Chapter 33, Problem 8P

(a)

To determine

Apparent brightness of the Sun.

Answer to Problem 8P

The apparent brightness of the Sun is $l\text{ = }1.3\times {10}^3{\text{ W/m}}^2$ .

Explanation of Solution

Given:

The solar constant is about $1.3\times {10}^3{\text{ W/m}}^2$ .

Calculation:

The solar constant is another term for apparent brightness.

So, the apparent brightness of the Sun is $l\text{ = }1.3\times {10}^3{\text{ W/m}}^2$ .

Conclusion:

Thus, the apparent brightness of the Sun is $l\text{ = }1.3\times {10}^3{\text{ W/m}}^2$ .

(b)

To determine

The absolute luminosity of the Sun.

Answer to Problem 8P

The absolute luminosity of the Sun is $L\text{ = }3.7\times {10}^{26}\text{ W}$ .

Explanation of Solution

Given:

The solar constant is about $1.3\times {10}^3{\text{ W/m}}^2$

Formula used:

Absolute luminosity is calculated as

  $L=4\pi d^{2}l$

Calculation:

The absolute luminosity of the Sun is

  $\begin{array}{c}l=\frac{L}{4\pi d^2}\\ L=4\pi d^{2}l\\ $ L\text{ = 4}\pi {(1.496\times {10}^{11}\text{ m})}^2(1.3\times {10}^3{\text{ W/m}}^2)$\text{= 3}\text{.7}\times {10}^{26}\text{ W}\end{array}$

Conclusion:

Thus, the absolute luminosity of the Sun is $3.7\times {10}^{26}\text{ W}$ .