Subjects physics

Venus Solar Constant 7986F1

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1. The problem asks to calculate the solar constant (Sp value) for Venus in watts per square meter (W m^{-2}). 2. The solar constant Sp for a planet is given by the formula: $$Sp = S_0 \times \left(\frac{R_0}{R_p}\right)^2$$ where $S_0$ is the solar constant at Earth's orbit (approximately 1361 W m^{-2}), $R_0$ is the average distance from the Sun to Earth (1 astronomical unit, AU), and $R_p$ is the average distance from the Sun to the planet (Venus in this case). 3. From Q1a (assumed data): - $S_0 = 1361$ W m^{-2} - $R_0 = 1$ AU - $R_p$ for Venus = 0.723 AU 4. Substitute the values into the formula: $$Sp = 1361 \times \left(\frac{1}{0.723}\right)^2$$ 5. Calculate the fraction inside the parentheses: $$\frac{1}{0.723} \approx 1.383$$ 6. Square this value: $$1.383^2 = 1.911$$ 7. Multiply by $S_0$: $$Sp = 1361 \times 1.911 = 2601.471$$ 8. Therefore, the solar constant for Venus is approximately: $$Sp \approx 2601.5 \text{ W m}^{-2}$$ This means Venus receives about 2601.5 watts per square meter of solar energy at its orbit.