Question

The solar constant for the Earth is 1368 W m\(^{-2}\). Consider the planet Jupiter whose mass is 320 times that of the Earth and distance from the Sun is 5.2 times that of the Earth. The solar constant for Jupiter is .......... W m\(^{-2}\). (Round off to the nearest integer.) [Assume the inverse square law for the solar radiation.]

Hint:

To calculate the solar constant for a planet, use the inverse square law, considering the distance from the Sun. The solar constant decreases with the square of the distance.

Answer 1

The solar constant \( S \) is inversely proportional to the square of the distance from the Sun. Using the inverse square law: \[ S_J = S_E \times \left( \frac{R_E}{R_J} \right)^2 \] Where:
- \( S_J \) is the solar constant for Jupiter,
- \( S_E \) is the solar constant for Earth,
- \( R_E \) and \( R_J \) are the distances from the Sun for Earth and Jupiter, respectively.
Given:
- \( S_E = 1368 \, {W m}^{-2} \),
- \( R_J = 5.2 \times R_E \).
Substitute the values: \[ S_J = 1368 \times \left( \frac{1}{5.2} \right)^2 \] \[ S_J = 1368 \times \frac{1}{27.04} \] \[ S_J \approx 50.5 \, {W m}^{-2} \] Thus, the solar constant for Jupiter is approximately 50 to 52 W m\(^{-2}\).