Star A has 3 times the surface temperature and 0.6 times the radius of Star B. What is the ratio of the luminosity of Star A to the luminosity of Star B? (Indicate your answer to an accuracy of 0.1).
To find the ratio of the luminosity of Star A to the luminosity of Star B, we can use the formula for the luminosity of a star. The luminosity of a star is proportional to the radius squared and the fourth power of the surface temperature.
Let's denote the surface temperature of Star A as TA, and the surface temperature of Star B as TB. We're given that TA = 3TB (Star A has 3 times the surface temperature of Star B).
Similarly, let's denote the radius of Star A as RA, and the radius of Star B as RB. We're given that RA = 0.6RB (Star A has 0.6 times the radius of Star B).
The ratio of the luminosity of Star A (LA) to the luminosity of Star B (LB) can be calculated using the following formula:
(LA / LB) = (RA^2 * TA^4) / (RB^2 * TB^4)
Substituting the given values, we have:
(LA / LB) = [(0.6RB)^2 * (3TB)^4] / (RB^2 * TB^4)
Simplifying the expression:
(LA / LB) = [(0.36 * RB^2) * (81 * TB^4)] / (RB^2 * TB^4)
(LA / LB) = (0.36 * 81) = 29.16
Therefore, the ratio of the luminosity of Star A to the luminosity of Star B is approximately 29.2.