How to Calculate Sunlight Intensity at Different Distances from the Sun

What is the intensity of the sunlight at a distance of 9.5 AU from the Sun (relative to Earth)?

A. 1/9.5 times the intensity on Earth
B. 9.5 times the intensity on Earth
C. The same as Earth's intensity
D. 9.5/2 times the intensity on Earth

Answer:

The intensity of sunlight at Saturn is (1/9.5)² times the intensity on Earth, which is about 1/90.25 or 0.011 times the intensity on Earth, making answer A the correct choice.

Explanation: The intensity of sunlight at Saturn, which is 9.5 astronomical units (AU) from the Sun, can be calculated using the inverse square law. This law states that the intensity of sunlight decreases with the square of the distance from the source.

Since Saturn is 9.5 times farther from the Sun than Earth, the intensity of sunlight it receives is (1/9.5)² times the intensity on Earth. To find the exact value, we calculate (1/9.5)² which is approximately (1/90.25). Therefore, the correct answer to the student's question is A - 1/9.5 times the intensity on Earth, which indicates that sunlight is much less intense on Saturn compared to Earth.

Despite the weaker intensity, if we consider the apparent magnitude of the Sun from Saturn, it would still be the brightest star in the sky due to its enormous absolute magnitude compared to other stars.