Question

Choose the best answer to each of the following. Explain your reasoning with one or more complete sentences. On an asteroid that is twice as far as Earth from the Sun, the strength of sunlight would be (a) twice as great as on Earth; (b) \(\frac{1}{2}\) as great as on Earth; \((\mathrm{c}) \frac{1}{4}\) as great as on Earth.

Short answer

(c) \(\frac{1}{4}\) as great as on Earth.

Step-by-step solution

Understand the concept of sunlight intensity and distance

The strength of sunlight (solar intensity) on a surface is inversely proportional to the square of the distance from the sun. This means that if you double the distance from the sun, the solar intensity will change by a factor of the inverse of the distance squared.

Apply the Inverse Square Law

According to the inverse square law, if the distance doubles, the intensity \[\text{Intensity} \propto \frac{1}{\text{distance}^2}\]When the distance to the sun becomes twice, \[\text{Intensity} \propto \frac{1}{(2)^2} = \frac{1}{4}\]Therefore, the intensity is \(\frac{1}{4}\) as great as on Earth.

Conclude with the correct answer

Based on the application of the inverse square law, option (c) is correct. The strength of sunlight on the asteroid would be \(\frac{1}{4}\) as great as on Earth, given that it is twice as far from the sun as Earth is.

Key concepts

Solar Intensity

Solar intensity refers to the power per unit area received from the Sun at a given location. It is a crucial aspect of solar energy and affects how much energy is harnessed from the Sun. The solar intensity decreases as the distance from the source of light increases. This drop in intensity occurs because the energy from the Sun spreads out over a larger area.
Understanding solar intensity helps in planning solar energy systems effectively. For example, areas closer to the equator tend to receive more intense sunlight than those near the poles. This knowledge is applied in designing locations for solar panels as well.
In essence, solar intensity is directly related to both distance and angle of sunlight. Therefore, knowing the concept helps in optimizing solar power harvesting and predicting climates in different regions of the Earth.

Distance from the Sun

The distance from the Sun fundamentally impacts how much solar energy, or sunlight, reaches any given point in space. This distance plays a key role in defining climate zones and energy availability on our planet and others. As the distance from the Sun increases, the sunlight spreads over a larger area, reducing its intensity.
For objects orbiting the Sun, such as planets and asteroids, knowing this distance is vital for understanding the specific environmental conditions they experience. For instance, in the case of the asteroid mentioned earlier, it is twice as far from the Sun as Earth. This means it receives considerably less solar energy.

• Twice the distance from the Sun means less heat and light reach the surface.
• It impacts temperature, atmosphere, and potential for supporting life.

Understanding the implications of this distance helps not only in astronomical studies but also in designing missions to these celestial bodies.

Sunlight Intensity Calculations

Calculating sunlight intensity is essential in many scientific and engineering applications, especially when dealing with space missions or designing solar power installations. The Inverse Square Law is used to calculate how the intensity of light varies with distance.
According to this law, the intensity of sunlight is inversely proportional to the square of the distance from the Sun. Therefore, if an object is placed twice as far from the Sun as another, the sunlight intensity it receives will be distributed over four times the area, making it \( \frac{1}{4} \) as strong.
To perform these calculations:

• Identify the new distance compared to the original benchmark, such as Earth's distance from the Sun.
• Determine the change in intensity using the formula \( \text{Intensity} \propto \frac{1}{\text{distance}^2} \).

Mastering sunlight intensity calculations is crucial for accurately assessing energy potential and environmental factors in space and on Earth.