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For simplicity assume hypothetically we make multiple copies of earth: XS, S, M, L, XL. The only difference between them is their size (radius), everything else is the same. S is half the size of earth, M is earth, L is twice the size of earth. XS is a quarter of the size of earth (the moon?), XL is four times the size of earth.

Will the fact these planets are different sizes noticeably alter the weather? How and why? Is gravity the biggest factor, or the size of the continents, the distance the wind has to travel, the height of the mountains, depth of the sea, the amount of energy absorbed from the sun... etc, etc, etc? Will L have more extreme weather and S have milder weather than M?

Bonus question: if each planet has the same gravity, because we like gravity as it is; how seriously would this change the previous question?

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    $\begingroup$ Just to point out that half the radius is one-eighth of the volume, and hence, the mass, and a quarter of the radius is $1 \over 64$th the mass $\endgroup$ – nzaman Aug 9 '17 at 12:23
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    $\begingroup$ The gravity resulting from planet size (assuming same composition) may affect the air pressure at sea level, resulting in different weather? If anyone wishes to research this, feel free to steal my idea! $\endgroup$ – Aric Aug 9 '17 at 12:35
  • $\begingroup$ "everything else is the same" would mean the weather is the same too btw $\endgroup$ – A. C. A. C. Aug 9 '17 at 15:55
  • $\begingroup$ @A.C.A.C. Making good questions is so hard. :( $\endgroup$ – inappropriateCode Aug 9 '17 at 16:00
  • $\begingroup$ Bonus question is the only part that makes sense to discuss weather. (And only if "gravity" is taken to mean "surface gravity.") $\endgroup$ – dmm Aug 9 '17 at 19:38
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You are probably aware that Jupiter has a big storm, known as Great Red Spot, which is lasting for at least 300 years and is roughly as big as our planet. So gravity is definitely going to affect the weather.

Same goes from energy flux from the central star (after all it is the main motor for the atmospheric flow) and for heat coming from nuclear decay in the core of the planet.

Solid continents will help dissipating the angular momentum, shortening the lifetime of weather perturbation (this is also proposed as reason why the Great Red Spot is so persistent).

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This is a question only a supercomputer running simulations could answer with a degree of usefulness, but the short answer is yes. Gravity should be the most noticeable difference.

Higher gravity means the atmosphere is comparatively denser near the surface and thins out more rapidly as you go up. Of course, other things being the same, higher gravity means the planet can retain more gases and so the atmosphere will be denser overall. Higher gravity means more gases and therefore a larger greenhouse effect. Heat will be retained more effectively, so there will be less variation between cold and hot regions, and between day and night temperatures. Winds at the surface will be slower, but storms will grow higher and larger.

Conversely, lower gravity will make the atmosphere less dense; depending on many things you haven't specified (such as the distance of the planet from its parent star, its magnetic field and the level of solar activity), lower gravity might mean the lighter gases in the upper atmosphere will be lost to space, carried off by solar wind. Less, colder gas means less mass and energy for severe weather to develop.

I don't think we have evidence that larger planets mean larger continents, or that gravity within the range we're talking about greatly affects the height of mountains; that's more up to details of geological activity and rates of erosion. A denser, hotter atmosphere will probably contribute to erode mountains faster, though, and mountains affect local weather patterns, so that will have to be taken into account. Same goes for the depth of seas.

Two terrestrial planets, one being half the radius of the other, cannot reasonably have the same gravity. If Small Earth is 1/2 the radius of Earth and is made of the same materials overall, its volume and therefore its mass will be 1/8 of Earth's and the surface gravity will be half (gravity is proportional to mass and inversely proportional to the square of the radius). You'd need your Small Earth made of much denser materials, which is unrealistic. Same goes for Large and Xtra-Large Earth, in the opposite sense.

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Ugh um okay, if we assume the same mass at those vastly different sizes, which seems to be what you're asking, then we get massive changes in atmospheric density because surface gravity is going to be really different. Gravity works on the equation F=G(Mm/r2) where F is the force of gravity a mass like you (m) experiences at a given distance (r) from the centre of an object of mass M; if you're increasing or decreasing r without changing M or m, F is going to be 4 times higher on S Earth for example, this also changes the escape velocity needed for gases and messes with the atmosphere both it's physical properties and it's chemical make up. On the XS and S Earths we're not going to be able to breath for a number of reasons, pressure, Oxygen toxicity, excessive Hydrogen etc... on the larger worlds the surface gravity will be so low at a fixed mass that there is no real atmosphere to speak of.

Smaller worlds are going to experience something of a lack of weather at ground level, the atmosphere will still extend to roughly the same point in the gravitational field so insolation is only going to reach so far down and the inner layers are going to be very dense and so they'll be less perturbed by the little radiation they do receive. Larger worlds will have next to no atmosphere so the weather is going to be violent and sustained much like we see with Martian sandstorms.

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I don't know how I should interpret this :

For simplicity assume hypothetically we make multiple copies of earth: XS, S, M, L, XL. The only difference between them is their size (radius), everything else is the same.

So basically, the only differences with these new Earthes and M Earth is that their volume and mass are divided or multiplied by 8 or 64.

In that case, be aware that you should prepare for a variety of noticeable differences... Damn, multiply Earth's radius by 4 and the only thing that would remain might be the spherical shape. Might.

In the end, it's mostly a matter of numbers :

  • Weather depends on climate.
  • Climate depends on temperature and atmosphere's composition and pressure.
  • How big the atmosphere is depends on gravity. That's why some planets are called Gas giants. They are so big that they attract a lot of gas, and at some point that gas is most of the planet.

So it all comes down to haw gravoty applies : Gravity increases with the mass of the involved objects and decrease with the squared distance between them. Since volumes is in cubic meters, a growth in radius means that the volume grows by the same amount but cubed. Mass follows directly (hum... until some point, but we'll come to it later...) volume, so same thing for mass. From this, we deduce that doubling the radius of a planet multiplies its mass by 8, meaning that from the same distance, the second planet has a 8 times stronger gravity. The planet's surface being 2 times further, it divides the gravity on the surface by 4 times more. The reuslt is 2 times stronger gravitionnal pull at the surface.

With a planet 4 times bigger, that makes 64 times the mass and a squared radius 16 times longer, thus a surface's gravity 4 times stronger.

So gravity on the surface grows directly following the radius, but at identical distances, it follows radius' increase to the cube. That means that your L and XL planets will capture a lot more gas, while S and XS not that much, and they might even lose whatever atmosphere they had at the begining of your thought experiment.

More gravity and more atmosphere mean more pressure. If some gases have greenhouse effects, more of them also means more greenhouse effects thus higher temperatures overall - and less day/night differences. You can actually have a planet so big that it attracts so much gas that **gas pressure is high enough to crush you. Or your car. Jupiter is like that. Any probe we could send to it would be crushed and even melted way before reaching its surface. That's how dense gases can get when as gravity rises - and we aren't at star-like gravity, only planet-like. Since pressure means more things in a reduced volume, that's in fact increasing the effects of gravity : by falling to the planet, crushing the gas below, and getting closer to the surface, being crushed by the other layers of gas above, the overall gases are more and more affected by gravity as the distance is reduced. Combined with the cube/square law, that makes size an escalating issue in solar systems.

To conclude : dividing or multiplying the radius of your planet by little numbers have mind blowing implication, turning them to either sterile moons or crushing gas giants. Our own planet would quickly become sensibly less hospitable to us if it radius was slight different in either direction, since we evolve to fit that range of pressure.

Pressure and temperature also have to do with state change : as pressure decreases and/or temperature increases, matter will reach/approach its liquid or even gas state, and the other way around. But if pressure is quite low, there is no liquid state at all. So if your planet is too little and doesn't have a significant atmosphere (like the Moon), there will be no liquid water on it. With too much pressure, you will be stuck with ice except if the water is heated a lot. And melting is what consumes most of the energy, not rising the water's energy, just changing its state.

To sum it up, if you intend to build a planet with climate, life and whatever based on water and would prefer it to be realistic, stick with an Earth-like radius : 2 times Earth radius is HUGE ! 4 times is COLOSSAL ! If you want a planet two times bigger, double the volume (and mass) instead, I believe that's what you actually had in mind.

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Weather on Earth is generated by the thermal energy the earth gets from the sun. If the Earth was smaller but has the same gravity and atmosphere, one difference would be the surface area that can receive sun light. Another would be the temperature delta between the equator and the poles that acts as an engine and is what primarily drives the global weather systems. Having the distance be smaller between the source and reservoir can dramatically change the systems that forms.

The real problem however with trying to figure out weather is that weather systems are chaotic in nature. Which means these systems can change drastically based on even minute differences in initial conditions. Even small changes can cause weather systems that are not stable in any way. Even if the Earth was 1% larger/smaller, the difference could be raging storms and runaway greenhouse to a cold dead world with little weather simply because solutions to these chaotic systems are extremely unpredictable.

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