# Why is there a discrepancy with calculated and given age of nebula

In the book "Horizons: exploring the universe-Cengage learning (2018)", page 206, it states that:

Simple observations tell astronomers about the nature of planetary nebulae. Their angular size and distances indicate that their radii range from 0.2 to 3 ly. The presence of emission lines in their spectra implies that they are excited, low-density gas. Doppler shifts show they are expanding at 10 to 20 km/s. If you divide radius by velocity, you find that planetary nebulae are no more than about 10,000 years old.

But when I calculate the radius divided by velocity (which is equal to the age of nebula), I get: $$t=\frac{3\cdot 365\cdot 86400 \cdot 3 \cdot 10^8 \rm\,m}{10000\rm\,\frac{m}{s}}=2.838\cdot 10^{12}\rm\,s=90\,000\rm\,yr$$ Which is greater than $$10\,000$$ years as stated in the book. Is wrong the age given in the book or have I made some wrong calculations?

• @B--rian, What was the point of the edit? except to change from Jack's L10n to your L10n Jun 5, 2021 at 13:56
• Maýbe thr velocity is not constant. Jun 25, 2021 at 16:48

The average velocity is thus bigger, and total time thus smaller. If we say, for example, that the average velocity is around $$50\rm\,\frac{km}{s}$$, then we get $$18000\rm\,yr$$ for largest nebulae with size of $$3\rm\,ly$$ (but smaller for example $$0.3\rm\,ly$$->$$1800\rm\,yr$$), which agrees with my search, that planetary nebulae are around 10000 light years old (not strictly less than this).