- Stars A and B are equally bright as seen from Earth, but A is 60 pc away while B is 10 pc away. Which star has the greater luminosity? How many times greater is it?
bA/bB = 1 = LA/4p(60 pc)2 / LB/4p(10 pc)2 = (LA*102) / (LB*602)
LA / LB = 602/102 = 36
- Suppose two stars have the same apparent brightness, but one star is 15 x farther away than the other. What is the ratio of their luminosities? Which one is more luminous, the closer star or the farther star?
This is the same mathematics as the previous problem. The farther star is 225 = 152 times as luminous as the closer star.
- The bright star Rigel in the constellation Orion has a surface temperature about 1.6 times that of the Sun. Its luminosity is about 64000 x the luminosity of the sun. What is Rigel's radius compared to the radius of the Sun?
LA / LB = sTRigel44pRRigel2 / sTSun44pRSun2 = 64000 = (1.6)4 RRigel2 / RSun2
RRigel2 / RSun2 = 64000 / (1.6)4 RRigel / RSun = 99
- Castor is an A1 V star with an apparent brightness of 4.4 x 10-12 that of the Sun. Determine the approximate distance from the Earth to Castor (in parsecs).
From the HR diagram we see that Castor has a luminosity of 101.8 = 63 times that of the Sun.
bCastor/bSun = 1 = LCastor/4p(dCastor)2 / LSun/4p(dSun)2
4.4 x 10-12 = 63 (dSun)2 / (dCastor)2 (dCastor)2 = 1.43 x 1013 (dSun)2
dCastor = 3780000 dSun = 18 pc