Question

luminosity
stars can appear bright or dim depending on how far away they are from earth. but stars also have actual, or absolute, magnitudes. luminosity is the true brightness of an object. the luminosity of a star is measured on an absolute magnitude scale. it depends on the stars temperature and size. it does not depend on its distance from earth.
a stars luminosity, apparent magnitude, and distance are related. if scientists know two of these factors, they can find the third using mathematical formulas.
explore/explain • page 179
apply it
enter your answer.
infer two stars are being compared. star a has a greater luminosity than star b. star a and star b have the same apparent magnitude. which star is more distant? explain how you know. check your answer.
done

Explanation:

The formula relating luminosity ($L$), apparent magnitude (which is related to apparent brightness $b$), and distance ($d$) is $b=\frac{L}{4\pi d^{2}}$. Since $b$ (apparent magnitude is related to $b$) is the same for both stars ($b_A = b_B$), and $L_A>L_B$, from the formula $d=\sqrt{\frac{L}{4\pi b}}$, when $b$ is constant, a larger $L$ requires a larger $d$ to keep $b$ the same.

Answer:

Star A is more distant. Because the formula $b = \frac{L}{4\pi d^{2}}$ (where $b$ is related to apparent magnitude, $L$ is luminosity, and $d$ is distance) shows that when $b$ (apparent - magnitude - related) is constant, a larger $L$ (luminosity) implies a larger $d$ (distance). Since $L_A > L_B$ and $b_A=b_B$, then $d_A>d_B$.