Some information is given about the Earth and solar radiation from the Sun.

Earth’s radius = 6371 km

Solar constant = 1366 W m–2

Albedo of Earth’s upper atmosphere = 0.3

Determine how much solar radiation from the Sun is reflected back into space per second. State your answer in PJ (peta joules) to four significant figures.

Assume that the Earth is a sphere and one half of the Earth’s atmosphere is available to receive this solar radiation, in full, at any latitude.



We can calculate the amount of solar radiation reflected back into space using the given dataWe can calculate the amount of solar radiation reflected back into space using the given 

### Step 1: Total Power Incident on the Earth
The total power \( P_{\text{incident}} \) received by Earth from the Sun can be calculated using the formula for the power incident on a spherical object:

\[
P_{\text{incident}} = \text{Solar constant} \times \text{Cross-sectional area of Earth}
\]

Since the Earth is approximately a sphere, its cross-sectional area is:

\[
A = \pi r^2
\]

Where \( r \) is the Earth's radius. So:

\[
A = \pi \times (6371 \times 10^3 \, \text{m})^2
\]

Substituting the given radius of the Earth.

### Step 2: Calculate the Incident Power
Now, use the given solar constant \( S = 1366 \, \text{W m}^{-2} \) to find the incident power on Earth:

\[
P_{\text{incident}} = 1366 \, \text{W/m}^2 \times A
\]

### Step 3: Reflected Power
The fraction of the incident radiation that is reflected back into space is determined by the Earth's albedo, \( \alpha = 0.3 \). The reflected power \( P_{\text{reflected}} \) is:

\[
P_{\text{reflected}} = \alpha \times P_{\text{incident}}
\]

### Step 4: Convert to PetaJoules per Second (PJ/s)
Finally, since \( 1 \, \text{W} = 1 \, \text{J/s} \), we can convert the reflected power to peta joules (\( 1 \, \text{PJ} = 10^{15} \, \text{J} \)).

Let me compute these steps for you.The amount of solar radiation reflected back into space per second is approximately **52.26 PJ** (peta joules), to four significant figures.

Do you want more details or have any questions?

Here are five related questions to expand on this topic:
1. How does the Earth's albedo affect global temperatures?
2. What would happen if the Earth's albedo increased or decreased significantly?
3. How is the solar constant measured, and does it vary over time?
4. Why does the calculation assume that only half of the Earth's atmosphere receives solar radiation?
5. How does the Earth's atmosphere influence the amount of radiation that reaches the surface?

**Tip:** Albedo is a key factor in understanding climate dynamics—it represents the reflectivity of a surface.

Determine how much solar radiation from the Sun is reflected back into space per second, given Earth's radius = 6371 km, Solar constant = 1366 W/m², Albedo of Earth's upper atmosphere = 0.3. State the answer in PJ (peta joules) to four significant figures. Assume that the Earth is a sphere and one half of the Earth’s atmosphere is available to receive this solar radiation, in full, at any latitude.

Learn how to calculate the amount of solar radiation reflected back into space using Earth's albedo, solar constant, and radius. This problem covers key concepts in energy and power calculations, spherical geometry, and the albedo effect. Suitable for high school students in Grades 11-12.

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