Roughly how large does a planetary nebula grow before it disperses? Use an expansion rate of \(20 \mathrm{km} / \mathrm{s}\) and a lifetime of 50,000 years.

The expansion rate is crucial in determining how fast something grows over time. In astronomy, when observing objects like planetary nebulae, scientists often measure their expansion rates to understand their development. The expansion rate given in this exercise is **20 kilometers per second (km/s)**.
Expansion rate helps in calculating the physical size of celestial objects at different stages of their life. For planetary nebulae, this rate remains largely constant over time. Thus, by knowing the expansion rate and how long the nebula has been expanding, you can determine its current size.
For instance, if a nebula expands at a rate of 20 km/s, it expands 20 km in one second. Over longer periods, this expansion continues steadily, building up to the nebula's final size.

Unit conversion is essential to making sure that all measurements align correctly for calculations. In this exercise, we convert the expansion rate from kilometers per second to kilometers per year. Here's how you do it:
- Note that there are **31,536,000 seconds in a year** (60 seconds/min × 60 minutes/hour × 24 hours/day × 365 days/year).
- Multiply the expansion rate by the number of seconds in a year to convert it: \[20 \text{ km/s} \times 31,536,000 \text{ s/year} = 630,720,000 \text{ km/year}\]
This conversion lets us work with the same units of time (years) in our final calculation, ensuring accuracy and consistency in our problem-solving.

Astronomy is the study of celestial objects, space, and the universe as a whole. Understanding phenomena like planetary nebulae gives us insight into the life cycles of stars and the dynamic processes that govern space.
Planetary nebulae are the remnants of stars that have shed their outer layers. They appear as glowing shells of gas and dust, expanding over thousands of years before eventually dispersing into space. By calculating their size and expansion rate, astronomers can learn more about the lifecycle of stars and the physical conditions in different parts of our galaxy.

• **Planetary Nebulae Formation**: Formed when a star like our Sun exhausts its nuclear fuel and ejects its outer layers.
• **Expansion**: The ejected material expands outwards due to the star's remaining energy, forming a nebula.
• **Dispersal**: Over tens of thousands of years, the nebula disperses into the surrounding space, enriching the interstellar medium with heavier elements.

Understanding these processes helps build a comprehensive picture of stellar evolution and the enrichment of the universe with elements essential for the formation of planets and, ultimately, life.