Question

Three cosmologists have each plotted a line on the Hubble-like graph of Fig. 44-11. If we calculate the corresponding age of the universe from the three plots, rank the plots according to that age, greatest first.

Short answer

The rank of graphs according to age are:

$3>2>1$

Step-by-step solution

Concept used to solve the question

Hubble’s law:

According to Edwin Hubble, Our Universe is expanding, with galaxies moving away from each other at a velocity.

The expression for the galaxy’s recessional velocity is given by,

$v=H·r$

Herev represents the galaxy's recessional velocity,

r is its distance from Earth,

H is a constant of proportionality called Hubble's constant.

Finding the order of graphs

Suppose T is the age of the universe,

We know,

$T=\frac{r}{v}=\frac{1}{H}$

From the graph, we can see that the first graph has the largest slope, therefore its Hubble’s constantis more.

Therefore, it represents the less age, and the third graph represents the greatest age.

So, the rank of graphs according to age are

$3>2>1$