What is the mass of the atmosphere on Uranus? in kg

Question

Uranus is much larger than Earth, with a surface area of 8.10 × 10¹⁵m²with an atmosphere of low-density gases: 82.5% H₂, 15.2% He, and 2.30% CH₄. The acceleration due to gravity is similar to that on Earth, 8.70 m/s², yet the atmospheric pressure on Uranus is estimated to exceed 1.00 ×10⁸Pa.

Answer 1

Hi Daisy G.,

I'll indicate how you might proceed. Don't know why the text "low-density" is in the question, since the pressure indicates high density! Think they mean, low-particle-mass.

1) First, realize that no molecules (essentially) have "escape velocity" from the planet, otherwise they would have left already! So, if they were just isolated molecules, they would be hopping in parabolic arcs, from the surface, into the sky, and back down. But, with a lot of them present, instead they establish a pressure gradient which scales as a decaying exponential with vertical height above the surface (the distance constant for each gas differs, but that doesn't matter here). Nonetheless, the pressure of each gas at the surface represents the mass of that gas above it which is being drawn down by gravity (gravity is essentially constant with height, atmospheres are thin by comparison with planet diameters). That is, mg = P (appropriately converted for area, etc.) -- the atmosphere is in balance. All three gases are acting by mass, and masses sum, so their composition is irrelevant!

2) OK, now you can calculate the mass of gas above each m^2 of surface.

3) Multiply by surface area, and you have total atmospheric mass.

4) The take-away on this, is that (particularly on a mole basis), the atmosphere on the outer planets is much more massive than that of Earth. Is it also deeper? That will depend on the gas type and the temperature -- you already know that it is on Jupiter and Saturn, right?

Cheers,

--Mr. d.