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

Step-by-step 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) ((L_1)/(L_2))`

Given that;

m_1 = 1 and

m_2 = 4

Therefore,

`1 - 4 = -2.5 log _(10) ( (L_1)/(L_2))`

`3 = -2.5 log _(10) ( (L_1)/(L_2))`

Making
`(L_1)/(L_2)` the subject of the formula:

`\implies (L_1)/(L_2)= 10^{((3)/(2.5))}`

=15.84

≅ 16

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