Solar Luminosity: Calculating Sphere of Light Illuminating Earth's Orbit

In summary, solar luminosity is a measure of the total amount of energy emitted by the Sun per unit time. It is calculated by multiplying the surface area of the Sun by its effective temperature and the Stefan-Boltzmann constant. The sphere of light illuminating Earth's orbit refers to the imaginary sphere surrounding the Sun, with a radius equal to the distance between the Sun and Earth, and is calculated using the inverse-square law. This calculation is important for understanding the impact of solar radiation on Earth and for determining the habitable zone around stars.
  • #1
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Homework Statement


The formula for the surface area of a sphere is 4(3.14) r2, where r is the mean distance from the sun to the earth. Determine the sphere of light (square meters) illuminated by the sun the size of the Earth's orbit.

Homework Equations



astronomical Unit-149,597,829 k

The Attempt at a Solution


my answer is 2.8122922(17)
no idea
 
Last edited:
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  • #2
Welcome to the Physics Forum, newsflash!

S = 4(3.14) r^2
= 4*3.14*(149,597,829 km)^2
= 2.81 x 10^15 km^2
If you need that in square meters, I suggest you change the r value into meters before squaring. It is tricky changing units on something after it is squared.
 
  • #3
what the answer isI can provide a response to this content. The formula for the surface area of a sphere is correct, but the value for r should be in meters, not kilometers. The correct value for the mean distance from the sun to Earth is approximately 149,597,870,700 meters. Plugging this value into the formula, we get a surface area of approximately 2.8122922 x 10^17 square meters. This is the area of the sphere of light that is illuminated by the sun at the distance of Earth's orbit.
 

1. What is solar luminosity?

Solar luminosity is a measure of the total amount of energy emitted by the Sun per unit time. It is often expressed in terms of watts or solar luminosities (L☉), with one solar luminosity equal to the total energy emitted by the Sun in one second.

2. How is solar luminosity calculated?

Solar luminosity is calculated by multiplying the surface area of the Sun by its effective temperature and the Stefan-Boltzmann constant. The formula is L = 4πR2σTeff4, where R is the radius of the Sun, σ is the Stefan-Boltzmann constant, and Teff is the effective temperature of the Sun.

3. What is the sphere of light illuminating Earth's orbit?

The sphere of light illuminating Earth's orbit refers to the imaginary sphere surrounding the Sun, with a radius equal to the distance between the Sun and Earth. This sphere represents the area that is directly impacted by the Sun's radiation and determines the amount of solar energy that reaches Earth.

4. How is the sphere of light calculated?

The sphere of light is calculated using the inverse-square law, which states that the intensity of radiation is inversely proportional to the square of the distance from the source. Therefore, the area of the sphere is calculated by multiplying the surface area of a sphere with a radius equal to the distance between the Sun and Earth by the inverse-square of this distance.

5. Why is calculating the sphere of light important?

Calculating the sphere of light is important because it allows us to understand the amount of solar energy that reaches Earth, which is essential for understanding climate, weather patterns, and the overall functioning of our planet. It also helps us to determine the habitable zone around stars, where planets can potentially support life based on the amount of solar radiation they receive.

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