# Shrinking the Atmospheric Greenhouse Effect closer to reality

Mainstream climate science claims that without an atmosphere, Earth’s surface temperature would be, on average, below freezing. It would be about 33 degrees C colder than it is with an atmosphere. Actually, they claim that without greenhouse gases (GHGs) that would be the case. Someone at NASA even made this ridiculous statement:

Remove carbon dioxide, and the terrestrial greenhouse effect would collapse. Without carbon dioxide, Earth’s surface would be some 33°C (59°F) cooler.

NASA: What is the greenhouse effect

Ha ha! I’m sure they meant to say GHGs, not CO2, but let’s laugh at NASA for employing someone secretly biased like this.

There’s a link on that site to UCAR (Center for Science Education): The Greenhouse Effect. Here we read:

Without the greenhouse effect, Earth’s temperature would be below freezing.

— UCAR

Without any heat-trapping greenhouse gases in our atmosphere, Earth would be a frozen ball of ice.

You can learn lots more details about the math at our Calculating Planetary Energy Balance & Temperature web page.

— UCAR

Great, we finally got to the meat. I was looking for this math page, but apparently it’s gone now from UCAR and links to an archive.org page. Maybe they are embarrassed? Anyway, here’s how this “iceball” theory works:

The math is mostly fine (Earth is not a perfect Sphere), but the real problem is the choice of 0.31 albedo. Most of the albedo comes from the atmosphere itself! And also this albedo value is only useful in observing Earth from space. ~30% of incoming shortwave solar radiation is indeed reflected from the Earth onto an observing satellite. But this is NOT a metric for figuring out how much solar radiation reaches the surface, which is what is in question. And so this entire calculation is utterly superficial and meaningless.

Some have suggested to use the Moon’s albedo to simulate Earth’s surface temperature without an atmosphere. Moon’s albedo is about 0.12, and the standard calculation method would yield:

``````\$ qalc -t '1361*(1-0.12)/4=5.670367e-8*x^4'

x ≈ 269.5674246   # (x = Temperature in Kelvin)``````

But the moon is the moon, and it’s not like the Earth, at least I don’t think.

Let us look at an Energy Budget diagram to see what the proper parameter is:

So 23 W/m2 is reflected at the surface, and that’s from (23+164)= 187 W/m2 that makes it past the atmosphere. 23/187 = 0.1229…

Ah, so that is indeed very close to the moon. Not a bad assumption.

Then again, 23 out of a total of 340 was reflected at the surface. Maybe the 187 is irrelevant? Can I be sure that the surface would not have rejected the same as the atmosphere? No, really, can I? I don’t know, but I don’t think so. If I’m right, then the surface albedo would be 23/340 = 0.0676.

This gives me more confidence:

The lunar average Bond albedo (at normal solar incidence) A is 0.12 (Vasavada et al. 2012). This is in agreement with the mean value of 0.122 found by Saari & Shorthill (1972). Vasavada et al. (2012) derived a mean albedo of 0.07 for mare and 0.16 for highland surfaces from measurements taken by the Diviner Lunar Radio Experiment. In a NASA summary of the Moon’s bulk parameters19, the Bond albedo is given by 0.11 and the geometric albedo by 0.12

The Moon at Thermal Infrared …

Mares are generally smooth and flat and take up ~16% of moon’s surface. On Earth, our equivalent of lunar mares would be the oceans, and any body of water in general. Water bodies have a small albedo, like 0.06 … similar to lunar mares. But our “mares” take up 71% of our surface. This fact alone makes me confident Earth’s surface albedo is much lower than the moon.

Moving on…

The main problem with the mainstream no-atmosphere formula shown above is that it lacks EMISSIVITY, which is a huge mistake. Here’s the correction:

Now things get interesting.

What is the emissivity of the moon? This paper suggests it is definitely somewhere between 0.92 and 0.97. But this is computed from a narrow set of channels. Such an analysis on Earth also leads to a high result: 0.97-0.98, whereas the actual emissivity is found in my previous article: What is Earth’s Surface Emissivity? : 0.93643.

I would even bet that the moon’s albedo is just one minus its emissivity.

For Earth, let’s go back to the energy budget … 23/340 is 0.067647.

1 minus 0.067647 is 0.932353

0.932353 and 0.93643 are too close to be a coincidence. I think they are saying the same thing:

Screw albedo and emissivity, and just assume Kirchoff’s Law of Radiation for this type of calculation? This implies:

S/4=σT⁴

A more accurate S/4 value is taken from my previous article: 339.22

``````\$ qalc -t '339.22=5.670367e-8*x^4'
x ≈ 278.1106181``````

If we take the surface outgoing longwave radiation from CERES: 399.56 (Average, year 2020), we get …

``````\$ qalc -t '399.56=5.670367e-8*x^4'
x ≈ 289.7294947``````

And the difference is about 11.62 degrees C

Now that is much less of a “greenhouse effect” than the fantastical 33 or 34 degrees claimed by mainstream climate scientists!

Without the atmosphere, the average temperature would be nearly 5 degrees C

Have a good day. -Zoe

Update

I don’t know how I missed this chart:

Averaging the emissivity accross 7 channels yields:

``````(0.965+0.938+0.912+0.766+0.777+0.827+0.787)/7 =

~ 0.853``````

That’s not exactly the right way to do it, as different channels yield different intensities via Planck’s Law, but I still think emissivity is very close if not exactly (1-albedo).

Update

Just in case I’m wrong, I’ll show the calculation for an albedo of 0.1229 (derived from energy budget):

``````\$ qalc -t '339.22*(1-0.1229)=0.93643*5.670367e-8*x^4'
x ≈ 273.5968031 ``````

The GH effect would then be 16.13 K.

https://phzoe.com

## 36 thoughts on “Shrinking the Atmospheric Greenhouse Effect closer to reality”

1. Stephen Persaud says:

Once again I’m left extremely impressed by your inductive and deductive reasoning, as well as your mathematical reasoning and “computation” skills…..You should have your own TV series and world tour. Instead “TPTB” promote Brian Cox with his outdated cosmology and analysis

https://briancoxlive.co.uk/northamericantour/

https://www.imdb.com/title/tt14716416/

https://www.imdb.com/title/tt15757074/

Before the invention of electronic computers, “computer” was a job description, not a machine. Both men and women were employed as computers, but women were more prominent in the field. This was a matter of practicality more than equality. Women were hired because there was a large pool of women with training in mathematics, but they could be hired for much less money than men with comparable training.

https://www.smithsonianmag.com/science-nature/history-human-computers-180972202/

https://ethw.org/Women_Computers_in_World_War_II

https://www.newscientist.com/article/2118526-when-computers-were-human-the-black-women-behind-nasas-success/

https://www.history.com/news/human-computers-women-at-nasa

Liked by 1 person

1. Uhm, ok. Thank you!

I don’t really care about women in STEM. If they are so great, I’d be quoting more papers by them. If they are so great, I’d be reading more books by them.

There are a few original oddballs like me, and that’s all there will ever be.

My real specialty is figuring which men have the skills to make me money. I employ them and reap the profits. My husband taught me well. I don’t hire women at all. lol

Like

1. thecliffclavenoffinance says:

Impossible not to like someone who calls
themselves Mrs. Smarty Pants, and
an original oddball, who is not
politically correct. And now five posts
in one week ! Almost a miracle.
recommended list, and hope some
https://elonionbloggle.blogspot.com/2022/06/the-four-climate-and-energy-websites.html

I’ve noticed for 25 years that government
bureaucrats often make climate statements
that are contradicted by their own data.
They assume no one will check.
But you do.
Keep up the good work.
We only have 12 years left,
or is that 9 years left? ha ha

Richard Greene
Bingham Farms, Michigan

Like

2. Pravda Pundit says:

Dear Zoe.
Nikolov & Zeller
https://tallbloke.wordpress.com/2022/05/02/ned-nikolov-karl-zeller-exact-calculations-of-climate-sensitivities-reveal-the-true-cause-of-recent-warming/
and
Mulholland & Wilde
https://www.researchgate.net/publication/342109625_Return_to_Earth_A_New_Mathematical_Model_of_the_Earth's_Climate
These two independent research pairs have concluded that it is the sun and the atmospheric pressure that determine the temperature at celestial bodies with atmosphere.

Like

3. bentstrut says:

Zoe… something simple to ponder. The earths atmosphere has 14.7 pounds of weight above each square inch of air at the surface compressing the air molecules. The sun rises and heats the surface. The surface heats the air and lifts the 14.7 pounds of weight. Work is done and hence, heat is generated and we live in 59f air…..Bent strut

Like

1. Why only lift “14.7 pounds”? Why not more? What’s missing?

Like

1. bentstrut says:

Zoe….the weight of a 1 inch square volume of earths atmosphere from the earths surface to the edge of space is 14.7 pounds. If the surface is heated from the sun it has to lift 14.7 pounds x amount of distance, work is done and the heat generated warms the atmosphere…. Forget math, use intuition and basic physics…..Bent strut aviator

Liked by 1 person

1. But heat is not generated, it is dissipated. Add more heat and gas molecules will leave the oceans. Atmospheric pressure increases … because you raised the temperature.

Like

2. bentstrut says:

Heat is generated by virtue of doing work. all work, force x distance, generates heat. The heat is dissipated into the atmosphere and warms it, entropy, second law of thermodynamics….Bent strut aviator

Like

3. solar -> heat -> work

there is no

solar -> heat -> work -> extra heat

However, when sun strikes water, the water will evaporate to gas, be transported to a colder area, and warm the surface. This will raise global average surface temperature. This is true.

But it’s not hotter WHERE the sun originally struck.

Like

4. thecliffclavenoffinance says:

“Mainstream climate science claims that without an atmosphere, Earth’s surface temperature would be, on average, below freezing.”

I stopped caring about most mainstream climate science
about 25 years ago — about one hour after I first began
That was when I developed my accurate
climate prediction: “The climate will get warmer,
unless it gets colder.” Still waiting for my
Nobel Prize.

It was my impression the greenhouse effect
protected outdoor plants from cold weather
damage every night during growing seasons.
Specific numbers scientists attached
seemed like they were pulled out of a hat,
or from two feet lower. It WOULD be colder,
so scientists get partial credit for that.

Like

5. Excellent analysis! May I contribute to further finetuning?
•The base is that the Sun is shining upon the Earth only half of its sphere, but each second while the Earth is moving at a speed of app. 455 m/s at the equator. In order to correctly estimate Sun’s warming we have to take that into account.
•It’s thus not correct to assume Sun’s irradiance divided by four in the equation named Stefan Bolzmanns Law (SBL). Remember the fourth potential of the temperature in the equation. It’s not even correct to divide by two, as the point estimate of Sun’s irradiance is not evenly spread over half the sphere. My own approximate estimate based on Lamberts Cosinus Law, is equavilent to the estimate made by Dr. Ron Murtagh on Principia Scientific on 18th Dec. 2020, namely 4/pi^2 of the Sun’s irradiance.
• Using Your albedo estimate as of 1st of June 2020, 0.2891, as well as Your emissivity estimate as of Oct. 2019, 0.93643, and above Sun’s irradiance 339,22×4=1356,88, I end up in the following equation, SBL:
1356,88(1-0.2891)×4/pi^2=0.93643×5,670367×10^-8×T^4
T=292.92466=about 19,8° C. This is the average temperature on half of the Earth each second moving forward at at speed of 455 m/s.

My conclusion is that there is no room for any GHG warming of the Earth surface whatsoever, at least not during daytime. Please elaborate a bit further with Your resoning above.

Like

1. Thank you very much.

Note that you can’t multiply 339.22 by 4. This value already takes into account that earth is an oblate sheroid.

The calculation for an area of an oblate spheroid is so complex, that the best humanity can do is use approximations. I use the faster one with ~0.02% error. See my article “Surface area of earth”. I can’t even touch the more precise one. My laptop will engulf in flames.

As for the “divide by 4” issue, other than being for a sphere, it is actually correct. I prove it in my very first post: “Calculating TOA Insolation”.

Like

1. Thanks for Your kind clarification. I presume that I can double the value from ‘Calculating TOA Insolation’ to arrive at a more consistent value of my Sun’s irradiation on half Earth, instead of my 4/pi^2, which means 50% of total irradiation of approx. 1359,9 W/m^2, instead of my 40,53%.
• Using SBL this means that Earth, as a Planckradiator, must achieve a potential temperature of average +35,7 °C, using Your emissivity rate of 0.93643, and Your air albedo rate of 0.2891, as of the ever sunlit half; daytime.
• This potential temperature must be followed by intensive, particularly in Tropical regions, convection and evaporation in order to maintain a liveable surrounding, bearing in mind that these two cooling processes both are functions of irradiation heat, converted as conductive heat dispersion.
• During nighttime, when no solar insolation, these processes are tapering off but accomponied by more IR-radiation from the Earth. The latter must be minor during daytime as the solar insolation suppresses the photonrelease at longer wavelenghts due to its corresponding Planck Curve, giving solar irradiance emitting many more photons at every concievable wavelength compared to IR-radiation depending on surface temperature.
• Above is what is being experienced. Total result, daytime plus nighttime, will let the Earth have an average temperature of about 15° C. I believe that will be achieved without any complementary effect of GHG.
• As to this I regard the first eqution of Your article a scam. Bear in mind that we cannot use an averaged solar insolation value (24 hours, during a full year) to calculate a potential Earth temperature, as suggested.There is no atmospheric albedo during nighttime, nor any surface albedo. This means that Your calculation of surface albedo must read 23/679,852×07109=4,8%.

Like

1. Albedo is determined by long time observation, including over NIGHT. Same for emissivity. These values are already determined off of a TOA insolation of ~339. You would have to double albedo for a halfday … but an average spot on Earth doesn’t have a 12 hr day. It’s more complicated than doubling.

Like

6. ShaunW says:

fantastic post Zoe, I’ve been arguing the same thing for some time (most recently some pointless arguing as RandomHomonid on Reddit https://www.reddit.com/r/climatechange/comments/um1hbl/climate_simulations_recognize_the_hot_model/i81dffu/?context=3) ( the same UCAR archived page from middle of reddit thread), but I’ve only got a layman’s understanding so don’t have the maths/physics to nail the new expected temp with a reduced albedo. I’m glad you’ve delved deeper in to the calcs to give a more accurate projected ghg’less temp. Considering a 1% change in cloud cover wipes out a century of ‘co2 induced warming’, what must a 20% reduction in albedo do it?

Would love to see a post on changes in atmospheric density (inc/dec humidity) and correlation with global temp change in some future post – my calcs using the ideal gas law, while simplistic, show since the 1970’s humidity changes of 4g/m3 correlates pretty damn well with ‘co2 induced warming’ for the same period. Again great post, thx

Liked by 1 person

7. John Doe says:

I really think we should make a couple of distinctions here. I know the term GHE is getting used ambiguously. Generally it means taking the albedo as given, and just looking at the LW component. Therefore saying “without an atmosphere Earth had only 255K” is indeed nonsense. But imprecision is all over the place in “climate science”. I suggest to use the term GHE for the LW component only, and use atmosphere effect for the combined LW and SW effects.

If we do so, the GHE yet is a little smaller than 33K. As pointed out the surface is not a perfect emittter and thus can not emit 390W/m2 (or more!) at a temperature of 288K. As surface emissivity MUST be very close to 0.91, surface emissions will be around 355W/m2 and the GHE about 115W/m2. Temperature wise that would be 27K or so, does not really matter. (0.7/0.91*342/5.67e-8)^0.25 = 261K

The relation of absorptivity to emissivity at the surface is dominated by the respective figures of water. With regard to land we are lacking of necessary data. With water hemispheric spectral reflectivities are 0.066 in the SW, and 0.092 in the LW range (best calculations so far). Accordingly absorptivity is 0.934 and emissivity 0.908. Water, as it is, would take on a temperature of (0.934/0.908*342/5.67e-8)^0.25 = 280.7K. Including land this figure should drop a little to 280K.

So it is 27K “GHE” and ~10K atmosphere effect.

Anyway, I think i provided the most basic and profound considerations hereto on my site. For example..

https://greenhousedefect.com/what-is-the-surface-emissivity-of-earth

Like

1. John Doe says:

PS. I would love to know what the giss data say on the specific emissivity of oceans.

Like

8. gbaikie says:

Earth average surface air temperature is controlled by average temperature of the entire ocean- which has average temperature of 3.5 C.
The ocean has 1000 times more heat than the atmosphere.
We are living in an ice house global climate {or Ice Age called, Late Cenozoic Ice Age}. We in it, because 3.5 C ocean is cold ocean.
If our ocean was instead 5 C, we still would be in ice house global climate {Ice Age} but average surface air temperature would a lot warmer.
The top surface of ocean, say top 1″ of water, is transparent and does not absorb much sunlight, and top meter of ocean water absorbs about 1/2 of the sunlight.
70% of surface of earth is ocean, what meant by surface, how meters of ocean surface.
Earth is unevenly heated, the tropics [40% of global surface] get more than 1/2 of the sunlight that reaches entire surface.
The atmosphere and ocean waters transport heat to poles. Alter this heat transport and effects global temperature.
That ocean water can flow into arctic ocean, effects global temperature.
If Earth just rock, it could be somewhere around -33 C.
“Global warming” is about making the world have a more uniform temperature.
If our ocean was 5 C, we wouldn’t have polar sea ice. If ocean was 3 C, we would have a lot more polar sea ice.
A Warm Earth is ocean with average of about 10 C, and world of far more uniform temperature. And less very cold and less very hot- world with less deserts, a world with much more water vapor, and more tropical world.
Last couple million years, has been coldest period in our Ice Age- we have not had Ocean as warm as 5 C, though have had oceans as warm as 4 C.
What we suppose to afraid is ocean which has average temperature of 4 C.

Like

1. “The atmosphere and ocean waters transport heat to poles. Alter this heat transport and effects global temperature. That ocean water can flow into arctic ocean, effects global temperature.”

Yes, and maybe Postma is correct that the sun alone is enough (not for Venus). He, the professional physicist or someone like that should model that. I need formulas and numbers. I’m kinda stumped, and I don’t see any guides to work with.

Like

1. gbaikie says:

“I need formulas and numbers. I’m kinda stumped, and I don’t see any guides to work with.”

The Moon is like a blackbody, but the Moon is not anything like an ideal thermal conductive blackbody.
And ideal thermal conductive blackbody is uniform surface temperature.
Which at 1 AU distance from the Sun is uniform temperature of about 5 C.
If moon was covered with enough water, it would have a more uniform temperature and would have average
If our moon had shorter duration day, it would have a more uniform temperature [and higher average temperature]
the rate a body spins effects “global warming”.
Venus rocky surface is slowest rotating planet, but it’s atmosphere rotates and gives upper atmosphere where has 4 to 5 day “day” because atmosphere spins, it a warming effect for Venus.
Or part of Venus runaway effect is it’s global wind.
But main reason Venus is hot is the sunlight heats the upper atmosphere [not it’s rocky surface] whereas with Earth it’s most about sunlight heating ocean’s meters of surface water.
Dry land warms ups and cools down fast, 70% of Earth surface is ocean, which doesn’t heat or cool down fast, and being 70% of surface it controls global average air temperature. Or generally, land starts it’s day warmer because ocean kept global air warmer at night.
Or without ocean a rocky surface starts daytime with colder air- though without water vapor, the air heats up faster [and cool down faster].
Earth is cold and dry world with 1/3 land being deserts, and it being in ice house climate, give it wider temperature extremes- less uniform temperatures.
It terms water vapor being a greenhouse gas, water vapor has more warming effect than just radiant effects- it’s fast and light molecule, and has latent heat- can be gas, liquid, and solid.
The tropical ocean is engine of world- but not really the tropical land.
The mystery is why is the ocean so cold.
A reason given was because weathering removed CO2 and ocean cooled, but I believe that has been disproved.
Our ice house started Antarctica moving and centering on south pole and surrounded by ocean [34 million years ago- but last 2.5 million years has been the coldest of this Ice Age}

Like

9. gbaikie says:

I am thinking, Zoe says Earth is a star.
And a star has to get hot before it can start nuclear processes.
Or our star didn’t warm by a greenhouse effect.
So our star got warm by it’s formation from gases.
Question, is our solar system growing or shrinking.
In 5 billion years has our solar system doubled in mass or halved in mass.
Are there period of time within the 5 billion years where our solar system gained
a lot and lost a lot of mass.
We have interstellar objects fall into and leave our solar system, we had other star system
get close to Sol. Or our solar system has ways of losing or gaining mass.
Lots we don’t know. But in terms of Earth [which we a bit more about] it seems most would guess
that Earth has gained mass over the 5 billion years.
The Sun loses mass by turning it into energy, but also things falling into it.
Most of mass of Earth is hot due to primordial heat: “The main contributions to the primordial heat are accretional energy – the energy deposited by infalling planetesimals – and differentiation energy.”
They say is added in first few million years, but maybe less than 1/2 of heat was added in first few million years.

Now, Venus might be more like a star than Earth, in terms of gaining primordial heat- due to it’s large atmosphere,
though Earth might more like a star because though atmosphere is small, it’s ocean retains 1000 times more hear
than it’s atmosphere- it’s ocean could cause Earth to retain more primordial heat then Venus.

I have wondered if Earth ocean makes the interior of Earth hotter, or does it cool it, I tend to think it make Earth hotter.

Like

1. I very much doubt the 5 billion year timeline because it’s all based on an assumption about radioactive isotopes: that there was zero daughter isotopes. What are the chances that whatever source provided us with matter only had rarer heavy isotopes?

Oceans can have higher cooling fluxes because of convection.

Like

10. pjmacha says:

Hi Zoe, been following your work and enjoying it as much as my fellow west Australian pen pal Erl Happ .
This paper came to mind.
Years ago, 2 physicists published a comprehensive 115-page scientific paper entitled “Falsification Of The Atmospheric CO2 Greenhouse Effects Within The Frame Of Physics” in the International Journal of Modern Physics.

Click to access 0707.1161v4.pdf

Gerlich and Tscheuschner, 2009

Like

1. pjmacha says:

Strange reply..picking on the location of Erl rather than something sciency.
But alas no, why would i claim to be a fellow west Australian? I’ve been to his vinyard.
https://happs.com.au/
He produces excellent wines in margaret river area, the pink Fruscia is my wife’s favorite.

Like

1. I like to be strange, sometimes. I thought he said he was from Mildura. My mistake if not.

Yes, I browsed that paper years ago. They have a problem with the concept of backradiation. I don’t like that term either. They, like professor Claes Johnson have a problem with two way fluxes. But it doesn’t matter if there is or is not an actual two way flow. The math works out the same. See my article “Real Steel Greenhouse Effect”.

Like

2. pjmacha says:

No probs. I’ve read all your blog topics , including steel tree and take interest in your comments on other blogs, like WUWT where I 1st came across steel tree analogy.
Cheers.

Like

11. ElectroNeutrino says:

A few points.

Kirchhoff’s radiation law states that the temperature and frequency dependent emissivity is equal to absorptivity at a specific frequency and temperature, ε(ν) = α(v). The frequency-independent version which you use here only applies if the two bodies are in thermodynamic equilibrium, i.e. the same temperature and therefore no net transfer of energy; the Earth and the Sun are definitely not in thermodynamic equilibrium and so it doesn’t apply. Your formula works for low albedo atmosphere free surface only because the 0.9 in the visual range of the surface absorptivity is close to the ~1 in the IR range of the surface emissivity.

When atmospheric scientists discuss the amount of warming from the greenhouse effect, they meant the equilibrium temperature if the atmosphere was not IR active but everything else were exactly the same. This isolates the point to specifically the effect from the greenhouse effect and nothing else. What you found was the total effect of the atmosphere, and not just the greenhouse effect. That is to say, you found that the non-greenhouse effect of the atmosphere works to cool the surface ~21K, while the greenhouse effect warms the surface ~33K, with a net changes of ~12K.

Like

I doubt the Kirchoff assumption myself. Though I can’t be sure that our current surface emissivity and albedo is not set by aftereffects of solar radiation over time. I can’t prove one way or another, so I’ll drop it as useless.

An atmosphere without GHGs would also have no atmo albedo, so I’m not just doing no atmosphere.

No, I dont’ think the atmosphere cools the surface.

Like

1. ElectroNeutrino says:

Thanks for the reply. The specifics is that they are isolating the contribution to specifically the greenhouse effect, e.g. the absorption and emission of longwave radiation in a thought experiment.

The presence of the atmosphere changes the albedo due to things like clouds and aerosols, which contribute to the cooling effect, since more energy is reflected away than would otherwise be absorbed by the planet.

Like

1. Well, I thought you said a non-IR active atmosphere, so it would not interfere with solar at all.

My math works with no atmosphere and a non-IR active atmosphere.

There’s no clouds because there is no water vapor.

Like

12. ElectroNeutrino says:

Right, but like I said, it’s a thought experiment that isolates just the effect of IR absorption while keeping everything else the same, including total albedo. It’s similar to using spherical frictionless cows to make a point about conservation of momentum.

Like