Energy from the Sun received at the Earth cross section

In summary: The Earth subtends a solid angle of ##2\pi## steradians. The solid angle is what the Sun "sees".In summary, the calculation for the energy received by the Earth from the Sun in a given year involves multiplying the energy per square meter received at 1AU by pi*R^2, the area of a circle. This is because the Sun doesn't care about the shape of the Earth and sends out the same power per unit solid angle in all directions. The Earth subtends a solid angle of 2pi steradians, which is what the Sun "sees".
  • #1
Puchinita5
183
0

Homework Statement



My homework involves calculating the amount of energy the Earth receives from the Sun in a given year. I actually have the answer, but what I'm confused with is that the calculation says that the Sun "sees the cross section of the Earth, a circle". So in the calculation, we multiply the energy per square meter received at 1AU by pi*R^2 (R is the radius of the Earth).

Why isn't it multiplied by half of the surface area of Earth? I picture half of the Earth facing the sun as the surface receiving the energy. So I would think to multiply by 2*pi*r^2.

Homework Equations

The Attempt at a Solution

 
Physics news on Phys.org
  • #2
Hi.

##\pi r^2## is the area of a circle. That's what the sun 'sees'.

You seem to be thinking of half a sphere, but then
  1. a sphere has area ##{4\over 3} \pi r^2##
  2. the angle of incidence has to be corrected for -- which brings you back to ##\pi r^2##
Make a little sketch showing this angle of incidence

Or check the shadow of a sphere on a wall !
 
  • #3
Puchinita5 said:
Why isn't it multiplied by half of the surface area of Earth?
Because the Sun doesn't care what shape the Earth is. It sends out the same power per unit solid angle in all directions. The power the Earth gets is proportional to the solid angle it subtends at the Sun.
 

FAQ: Energy from the Sun received at the Earth cross section

1. How does the Sun's energy reach the Earth?

The Sun's energy reaches the Earth through a process called radiation. The Sun emits electromagnetic radiation, which travels through space and reaches the Earth's atmosphere. Some of this radiation is absorbed by the Earth's atmosphere, while the rest reaches the Earth's surface.

2. How much energy from the Sun reaches the Earth's cross section?

The amount of energy from the Sun that reaches the Earth's cross section is known as the solar constant, and it is approximately 1361 watts per square meter. However, this value can vary slightly due to factors such as the Earth's distance from the Sun and changes in solar activity.

3. How does the Earth's tilt affect the amount of energy received from the Sun?

The Earth's tilt does not significantly affect the amount of energy received from the Sun at the Earth's cross section. This is because the Earth's tilt only affects the distribution of energy across the Earth's surface, not the total amount of energy received.

4. What happens to the Sun's energy when it reaches the Earth's surface?

When the Sun's energy reaches the Earth's surface, it can be absorbed, reflected, or scattered. The amount of energy that is absorbed depends on the surface's characteristics, such as color and texture. Some surfaces, like snow and ice, reflect a large portion of the energy back into space.

5. How is the Sun's energy used by living organisms on Earth?

Living organisms on Earth use the Sun's energy through the process of photosynthesis, where plants convert sunlight into chemical energy that can be used as food. Other organisms, like animals, indirectly use the Sun's energy by consuming plants or other animals that have used the Sun's energy through photosynthesis.

Similar threads

Back
Top