, so the redshift is z = 0.970. The distance to the object is then given by the equation d = c*t, where t is the light travel time. Substituting the values for c and z, we get d = (3*10^8 m/s)*t. The estimated age of the universe is 13.4 billion years, which is equal to 4.22*10^17 seconds. The light travel time as a percentage of the estimated age of the universe is then given by the equation (t/4.22*10^17 s)*100%. Substituting the value for t, we get ((3*10^8 m/s)*t/4.22*10^17 s)*100% = 97.0%.

The Farthest Object We Have Seen (In 2011) Has a Redshift