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zjmarlow
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Homework Statement
The intensity of the Sun's radiation just outside the Earth's atmosphere is approximately 8 \cdot 10^4 \frac {joules}{m^2 \cdot min}. Echo II is a spherical shell of radius r_0 = 20.4m. Its skin consists of a layer of Mylar plastic ... between two layers of aluminum. ... Aluminum's reflection coefficient is .81.
Approximately what force does [the Sun's] radiation exert on the Echo II reflecting satellite balloon?
Homework Equations
(From experiment explained earlier in the chapter)
c = \frac {W(1 + ρ)}{F}
(Solved for force)
F = \frac {W(1 + ρ)}{c}
Where W is the rate of arrival of energy, F is the rate of change of momentum (force), ρ is the reflection coefficient, and c is the speed of light in a vacuum.
The Attempt at a Solution
This seemed like a flux problem, so
\iint_D{F(r(\varphi,\vartheta)) \cdot (r_\varphi \times r_\vartheta) dA}
Where
r(\varphi,\vartheta) = r_o sin \varphi cos \vartheta \textbf{i} + r_o sin \varphi sin \vartheta \textbf{j} + r_o cos \varphi \textbf{k}
F = -\frac{W(1 + ρ)}{c}\textbf{k}
r_\varphi \times r_\vartheta = r_o^2 sin^2 \varphi cos \vartheta \textbf{i} + r_o^2 sin^2 \varphi sin \vartheta \textbf{j} + r_o^2 sin \varphi cos \varphi \textbf{k}
so
F(r(\varphi,\vartheta)) \cdot (r_\varphi \times r_\vartheta) = -\frac{W (1 + ρ)}{c} r_o^2 sin \varphi cos \varphi \textbf{k}
-\frac{W (1 + ρ)}{c} r_0^2 \int_0^{2\pi}{\int_0^\frac{\pi}{2}{sin \varphi cos \varphi d\varphi d\vartheta}}
my problem : I get .0105 N when the back of the book solution is .00576 N
Did I set something up wrong?
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