Astronomers use the following relationship to determine the distance, d, to a star - Scottish Highers Physics - Question 20 - 2017

To find the distance, we can rearrange the formula: $d = \sqrt{\frac{I}{4\pi F}}$ Substituting the known values:

• Luminosity, $I = 6 \times 10^{30} \text{ W}$
• Apparent brightness, $F = 4.4 \times 10^{-10} \text{ W m}^{-2}$

Now, calculate: $d = \sqrt{\frac{6 \times 10^{30}}{4\pi \cdot (4.4 \times 10^{-10})}}$ Calculating the denominator: $4\pi \cdot (4.4 \times 10^{-10}) \approx 5.52 \times 10^{-9}$ Now, perform the division: $\frac{6 \times 10^{30}}{5.52 \times 10^{-9}} \approx 1.087 \times 10^{39}$ Finally, take the square root: $d \approx 3.3 \times 10^{19} \text{ m}$