The shell of a planetary nebula is measured by the Doppler shift of emission lines to be expanding outward at a speed of 10⁴ m/s, while its radius is measured to be 1 ly, or about 10¹⁶ m. Roughly how long has the shell been expanding? (Hint: 1 year = 3.15 *10⁷ sec.)

Question

Quizplus · Accepted Answer

To find the time it took for the shell to reach its current size, we can use the formula $ \text{time} = \frac{\text{distance}}{\text{speed}} $. Given the radius of the shell is $10^{16}$ m and the speed of expansion is $10^{4}$ m/s, the time it took for the shell to expand to its current size is approximately $ \frac{10^{16} \text{ m}}{10^{4} \text{ m/s}} = 10^{12} \text{ seconds} $. Converting seconds to years using $1 \text{ year} = 3.15 \times 10^{7} \text{ seconds}$, we get $ \frac{10^{12}}{3.15 \times 10^{7}} \approx 30,000 $ years.

The Shell of a Planetary Nebula Is Measured by the Doppler