Fig. 1.1 shows a graph of recession velocity against distance for several galaxies. What does the gradient of the best-fit line represent?
Question 1 Report
Fig. 1.1 shows a graph of recession velocity against distance for several galaxies.
What does the gradient of the best-fit line represent?
Answer Details
Hubble's law is expressed as \( v = H_0 \, d \), where \( v \) is the recession velocity of a galaxy, \( d \) is its distance from Earth, and \( H_0 \) is the Hubble constant.
The graph plots recession velocity (\( v \)) on the vertical axis against distance (\( d \)) on the horizontal axis. Rearranging Hubble's law gives:
\[ H_0 = \frac{v}{d} \]
This is exactly the definition of the gradient of a straight line passing through the origin on a \( v \) versus \( d \) graph. The gradient of the best-fit line therefore represents the Hubble constant.
The reciprocal \( 1/H_0 \) gives an estimate of the age of the universe, but it is the Hubble constant itself that is read directly from the gradient.
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