# Helium in Uranus atmosphere

I read that in 1986 Voyager 2 measured the composition of Uranus' atmosphere, which turned out to be composed of $$85 \%$$ hydrogen and $$15 \%$$ helium.

It's not clear to me how this relevant amount of He can be present. The force of gravity on Uranus ($$8.69 \space \rm m/s^2$$) is lower than that measured on Earth ($$9.780 \space \rm m/s^2$$). Why does helium remain in the atmosphere of Uranus?

• See also physics.stackexchange.com/q/615311. It shows Uranus is well in the region that should be expected to retain helium. Commented Mar 26 at 17:21
• As the question linked by BowlOfRed says, the escape speed is a function of the gravitational potential, not the gravitational acceleration. Commented Mar 26 at 22:48
• I don't follow - why wouldn't you be more surprised that the hydrogen remains in the atmosphere? Commented Mar 27 at 7:53

There are several reasons why Uranus retains Helium better than Earth.

1. Escape velocity: The gravitational acceleration (at the equator of Uranus) may be lower than that on Earth, but the escape velocity of Uranus is almost twice as great - $$21.4 \space \text{km/s}$$ compared with $$11.2 \space \text{km/s}$$. So a gas molecule has to be moving much faster to escape from the gravitational well of Uranus.

2. The velocity distribution of gas molecules follows the Maxwell-Boltzmann distribution, $$f(c)=4\pi c^2(\frac{m}{2πkT})^{\frac{3}{2}}\exp{(\frac{−mc^2}{2kT})}$$, where $$c$$ is a velocity, $$T$$ is temperature (in Kelvin), $$m$$ is the molecular mass, and $$k$$ is the Boltzmann constant. The probability for a molecule to move faster decreases rapidly (once above the average molecular velocity. So faster moving molecules (bigger value of $$c$$) are much rarer.

3. The average temperature of the atmosphere of Uranus is much lower than that of the Earth's atmosphere (things are a bit complicated here, as molecules typically leave from the upper atmosphere rather than from sea-level, where temperatures are lower on both planets - but the observation still holds). So similar to to 2) above, a gas at lower temperature has less fast moving molecules.

4. The solar wind is much less intense at the orbit of Uranus than it is near Earth. Part of the reason gases are eroded from a planet's atmosphere results from collisions between gas molecules and fast-moving solar wind particles, so that has less of an effect near Uranus.

5. The assumed history of the inner rocky planets is that when originally formed they initially had a lot less volatile gases (Hydrogen, Helium) to lose. So the outer gas giants started with a lot more Helium. In addition, Earth is assumed to have been re-heated significantly during the collision that produced the moon, further boiling volatile gases away from Earth.

So overall, Uranus started with vastly more He (proportionally) than Earth, and loses it much more slowly.

Uranus is an (ice) giant. Of it's 14 earth masses about a few, i.e. 2-3 earth masses (this is model dependent) of solar metallicity gas was accreted and that sits on top of the ~12 earth mass core of the planet.

Solar metallicity gas means it's a mostly primordial H/He mixture that makes up the atmosphere that we see and that's what Voyager measured.

As was pointed out in another comment - the presence of Helium is typically less surprising than that of Hydrogen. But the retention of both gases against the typical atmospheric loss mechanisms to space is explained by the planets' high mass and cold temperature.

• Isn't the core closer to 0.5 earth masses and it has 13.5 gases of just gases like methane? Commented Apr 6 at 20:00