Q46P - Fundamentals Of Physics

Question

Question: Figure 44-12 is a hypothetical plot of the recessional speeds v of galaxies against their distance r from us; the best-fit straight line through the data points is shown. From this plot determine the age of the universe, assuming that Hubble’s law holds, and that Hubble’s constant has always had the same value.

Step-by-Step Solution

Answer

$\mathrm{T}=13\times {10}^9\mathrm{y}$

Step 1: Given information

Figure:

 

Step 2: formula formation for the age of the universe by the figure

Assuming the time passes through the origin, its slope = $\frac{0.4 \mathrm{c}}{5.3\times {10}^{91}}$

Step 3: solution by the graph

 $$\begin{gathered} \mathrm{T}=\frac{1}{\mathrm{H}} \\ =\frac{1}{\mathrm{Slope}} \\ =\frac{5.3\times {10}^{91}}{0.40\mathrm{c}} \\ =13\times {10}^9\mathrm{y} \end{gathered}$$