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

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The discussion focuses on calculating the surface area of the sphere of light illuminated by the sun, specifically regarding the Earth's orbit. The formula used is S = 4(3.14) r^2, with r being the mean distance from the sun to the Earth, approximately 149,597,829 kilometers. The initial calculation yields a surface area of about 2.81 x 10^15 km^2. A key point emphasized is the importance of converting the radius into meters before squaring to avoid complications with unit conversion. This calculation is crucial for understanding solar luminosity in relation to Earth's orbit.
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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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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.
 

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