Question

(b) What is the luminosity L of Altair in units of the solar luminosity L⊙? (4 points)

Answer 1

Question:

(b) What is the luminosity $L$ of Altair in units of the solar luminosity $L_{\odot}$? (4 points)

Solution:

We can use the formula:

$$f \propto \frac{L}{d^{2}} \quad \text{or} \quad f = C \times \frac{L}{d^{2}}, \quad \text{where } C \text{ is a constant}.$$

So we can write:

$$\frac{f(\text{Altair})}{f(\text{Sun})} = \frac{L(\text{Altair})}{L(\text{Sun})} \times \frac{d^{2}(\text{Sun})}{d^{2}(\text{Altair})}$$ $$\frac{L(\text{Altair})}{L(\text{Sun})} = \frac{f(\text{Altair})}{f(\text{Sun})} \times \frac{d^{2}(\text{Altair})}{d^{2}(\text{Sun})}$$ $$L(\text{Altair}) = \frac{9.4 \times 10^{-12} \times (5pc)^{2}}{\left(\frac{1}{206265pc}\right)^{2} L(\text{Sun})} = 10L(\text{Sun})$$

Answer: $10 \, \text{L}_{\odot}$

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