# 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

Things are not as simple as stated in the book: the nebula expands rapidly at first, but then at a slower velocity. Thus, you can't just divide radius by velocity as stated in the book. (I think they just wanted to give an insight how that can be approximately calculated. People often think that scientists and astronomers get some information just using some "special instruments" (time machine for age of nebulae, for example) and the author tells us that this can be achieved pretty logically.)

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).

• Hi, I was wondering why the author don't state that the velocity is around 100km/s just for coherence, and is there any source of reference for this figure? Jun 5, 2021 at 14:38
• @JacktheRanger I just said some "example" number :) But when a supernova explodes, the velocity of gas is obviously larger than even 100000 km/s, so the real number may be something around 100 km/s. Jun 5, 2021 at 17:24
• I just have a search on google, and one site suggests that "the spectra of planetary nebulae reveal another interesting fact: they are expanding from the central star at 24–56 km (15–35 miles) per second.", and unfortunately there wasn't much data related to the age of the planetary nebula, so I was wondering that maybe it just the conclusion "planetary nebulae are no more than about 10,000 years old" is incorrect? Jun 6, 2021 at 2:43