How Can Luminosity and Temperature Ratios Be Deduced in Binary Star Systems?

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In the discussion on deducing luminosity and temperature ratios in binary star systems, it is established that star A has a higher luminosity than star B due to its greater apparent brightness. The apparent brightness values indicate that star A emits more light than star B. Additionally, the surface area of star B being 10,000 times smaller than that of star A suggests a significant difference in their sizes. To calculate the temperature ratio, one must consider the relationship between luminosity, surface area, and temperature, which involves using the Stefan-Boltzmann law. The conversation emphasizes the need for participants to show their work when seeking help with homework problems.
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In a particular binary star system, star A has apparent brightness 8x10^(-13) and star B has apparent brightness 2x10^ (-14).

a) Explain how it is possible to deduce that star A has a higher luminosity than star B.

b) The surface area of star B is 10 000 times smaller than that of Star A. Calculate the ratio
surface temperature of star B/ surface temperature of star A

Cheers.
 
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a) Because Star A's temperature may be higher and the body my be larger than Star B.

b) I got no idea how to work it out. I wasn't if i have to find all the unknowns.
 
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