In the approximately 5 billion years since the Sun began its main-sequence phase, its radius has increased by 6% and its surface temperature has increased by 5%. How has its luminosity changed?
A)decreased by 10%
B)decreased by 5%
C)increased by 5%
D)increased by 40%

Question

Quizplus · Accepted Answer

The luminosity of a star is proportional to the fourth power of its radius and surface temperature. Using the formula L = 4πR^2σT^4, where R is the radius, σ is the Stefan-Boltzmann constant, and T is the temperature, we can calculate the change in luminosity.

Assuming the mass of the Sun has remained constant over the past 5 billion years, the increase in radius by 6% means that the new radius is 1.06 times the original radius. The increase in temperature by 5% means that the new temperature is 1.05 times the original temperature.

Plugging these values into the formula, we get:

L_new = 4π(1.06R)^2σ(1.05T)^4 = 1.4L_original

Therefore, the luminosity of the Sun has increased by 40%, or D.

In the Approximately 5 Billion Years Since the Sun Began