# Lifting Gas in a world with 1/3 of earth's gravity

As many of us probably know airships were one of the great forms of transportation in the 20th century but a great hindrance to their development was weight. In a world I am currently constructing the gravity is 1/3 as that on earth so metals and material are lighter but have the same strength as on our world. They are so light that steel weighs the same as aluminum here on earth and can be used in airship construction. Because of the reduced gravity airships can now carry bigger loads per same volume of gas here on earth but there is one detail that eludes me. Would lifting gas have 3 times the lift per 1,000 cubic feet in this lower gravity environment or would it stay the same as here on earth? Note that although the gravity is 1/3 the atmosphere is the same pressure, density and composition as here on earth. Also would metal retain the same strength in a lighter gravity world as I do not know the effects of lighter gravity on metal production.

• Lifting gas would have one third of the lift it has on Earth, but it would lift the same amount of cargo. (The lifting force is the difference between the weight of the displaced air and the weight of the gas. Archimedes lived in the 3rd century before the common era; that was more than 2,200 years ago.) On Earth, one kilogram of cargo weighs one kilogram-force, and needs about one cubic meter of hydrogen to lift it. On a world with one third the gravity, one kilogram of cargo would weigh one third of a kilogram-force and would need the same cubic meter of hydrogen to lift it. – AlexP Oct 17 '18 at 16:15
• @AlexP Isn't the lift purely a function of gas displacement? There's no reason a planet with less gravity must have a thinner atmosphere so the displacement and thus lift won't change will they? – Ash Oct 17 '18 at 16:44
• @Tyler Phelps Talking about the plain "gravity" of a world is rather vague. There are two separate factors to considered. The mathematical relationship between the world's escape velocity and the average speed of molecules at the top layer of the atmosphere determines how fast those molecules will escape into space. The surface gravity determines how much things weigh. And there are different formulas to calculate them. en.wikipedia.org/wiki/Escape_velocity en.wikipedia.org/wiki/Surface_gravity – M. A. Golding Oct 17 '18 at 16:51
• @M. A. Golding: But things like escape velocity are irrelevant in the context of "now". They'd only come into play if you were trying to reconstruct the past composition of the atmosphere. – jamesqf Oct 17 '18 at 18:24
• @Ash: Lift is the difference between the weight of the displaced air and the weight of the gas. If everything else is the same but gravitational acceleration is one third of what we have on Earth, it follows that lift is also one third, because both the displaced air and the lifting gas weigh one third of what they weigh on Earth. The amount of cargo remains the same, because the same cargo will also weigh one third of what it weighs on Earth. – AlexP Oct 17 '18 at 18:56

Actually, they lift exactly the same amount of mass, even though it may weigh less because of the decreased gravity.

Lifting gasses generate lift via buoyancy. Basically, they displace heavier fluids with lighter ones. The most energy efficient way to do this is for the heavier fluids to flow underneath the lighter ones. However, since the lifting capabilities are based on the weight of the displaced fluid, which is also 1/3 lighter, your lifting gasses all produces 1/3 as much lift. The weight of the airship is also 1/3 as heavy, so the effects cancel.

If you want lifting gasses to be more effective, what you want is a more dense atmosphere at the same pressure, such as having lots of sulfur hexaflouride in the atmosphere (which is decidedly unnatural, so you'd have to work at it). Alternatively, if you had a hard-shell around the lifting gas, rather than the more typical fabric, you could evacuate the insides. Then all you would need is an atmosphere which is more dense, regardless of what pressure it's at. A thicker atmosphere would be sufficient.

Ironically, that calls for a planet with more gravity, to hold onto the atmosphere better.

• In Earth's atmosphere, a volume of vacuum has only 7% more buoyancy than the same volume filled with hydrogen. But, unlike hydrogen, the vacuum has no pressure; the walls of the balloon need to be strong enough to withstand the crushing pressure of the surrounding air, whereas a ballon filled with hydrogen can be made of goldbeater's skin... – AlexP Oct 17 '18 at 16:20
• Not you too, Cort ! :-) A smaller mass planet doesn't mean it can't have a thick or dense atmosphere. Consider the satellite Titan or our slightly smaller "sister" planet Venus. Earth's atmosphere is a bit puny compared to what it could be. And if y'all don't tackle greenhouse gases, it's going to get a lot less puny very quickly ! :-) – StephenG Oct 17 '18 at 17:01
• @StephenG, The examples you're using are all examples of planets with very different atmospheric compositions or atmospheric temperatures, both of which makes their atmospheres thicker. This answer even addresses the option of using a heavier atmospheric gas (SF6) to make this possible. We'll leave the tackling of greenhouse gasses to you I think. – Mathaddict Oct 17 '18 at 17:42
• "1/3 lighter" did you mean "1/3 as heavy"? "1/3 lighter" ~ 67% as heavy; I don't think that was your intent. – a CVn Oct 17 '18 at 18:17
• @Mathaddict: So explain why a planet could not have an Earthlike atmospheric composition, but higher pressure? As in fact Earth's atmosphere probably has been in the distant past: e.g. the giant flying insects of the Carboniferous. – jamesqf Oct 17 '18 at 18:54

Believe it or not, airships would be harder to make on a lower gravity world, not easier.

Hot air balloons and airships are able to float because their systems have a lower density than the surrounding air. This is why they can only fly to a certain altitude: eventually, they will reach a point where the atmosphere is too thin to allow them to rise.

In a world with only 1/3 the gravity of earth, the atmosphere is going to be significantly thinner at sea level than on earth itself. That means that any airship will need to either displace a larger amount of gas (with a bigger balloon) , have a lower mass, or use an internal gas with a much lower density than the surrounding air.

• That is not exactly correct. The important quality for retaining atmosphere is the escape velocity, and the important quality for airship lift is the surface gravity, and they need not be proportional to each other. I also note that the atmosphere of Titan is denser than Earth's despite having a much lower surface gravity and escape velocity. – M. A. Golding Oct 17 '18 at 16:45
• It is a common mistake that a smaller gravity will result in a less dense, smaller or thinner atmosphere. Try working out the numbers for the satellite Titan and comparing them with Earth. The total mass of Titan's atmosphere is a little larger than Earth's atmospheric mass and surface atmospheric density is greater (and the surface pressure is about 1.5 times higher). – StephenG Oct 17 '18 at 16:56
• The comparison to Titan is a bad one. Gas densities are inversely proportional to absolute temperature (and directly proportional to pressure) so comparing (assuming equal pressures) the atmosphere of the earth at about 288 K to titan at about 93 K you would expect Titan's atmosphere to be 3 times as dense. It's true that escape velocity is key, and the lower temperature means that the gas molecules are moving roughly 3 times slower. – Mathaddict Oct 17 '18 at 17:33
• @Mathaddict: If Titan is a bad example because of lower temperature, try Venus :-) Escape velocity is not useful for determining atmospheric composition & pressure unless you know what the planet started with. – jamesqf Oct 17 '18 at 18:59
• @jamesqf Venus has a different chemical composition, since the molecules are heavier, they need more energy (temperature) to achieve escape velocity. The density of a gas is defined by D= MP/(RT) where M is the molar mass of the gas, P is the pressure, R is the gas constant, and T is the absolute temperature. – Mathaddict Oct 17 '18 at 20:09

# Reducing the Gravity would increase the gas needed to lift a ship.

In order for an airship to hover its mass must be equal to the mass of the fluid which it is displacing (less if it is going to float). In quantitative terms mg = dV*g. (m is the total mass of the ship including flotation gas, g is the gravitational acceleration, d is the density of the atmosphere the ship will float in, and V is the total displaced volume of the airship).

Based on this you get m = d*V so it seems independent of the gravitational acceleration constant. However, the density of the gas the ship will float in is not independent of the gravitational acceleration constant. The density of the gas is given by the barometric formula combined with the ideal gas law:

d = p/(RT)= ce^(-gMh/(RT))/(RT).

Therefore if you decrease the gravity, you will have to compensate by either raising the molar mass of the atmosphere or decreasing the temperature in order to maintain the same density in your planets atmosphere. And that's just to make everything the same.