Acceleration ≈ gravity

The effects of acceleration and gravity aren't exactly the same of course, but we can generate 'artificial gravity' by spinning things round, like swinging a bucket of water in a horizontal plane - the water stays in, the same as it would if you just put the bucket down. As a reality check, I put some marbles in the centre of a smooth, flat plate on a record player turntable. When I lifted the needle to get it turning, all the marbles hit the edge of the plate within a second or so.

For all the 'Physics Deniers' out there, let's work out what would happen if you had a large, well-insulated tube of air (the larger and longer the better) being spun around an axis at one end (the faster the better).

1. While standing still, the density, pressure and temperature are constant along the whole length (I haven't bothered with units or numbers on the axes, this is about basic principles):
2. When it is spinning around the axis, the gas will be pushed towards the outer end (the same as the marbles on a plate). So density goes up at the outer end and down at the axis end. I've assumed that the increase is linear for now:
3. The pressure at any point along the tube is the mass of all the gas to the left of it pressing 'down' on it, which is the area of the 'density' shape to the left of that point (multiplied by the strength of the artificial gravity). The length and height of the upper triangle both increase by the same multiple with each step to the right, so the area increases by that multiple to the power of 2. So pressure increases geometrically from left to right: 4. Temperature is proportional to pressure divided by density. There are no physical barriers along the tube, it's all in equilibrium, so you can use the Gas Laws to calculate T if you know D and P (or indeed, calculate any variable if you know the other two). The ratio of P/D increases from left to right. So temperature goes up from left to right in a straight line (crudely speaking, T ∝ P/D and P ∝ D^2, so T ∝ D^2/D => T ∝ D): This is the bit the Physics Deniers can't or won't understand. The gas can't become isothermal again, because the density and pressure at each point in the tube are dictated by the amount of gas, the length of the tube, how fast it is spinning etc, and temperature is the result of all that, temperature can't just make up its own mind what to do. So the inner surface at the outer end becomes warmer than when it was standing still, and the inner surface at the axis end becomes cooler. No thermal energy has been added to the gas - it is just distributed differently.

A real life application of a similar effect is the vortex tube, which uses centrifgual forces to split air at a certain starting temperature into a stream of much colder air and a stream of much warmer air.

5. What relevance does this have to the gravito-thermal effect? Simple, you just rotate Diagram 4 clockwise by 90 degrees and relabel the axes. This now resembles the measured profile of the troposphere. You can multiply T and D at any altitude, divide that by P at that altitude and you get the same answer.
The other and even easier to understand explanation for the temperature profile in the atmosphere is that when air rises, it converts thermal energy to potential energy (cools); when air falls (or presses down on air beneath it), it converts potential energy to thermal energy (warms). Actually it is gravity and the Gas Laws that says there must be a lapse rate and the formula g/Cp just tells us how much the lapse rate is.

So the other way of modelling the whole thing is by just knowing the effective/average temperature and the lapse rate. We know that Earth receives enough sunshine to warm the atmosphere to an average of ~255 degrees (effective temperature), which is (by definition) the temperature half-way up the troposphere (the same as the temperature half-way along the spinning tube = the starting temperature). So you subtract ~5.5 x lapse rate ~6.5 degrees to find temperature at tropopause and add the same amount to find the temperature at sea level. You can work backwards to find pressure and density at different altitudes (for example by using the Barometric Formula or trial and error).

The equilibrium and actual observed profile is that for every 100m fall, density increases by ~1.115%; pressure increases by ~1.373%; and the ratio pressure-to-density increases to give a lapse rate of ~6.5 degrees/km. These three variables are inter-dependent, one does not 'cause' the others, they are in balance, like two playing cards balanced in an inverted 'V'. Each card is holding the other one up.

And if we have two different approaches which both give you the correct answer, you can be fairly confident that the approaches themselves are correct.

But whatever the explanation, it reminds us that the effects of gravity and artificial gravity/acceleration are very similar; and acceleration due to gravity is a lot, it is slightly more than the acceleration of a car that can do 0 to 60 mph in three seconds*. The laws of physics that apply to a bucket of water also apply to a spinning tube also apply to the troposphere.
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6. "But what about radiation and greenhouse gases?" shout the Physics Deniers. Well, what about them? You can explain what happens in the spinning tube or the vortex tube without mentioning them and they are irrelevant when you rotate the diagram and have real gravity instead of artificial gravity. In the spinning tube, there was a fixed amount of thermal energy to start off with, which was recycled towards the outer end. Earth gets enough sunshine to keep the whole system at a steady average ~255K (fixed - see 7.) and the laws of physics ensure that the thermal energy is recycled downwards to cool the air at higher altitudes to ~220K and warm the surface to ~288K.

7. For sure, land and the ocean surface are emitting more radiation than actually gets to space (which must be approx. equal to the amount received from the Sun each day) but there's no point subtracting one from the other, it's not comparing like with like. We calculate the effective temperature ~255K by treating clouds as part of the 'surface', so the 288K at the hard surface/ocean surface is a red herring; the effective temperature should be compared with the overall average temperature of the top surface of clouds (two-thirds) and land and ocean surface (one-third), which is a lot closer to ~255K than ~288K.

The surface is as warm as it is, and emits the corresponding amount of radiation, it simply doesn't care what happens higher up. Somehow or other, the whole system will ensure that incoming and outgoing radiation balance, whether we point the finger at greenhouse gases trapping radiation or the low emissivity of clouds. Nature finds a way**.

* People picture the atmosphere (or anything else) resting on the Earth's surface as a static situation. In some ways, you can imagine the surface accelerating upwards at 9.8 m/s (a car doing 0 to 60 mph in three seconds) and pushing everything up accordingly. Imagine a ship moored in a river flowing at 10 knots, there's a bow wave in front of it. Or the same ship travelling up a canal at 10 knots, there's the same bow wave. If you lean over the bow and look straight down, you can't tell whether the ship is moored or moving. So it's like the Earth's surface is a giant piston pushing and compressing (hence warming) a ten-ton 'bow wave' of air in front of it.

** The top 1m of the ocean surface only radiates away about 1.4% of its total (thermal) energy overnight, sufficient to cool it by ~4K, which matches up with the typical diurnal temperature range for the surface of a fairly still ocean and the air immediately above it. Losing energy by radiation is a slow and inefficient process - blacksmiths quench red hot steel by plunging it into water; how much longer would it take if they held the red hot steel just above the surface of the cold water and allowed radiation to do its thing?

Here endeth today's lesson. I'd rather be a Climate Denier than a Physics Denier.