You're asking about the solar irradiance (power per unit area) at a distance four times farther from the Sun than Earth. Here's how to calculate that:

Understanding the Inverse Square Law

The intensity of light (or any radiation) decreases with the square of the distance from the source. This is called the inverse square law.

Calculation

1. Earth's distance: Earth is approximately 1 Astronomical Unit (AU) from the Sun.

2. Four times the distance: 4 AU

3. Solar Irradiance at Earth: The average solar irradiance at Earth is about 1361 W/m² (watts per square meter).

4. Irradiance at 4 AU: Since we're four times farther away, the irradiance will be 1/16th (1/4²) of the irradiance at Earth.

Calculation:

(1361 W/m²) / (4²) = 85.06 W/m²

Therefore, the solar irradiance at a distance four times farther from the Sun than Earth is approximately 85.06 W/m².