Question

part a
what size should the solar panel on a satellite orbiting jupiter be if it is to collect the same amount of radiation from the sun as a 1.0 - m² solar panel on a satellite orbiting earth?
express your answer using two significant figures.
s = m²

Explanation:

Step1: Use the inverse - square law of radiation

The intensity of radiation \(I\) from the Sun follows the inverse - square law \(I=\frac{P}{4\pi r^{2}}\), where \(P\) is the power of the Sun. The power collected by a solar panel is \(P_{collected}=I\times A\). If the power collected is the same (\(P_{1} = P_{2}\)), then \(I_{Earth}\times A_{Earth}=I_{Jupiter}\times A_{Jupiter}\). Since \(I=\frac{P}{4\pi r^{2}}\), we have \(\frac{P}{4\pi r_{Earth}^{2}}\times A_{Earth}=\frac{P}{4\pi r_{Jupiter}^{2}}\times A_{Jupiter}\). The \(P\) and \(4\pi\) terms cancel out, and we get \(A_{Jupiter}=A_{Earth}\times(\frac{r_{Jupiter}}{r_{Earth}})^{2}\).

Step2: Substitute the known values

The average distance of Earth from the Sun \(r_{Earth}= 1.5\times10^{11}\ m\) and the average distance of Jupiter from the Sun \(r_{Jupiter}=7.8\times 10^{11}\ m\), and \(A_{Earth} = 1.0\ m^{2}\).

$$
LATEXBLOCK0
$$

Answer:

\(27\ m^{2}\)