A 1.0 m^2 solar panel on a satellite that keeps the panel...

A $1.0 \mathrm{m}^{2}$ solar panel on a satellite that keeps the panel oriented perpendicular to radiation arriving from the Sun absorbs $1.4 \mathrm{kJ}$ of energy every second. The satellite is located at $1.00 \mathrm{AU}$ from the Sun. (The Earth-Sun distance is approximately 1 AU.) How long would it take an identical panel that is also oriented perpendicular to the incoming radiation to absorb the same amount of energy, if it were on an interplanetary exploration vehicle 1.55 AU from the Sun?

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Key Concepts

Inverse-Square Law

The inverse-square law describes how a physical quantity or strength diminishes with increasing distance from its source. In the context of solar energy, the intensity of sunlight decreases proportionally to the square of the distance from the Sun. This means that if you move further away from the Sun, the solar irradiance, or power per unit area, drops significantly, affecting the rate at which energy is absorbed.

Solar Irradiance

Solar irradiance is the power per unit area received from the Sun in the form of electromagnetic radiation. It is a crucial concept in understanding how much energy a solar panel can absorb at different distances from the Sun. The value of solar irradiance at a given distance is determined by both the intrinsic luminosity of the Sun and the spreading out of the energy over a larger area as the distance increases.

Energy Absorption Rate

The energy absorption rate refers to the amount of energy a solar panel or any absorbing surface collects per unit time. This rate depends on factors such as the area of the panel, its orientation relative to the incoming radiation, and the local solar irradiance. Changes in any of these parameters, especially due to varying distances from the Sun, will alter the time required to absorb a specific amount of energy.

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