Chapter 33, Problem 12P

To determine

Angular width of the Sun from the present distance to Earth, when it becomes a white dwarf.

Answer to Problem 12P

Angular width of the Sun from the present distance to Earth, when it becomes a white dwarf is $4.79"$

Explanation of Solution

Given:

Moon diameter is $3.48\times {10}^6\text{ m}$ . Distance of Sun to Earth is $1.496\times {10}^{11}\text{ m}$ .

Formula used:

Angular width is calculated as

  $\theta ={\tan }^{-1}\frac{\text{Moon diameter}}{\text{Distance to Sun}}$

Calculation:

Angular width of the Sun from the present distance to Earth, when it becomes a white dwarf is

  $\begin{array}{l}\theta ={\tan }^{-1}\frac{3.48\times {10}^6\text{ m}}{1.496\times {10}^{11}\text{ m}}=2.33\times {10}^{-5}\text{ rad}\\ \theta \approx \text{(1}\text{.33}\times {10}^{-3}\text{)}°\approx 4.79"\end{array}$

Conclusion:

Thus, angular width of the Sun from the present distance to Earth, when it becomes a white dwarf is $4.79"$