a) Two stars (call them Alpha and Beta Carinae) are known to have the same lumin

Question

a) Two stars (call them Alpha and Beta Carinae) are known to have the same luminosity. Alpha Carinae is however 100 times brighter than Beta Carinea. How much closer or farther is Beta compared to Alpha from us? b) Suppose instead they are at the same distance, and Alpha Carinae is 100 times brighter than Beta Carinae. In addition, suppose that they have the same radius. How much hotter or cooler is Alpha than Beta? c) Suppose again they are at the same distance, and Alpha Carinae is 100 times brighter than Beta Carinae. But now, suppose the have the same temperature but different radii. How much larger or smaller is Alpha than Beta?

Explanation / Answer

as intensity is inversley proportional to the square of the distance

so the beta is 10 times farther than alpha from us .

b)if same luminosity

then the radius is also same then

L= ?AT4.

so where T =temperature

so alpha is (Talpha /Tbeta )^4=100

so Taplha=3.16Tbeta

c)so Aalpha /Abeta =100

so the radius alpha =10 *radius beta

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