The solar constant is equal to 1370 W/m^2. What would the distance between the earth and the sun...?
Question:
Answer:
The amount of energy that reaches a point at a given distance from the sun is the inverse square of the distance.
So for the earth (earth = 1 and sun = 1):
1(luminosity)/1(AU)^2 = 1(energy rec'd)
or 1370 watts at 1 AU (93 million miles) for a star with the luminosity of the sun.
To answer your question, we have to re-arrange the problem.
First-- 1 W/m^2 / 1370 W/m^2 = .00073 (energy rec'd)
Now since Energy and Luminosity are known, we move distance to a place by itself:
1 / AU^2 = .00073
AU^2 = 1 / .00073
AU = sqrt(1 / .00073) ~ 37 AU or 3.4 billion miles.
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