Question

Star X has an apparent magnitude of 1. Star Y has an apparent magnitude of 4. Both stars are in the same star cluster. Which star is more intrinsically luminous and by what factor

Answer 1

Answer:

Explanation:

From the given information:

Since both stars are in the same cluster, the magnitude and luminosity relationship can be calculated as:

$m_1 - m_2 = -2.5 log _{10} (\dfrac{L_1}{L_2})$

Given that;

m_1 = 1 and

m_2 = 4

Therefore,

$1 - 4 = -2.5 log _{10} ( \dfrac{L_1}{L_2})$

$3 = -2.5 log _{10} ( \dfrac{L_1}{L_2})$

Making $\dfrac{L_1}{L_2}$ the subject of the formula:

$\implies \dfrac{L_1}{L_2}= 10^{(\dfrac{3}{2.5})}$

=15.84

≅ 16

Hence, we can conclude that star X is more luminous by a factor of 16