11 The intensity of the sun's radiation, \(y\) watts per square metre, and the average distance from the sun, \(x\) astronomical units, are shown in Fig. 11 for the planets Mercury and Jupiter.
\begin{table}[h]
| \(x\) | \(y\) |
| Mercury | 0.3075 | 14400 |
| Jupiter | 4.950 | 55.8 |
\captionsetup{labelformat=empty}
\caption{Fig. 11}
\end{table}
The intensity \(y\) is proportional to a power of the distance \(x\).
- Write down an equation for \(y\) in terms of \(x\) and two constants.
- Show that the equation can be written in the form \(\ln y = a + b \ln x\).
- In the Printed Answer Booklet, complete the table for \(\ln x\) and \(\ln y\) correct to 4 significant figures.
- Use the values from part (iii) to find \(a\) and \(b\).
- Hence rewrite your equation from part (i) for \(y\) in terms of \(x\), using suitable numerical values for the constants.
- Sketch a graph of the equation found in part (v).
- Earth is 1 astronomical unit from the sun. Find the intensity of the sun's radiation for Earth.