Home/BlogI’ve always wanted to capture this kind of cloud as a time lapse. I noticed them on my way to work this morning, and had a camera and tripod with me, so this was my chance.
These are altocumulus clouds with strong upward motion in them producing precipitation, in this case snow, falling in streaks and not reaching the ground (“virga”). They form when the upper troposphere is unstable, and warm advection (a warm air mass moving into a cool air mass) produces the uplift.
Where’s the Like button? 🙂
Had to do a double take – thought the tease said:
Time Lapse Video of Altocumulus with Viagra
You should spend more time in CO. We get this a lot.
Very cool i think i saw a jellyfish at :18 LOL
Лютые приколы РІ играхWDF 198РРќРћРџР РШЕЛЕНЕЦ
I read it the same way and was wondering what Dr Roy was up to.
Hi Dr. Spencer,
being an engineer and not a meteorologist, thank to you today I learnt something I was not aware before.
Thank you for sharing this nice and interesting movie.
Massimo
Spooky Situations When You’re Home AloneAnimated Shorts by Avocado Couple
Beautiful!
And a rare chance to see energy flowing upwards in the troposphere in real time.
ROBLOX ZOMBIE STORY
Those were beautiful. Thank you for sharing that.
Off Topic except that it’s a time lapse:
Astronomy Picture of the day
Rotating Moon from LRO
https://apod.nasa.gov/apod/ap200719.html
As I recall, the Moon rotates – doesn’t does doesn’t etc. is a fun diversion on these pages.
Nice!
Moon does not rotate on it’s axis in relation to the earth…….it is locked in… no spin no twist no rotation. (again just for clarity …in relation to the earth…no rotation)
The picture shows it does so at a steady rate.
It’s orbital speed is varying.
So we went through this exercise previously… the moon moves through our solar system as do all of its ‘objects’. HOwever, in relation to ONLY the earth the moon does not rotate. not once ..not half ..not at all. the simple thought exercise proves this out: anchor a super stretchy string to both centers of the moon and the earth…. and after just a couple days….weeks or months (your choice) only one object will be all wrapped up in this string…the other body… will not. If as science shows, the moon is tidal locked to the earth….it is not going to show any other side to the earth…therefore from the earths perspective and relation it does not spin on an axis around the earth during it’s orbit.
Yes Steve Case, it is a fun diversion. But it also allows us to see how some people refuse reality. Svante is always confused. But, Martin gets it correct.
“LRO” is the acronym for “Lunar Reconnaissance Orbiter”. The LRO orbits Moon, taking photos that can be processed into such a video. The LRO is orbiting Moon. Moon is orbiting Earth. But Moon is not rotating about its axis. As Martin mentioned, if Moon were actually rotating like the video, we would see that motion from Earth.
… unless it was tidally locked of course.
Svante, the “tidal locking” is also nonsense, but let’s assume Moon is “tidally locked”, just for the sake of proving you wrong. Then, Moon cannot rotate about its axis. Once again, you get tangled in your own beliefs.
Something that cannot possibly be rotating about it axis is then NOT rotating about its axis.
кіЁн”„ н•њ 달 л°°мљ°кі н”„лЎњ кіЁнЌј мћЎлЉ” л°©лІ•
Virga… My lazy speed reading brain filled in a different word before I went back and read closer LOL. I like these last two posts ,informative and beautiful. But, I worry Dr Roy. is getting distracted. The Arctic Ice extent has just recently dipped below the 2012 records low year. Looks like we may break that record after it holding for 8 years. He needs to get to work cherry picking an explanation. Also, in thinking about his post about mild Midwest summers..might want to look at Bahgdad Iraq, Thursday through Tuesday 122,123 and tying their record of 124. Its not mild elsewhere.
“I should have done a much better job”Lando Norris hard on himself after wet Styrian qualifying
Off topic. What happens tectonically if three gorges dam breaks?
Ken,
you have my interest. Are you implying the release of the load on the plate from the water in the reservoir behind the damn would potentially create tectonic scale events like Earthquakes or major faults? Or maybe vice versa and a fault breaks the damn releasing the water? The former is actually more interesting to me because I have never done the math to understand the mass associated with the water in the reservoir, but I imagine it has loaded and strained the plate. It would most likely rebound a bit, but I am not sure how you would make the jump to triggering additional events unless there are active tectonics currently in equilibrium with the loaded plate from the reservoir. My hypothesis is that likely rapidly removing the water would just unload the strain as elastic deformation.
Off the cloud topic myself, but on topic for climate. A La Nina is starting to appear likely this winter. If a “really big” La Nina emerges the media response would be interesting since it has been about 20 years since we had a big one. I anticipate mass media would blame or at least associate hurricanes, floods and other abnormal climate events that are from a natura La Nina event on man made climate change from CO2, but the natural short term cooling would be associated with the La Nina itself.
I would love to see a system in place where such media practices are flagged and each article is categorized and labeled. So why doesnt the government use algorithms to call fake news out? Even if a researcher creates a model showing AGW enhanced the response this sort of science is merely a working hypothesis and the Media using this as other still constitutes fake news. We have the means to create balanced news why do we refuse to do it?
It used to be law and the media was better.
https://en.m.wikipedia.org/wiki/FCC_fairness_doctrine#:~:text=The%20fairness%20doctrine%20of%20the,honest%2C%20equitable%2C%20and%20balanced.
Yes, people like to have something to get uptight about.
Our only hope is science.
https://climate.nasa.gov/evidence/
Svante,
Try to be objective. Your NASA propaganda shows the proxy data of CO2 from ice cores corresponding to temperature changes of around 10K/100ppm. The spike in CO2 since 1950 corresponds to a sensitivity of at most 1K/100ppm.
The follow up evidence NASA provides is a laundry list of the effects of the 1k rise in global temperature. All of those effects occur regaradless of the cause of the rising temperature. Why hasn’t NASA proven conclusively with data how the rise in temperature is due unequivically to the rise in CO2?
In case you missed it, the propaganda is NASA using a graph showing a spike in CO2 to suggest that the spike caused all the effects due to global warming. Very deceptive and easy for people to be duped by it.
If the climate science division of NASA is our only hope, we are in deep doo-doo.
Chic Bowdrie says: “NASA propaganda”.
The audience is laughing at you:
https://tinyurl.com/y4jptx8r
Sva,
The audience has been falsely indoctrinated by people with confirmation bias.
The only direct evidence that the alarmists have is a rather poor correlation between CO2 increase and temperature increase. They completely ignore the fact that correlation does not prove causation.
Allocation of 16.3 % to a proxy for solar effect, 18.7 % to an approximation of SST cycles and 65 % to TPW increase produces a 96.6 % match with measured average global temperatures from the low in 1909 thru 2019. Analysis using data thru 2018 is in Section 17 at http://globalclimatedrivers2.blogspot.com
Dan Pangburn says:
“They completely ignore the fact that correlation does not prove causation.”
The causation is predicted by physics and first calculated by Svante Arrhenius.
The opposite causation is weak.
Svante says:
July 22, 2020 at 11:45 PM
The causation is predicted by physics and first calculated by Svante Arrhenius.
The opposite causation is weak.
Physics says about 1.2 Celsius degrees per doubling. The rest is feed back and debatable.
You can find that in the IPCC’s AR4 Chapter 8 Page 631
https://www.ipcc.ch/site/assets/uploads/2018/02/ar4-wg1-chapter8-1.pdf
“In the idealised situation that the climate response to a doubling of atmospheric CO2 consisted of a uniform temperature change only, with no feedbacks operating (but allowing for the enhanced radiative cooling resulting from the temperature increase), the global warming from GCMs would be around 1.2C (Hansen et al., 1984; Bony et al., 2006).”
Steve,
“Physics says about 1.2 Celsius degrees per doubling.”
This is only partially correct. Physics is used to make the 1.2 K estimate, but that ignores the conflating effects of weather. Convection and wind are constantly moving the goal posts preventing any accurate estimation of direct CO2 sensitivity from the spectroscopic measurements used to come up with the 1.2 K value.
As you say, feedbacks only make the situation worse.
Chic Bowdrie … at 10:46 AM
Steve,
Physics says about 1.2 Celsius degrees per doubling.
This is only partially correct. Physics is used to make the 1.2 K estimate, but that ignores the conflating effects of weather. Convection and wind are constantly moving the goal posts preventing any accurate estimation of direct CO2 sensitivity from the spectroscopic measurements used to come up with the 1.2 K value.
As you say, feedbacks only make the situation worse.
I didn’t say that, I said the rest is feed backs, and I didn’t provide a sign. Besides there’s this wonderful quote from the IPCC:
IPCC’s TAR Report Chapter 14
https://www.ipcc.ch/site/assets/uploads/2018/03/TAR-14.pdf
Page 774 section 14.2.2.2 which among other things, says:
“In climate research and modelling, we should recognise that we are dealing with a coupled non-linear chaotic system, and therefore that the long-term prediction of future climate states is not possible.”
You’ve probably seen that one before (-:
Steve Case says:
“Physics says about 1.2 Celsius degrees per doubling. The rest is feed back and debatable.”
Yes, there you can have a reasonable debate.
Svante,
“causation is predicted by physics and first calculated by Svante Arrhenius” results from a shallow application of the physics. The physics is fine; it’s the application that is bogus. The shallow application of the physics perhaps results from not understanding the output of Hitran. Hitran does the Quantum Mechanics calculations to determine the intensity of transitions at each wavenumber of interest.
A rather simple calculation, using data from Hitran shows that, on average, WV increase has been about 10 times more effective at causing ground level warming than CO2 increase.
Although most know that water vapor is a ghg, hardly anyone appears to have noticed that water vapor has been increasing about 1.5% per decade. WV increase has been more than POSSIBLE from temperature increase (feedback). All of the reported average global temperature sets show this and one of them shows measured WV to be about 58% more. The added cooling from increased CO2 in the stratosphere counters the small warming from CO2 at ground level with the net result that CO2, in spite of being a ghg, has no significant effect on climate. https://watervaporandwarming.blogspot.com
Dan Pangburn says:
Adding insulation to your house, the cooling on the outside counters the warming on the inside, with no significant effect on temperature.
Steve Case believes: “Physics says about 1.2 Celsius degrees per doubling.”
That’s not “physics”, Steve. You won’t find such nonsense in any credible physics book.
Svante,
You say :” Adding insulation to your house, the cooling on the outside counters the warming on the inside, with no significant effect on temperature.” This is not even a little bit analogous to what I explained is going on in the stratosphere. (Which is the same as expressed by the ‘consensus’).
Both act as thermal insulation Dan.
The GHE depends on the lapse through, so it operates in the troposhere, not in the stratosphere.
Svante, does adding more CO2 to the atmosphere allow more emission to space?
Svante,
You say “GHE depends on the lapse…”. Not much, if any. GHE depends on the relaxation time of molecules. If relaxation time was zero, GHE would be zero.
Dan Pangburn says:
“GHE depends on the relaxation time of molecules. If relaxation time was zero, GHE would be zero.”
The amount of emitted IR depends on temperature.
The trick is to have emission to space from a higher/colder level.
It’s all the same with zero lapse rate.
Glass pane calculations show this effect without any relaxation time. Please correct me anyone, except people that operate in the inverted lunatic reference frame.
Svante,
You get part credit but apparently you still do not understand. You say “The amount of emitted IR depends on temperature.” This, of course is correct. But the radiation flux produced by WV and CO2 depends on the temperature of the molecules. The temperature of the molecules depends on the relaxation time (and other stuff).
Temperature of a fraction within a well mixed gas is limited by average temperature.
So CO2 temperature depends on altitude.
That means emission rate to space depends on altitude.
More CO2, more opaqueness, increased altitude, less radiation.
Svante is now trying to claim adding more CO2 to the atmosphere will cause CO2 to emit less to space. If CO2 is emitting less to space, then its emitting less to the surface!
Svante always gets so tangled up in his nonsense.
Gentlemen,
Discussions like these without considering the implications of convection are fruitless. Talking about altitudes increasing and emission temperatures is nonsense. How do you account for daily changes in cloud cover and humidity? Svante, where is the data to support your assertions?
Steve Case nailed it with this from the IPCC:
“In climate research and modelling, we should recognise that we are dealing with a coupled non-linear chaotic system, and therefore that the long-term prediction of future climate states is not possible.”
ClintR says:
“If CO2 is emitting less to space, then its emitting less to the surface!”
Lower layers add more to the surface.
Wrong again, Svante. Each layer emits about the same up as down. Actually, because of the geometry of a sphere, the higher the level, more goes up than down.
So adding more CO2 results in more emission to space, no matter how you try to pervert reality.
It’s over your head, figuratively and literally.
Use your math skills, the sphere effect is negligible.
The layer effect is much stronger.
Here’s surface at layer N=0, and four layers emitting the same up and down:
N Dwn Inp Up
0 000 400 400
1 320 640 320
2 240 480 240
3 160 320 160
4 080 160 080
So that’s 400 W input at the surface, and 80 W out to space.
Particle physicist Brian Cox seems to be getting too far out in front of his skis. Australian Senator Malcom Roberts cleaned his clock. The biggest laugh came when Cox threw his data at Roberts.
Yes, what can you do?
An Australian politician tells a professor of Physics that there is no greenhouse effect.
It’s ridiculous beyond words.
I trust Brian Cox. Others trust this politician.
Cox was unable to present any physics to support his nonsense. He could only rely on “models”. He believes making measurements now and projecting that into the future is “science”. He’s “cherry-picking”. That’s NOT science. And, it’s certainly NOT physics.
Cox would fail Feynman’s criteria for valid science.
Feynman had no objection to the physics of climate change.
Of course Feynman had no objection to climate change. Only an idiot would believe the climate doesn’t change. Earth is currently in a warming cycle since the climate of the 1960s. The 1960s experienced a cooling from the 1930s. The planet has warmed since the LIA.
Feynman was a great scientist. He would never consider denying reality, or perverting it. He had the personal integrity to speak out against those that were perverting science:
“The term Cargo cult science was first used by physicist Richard Feynman during his 1974 commencement address at the California Institute of Technology.”
https://en.wikipedia.org/wiki/Cargo_cult_science
Yes, he would never consider denying reality.
That’s why he did not deny the greenhouse effect.
A well known physical fact in his time.
You’re making up stuff again, Svante. Feynman never even mentioned the GHE because it is nothing but nonsense.
The GHE is NOT a “well known physical fact”, never was, never will be. You believe it is “fact”, just as you believe something that is not rotating about its axis is rotating about its axis. “Beliefs” are not science. Feynman labeled such nonsense “cargo cult science”.
Earth’s surface radiates more IR than the total absorbed solar radiation.
The GHE is the only way to explain that.
If not, Feynman would surely say so.
Svante, the bad accounting is explained by the idiots doing the accounting.
Feynman would surely say so. In fact, he had a term for such nonsense, “cargo cult science”.
Yeah, that’s what you’re doing.
Misrepresenting others just demonstrates the emptiness of your beliefs, Svante.
Brian Cox is a charlatan.
Why does anyone take such imbeciles seriously?
Because he’s brilliant to any sensible person.
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In three days in the south of Texas, up to 15 inches of rain can fall.
How unusual is that?
Dan Pangburn, how do you propose we stop global warming?
Simple. Add more CO2 to the atmosphere.
Clint,
Adding CO2 won’t work because CO2 has no net effect on climate. Over the entire Phanerozoic eon (the last 550 million years or so) CO2 level has been up to about 10 times the present and has never driven climate. During the current Ice Age (we are now enjoying the warmth of the Holocene interglacial which allowed the establishment of civilization) as recorded in the Antarctic ice cores, the CO2 level followed the many temperature changes as a result of emit/dissolve in the oceans. The planet came perilously close to extinction of all land life at the end of the last glaciation because of low atmospheric CO2.
Dan, more CO2 in the atmosphere means more emission to space. More emission to space means Earth cools.
Clint,
The past does not support that CO2 has any net causative effect on climate. Apparently the added cooling in the stratosphere from more CO2 effectively cancels the slight warming that it causes at ground level.
Dan, the thermometers they used 550 million years ago weren’t very accurate. And CO2 does not cause any slight warming at ground level.
Clint,
Analysis shown in Sect 3 of https://watervaporandwarming.blogspot.com using Hitran output (Hitran solves the Quantum Mechanics stuff) demonstrates that the amount of ground level warming from CO2 increase has been about 1/10 of that from WV increase.
Dan, I’m glad you didn’t try to claim the thermometers from 550 million years ago were accurate. Anything to do with 550 million years ago is belief, not science.
WV and CO2 do not warm the ground. If you believe HITRAN is a credible source for physics and thermodynamics, you could use a refresher course:
https://www.amazon.com/dp/B01K3RNLVE?tag=duckduckgo-exp-b-20&linkCode=osi&th=1&psc=1
Clint,
As you should know but from your words apparently do not know, scientists use proxies to estimate paleo temperatures. Although there have been updates in the past, the work of Veizer, et al has been accepted for two decades now.
Your statement about Hitran reveals that you know nothing about it and apparently ignored what I said that it does: “Hitran solves the Quantum Mechanics stuff”
Dan, when “scientists use proxies to estimate paleo temperatures”, that is nothing more than guesswork. In science, a “guess” is called a “hypothesis”. But a hypothesis is not a fact. Too often people confuse guesses with facts, and that leads to nonsense, as we’ve seen with the Moon issue.
The proper use of the “scientific method” keeps nonsense from entering the fields of science. The scientific method requires adherence to both the laws of physics and reality.
HITRAN is just more computer modeling. If a person does not know how to use it, the results can result in nonsense.
Clint,
So you think using a proxy is guessing. You are the only person I know of who thinks that.
The scientific method applies to measuring things. Not everything can be easily measured so inference is from the predominance of evidence. Proxies are used as evidence. For example, having a temperature is a proxy indicating that you are probably sick. Not recognizing the GHE is evidence that you are not competent in heat transfer analysis. Your failure to grasp the ‘moon issue’ is evidence that you lack engineering/science skill.
Dan, avoiding reality is not science. Avoiding reality is what a cult does.
Something that cannot possibly rotate on its axis is not rotating on its axis. But, you cannot admit that simple fact. You avoid truth. You avoid reality. That makes you a cult member.
Svante,
There is little evidence that the planet has experienced the last of glaciations. No one knows if global warming will be enough to prevent the next glaciation but it will certainly mitigate it. There is little downside to warming. With warming, farming can be successful farther from the equator. Increased TPW should result in increased low altitude cloud cover which will limit the amount of warming. At this point, I don’t believe it would be wise to try to stop Global Warming.
To answer your question, the first step is to recognize what is causing climate change. My latest assessment of allocations thru 2019 found that properly attributing 16% to solar, 19% to approximated SST cycles and 65% to increased TPW resulted in 96.6% match with measured Had*RUT4 average global temperatures 1895-2019. The human contribution to increased TPW is nearly all (about 96%) from irrigation. All except TPW increase are cyclic with no permanent effect. To reduce TPW requires the reduction of evaporation of water from irrigation. Here in the desert, drip irrigation is used to reduce water use (and incidentally evaporation). The challenge is to devise cost effective method of irrigating with less water evaporation. This would inherently reduce unintended consequences of buildup of undesirable salts which is a growing problem.
Dan, what was TPW in 1895, and 2019?
Clint,
I am unaware of any estimate except my own rational extrapolation as shown at Fig 3 in http://globalclimatedrivers2.blogspot.com . It estimates the WV in 1895 to have been about 9 to 10% less than now. I demonstrated that nearly all (about 96%) of the added WV comes from irrigation. Perhaps enough records of irrigated area are available to use as a proxy to improve on the estimate (if anyone cares).
The trend line of the values measured by NASA/RSS, which is also shown in Fig 3, shows that the TPW in Jan 1988 was about 5% less than now. The value in 2019 can be picked off the graph. The trend line looks to be about 29.6 kg/m^2 (which is equivalent to a liquid water depth of 29.6 mm).
Thanks for the response, Dan.
The 1895 estimate would then be about 26.6 mm. But with tolerance of about +/-10%. Even the 2019 estimate would have a tolerance of about +/-5%. So any increase in TPW is within the error range.
Beyond that, there is the “horse/cart” problem. Evaporation from the surface cools the surface. Evaporation is a form of energy transfer. The latent heat is moved to the upper atmosphere where it is radiated to space after condensation. A warm atmosphere can contain more WV than a cooler atmosphere.
Clint,
As you should know but from your words apparently do not know, scientists use proxies to estimate paleo temperatures. Although there have been updates in the past, the work of Veizer, et al has been accepted for two decades now.
Your statement about Hitran reveals that you know nothing about it and apparently ignored what I said that it does: “Hitran solves the Quantum Mechanics stuff”
Dan, your comment is a duplicate of your one above. I will only answer once, so people will not think we’re both senile.
http://www.drroyspencer.com/2020/07/time-lapse-video-of-altocumulus-with-virga/#comment-505055
Clint,
Sorry about that, this is what I had intended to post.
The temperature in 1895 is given with respect to the temperature in 2019 so the uncertainty in the 2019 temperature is not relevant and the uncertainty is the uncertainty of the magnitude of decrease.
I see, irrigation with less evaporation.
Tropical rains are flooding New Orleans.
The North Jet Stream traps tropical moisture in the US South. It portends heavy thunderstorms.
Saying “temperature depends on altitude” might be misleading. It would be more correct to say ‘temperature decreases with altitude’. Temperature depends on other stuff like latent heat, convection, radiation absor-p-tion and emission, and relaxation time of absorbed radiation. Relaxation time is long enough that radiation energy absorbed by a ghg molecule (which raises the temperature of the ghg molecule) can be shared by gaseous thermal conduction with surrounding molecules. The process is called thermalization.
Temperature decreases with altitude in the troposphere because the radiation depth is inversely proportional to the square of the pressure.
In the stratosphere, temperature increases with altitude since the radiation depth is inversely proportional to pressure.
The transition region is called the troposphere where temperature is roughly constant.
Emission rate to space varies also with wavenumber as shown on the TOA graph at https://drive.google.com/open?id=1k9OpSeNkiavyKjxzgU22i33m_QHNiUt3 The graph is described in Sect 10 of the analysis reached by the hot link there. A key take-away from the graph is that, for example, in the wavenumber range 500-600/cm and altitude range 2-6 km essentially all the outward emitted radiation makes it all the way to space. This is a major factor in how radiation energy absorbed by CO2 molecules gets redirected to WV molecules which radiate it to space. A lot of the radiation to space results from the huge population gradient in WV molecules of about 1200 to 1 on average from ground to tropopause. Although emission is omnidirectional, the ghg molecule population gradient is such that the outward directed radiation gets farther before it runs into other ghg molecules. It is at the tropopause that the ghg molecules have thinned out enough for outward directed radiation from CO2 molecules to make it all the way to space. At even higher altitudes, there is warming and insignificant pressure broadening resulting in the spike.
The day-to-day variations in cloud cover, humidity, etc. average out for the most part but in the way of random events they occasionally result in local droughts or precipitation related flooding. Messy systems like climate can be addressed using ‘emergent structures analysis’ which as described by Dr. Roy in THE GREAT GLOBAL WARMING BLUNDER, “Rather than model the system from the bottom up with many building blocks, one looks at how the system as a whole behaves.”
Think about it. The thickness of the atmosphere on the spherical earth has been described as like the peeling on an apple. It’s like 30 miles to 4000. The fact that the earth is a sphere can usually be ignored with no significant error.
In two days, tropical storm will cause flooding in Florida.
I am familiar with virga (precipitation that does not reach the ground) but while visiting Hawaii I experienced droplets of rain out of a cloudless sky.
This completely baffled me. Is there a simple explanation?
I hate anime now…
Was in your neck of the woods again Doc. Picked up catalyst for automotive exhaust systems at BASF by the airport across from the Gulf course. Departed there at 22:30 your time and then had a blow out of a super single trailer tire before I even got to I-65 that cost me a couple hours. Finally got back here to Anderson, IN at 09:30 this morning.
Dr. Spencer, thank you for all you do and the videos. Really cool.
Even on the humid Va/NC border near the ocean we get Virga. Flagstaff is so high up I believe the snow falling.
Anyone – due to altitude – does virga normally fall as snow? Virga shows up on radar pretty well.
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Hurricane Isaias will move closely along the US east coast all the way to Canada. Will cause huge material losses.
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I see above:
” By the way, Newton and Galileo are the scientists you should be studying, if you want to debunk the rotating nonsense. ”
Here is what Newton wrote in his Principia Mathematica, Book 3, Proposition XVII, Theorem XV:
That the diurnal motions of the planets are uniform, and that the libration of the moon arises from its diurnal motion.
The Proposition is proved from the first Law of Motion, and Cor. 22, Prop. LXVI, Book I.
Jupiter, with respect to the fixed stars, revolves in 9h.56′; Mars in 24h.39′; Venus in about 23h.; the Earth in 23h.56′; the Sun in 25½ days, and the moon in 27 days, 7 hours, 43′.
These things appear by the Phænomena.
The spots in the sun's body return to the same situation on the sun's disk, with respect to the earth, in 27½ days; and therefore with respect to the fixed stars the sun revolves in about 25½ days.
But because the lunar day, arising from its uniform revolution about its axis, is menstrual, that is, equal to the time of its periodic revolution in its orb, therefore the same face of the moon will be always nearly turned to the upper focus of its orb; but, as the situation of that focus requires, will deviate a little to one side and to the other from the earth in the lower focus; and this is the libration in longitude; for the libration in latitude arises from the moon's latitude, and the inclination of its axis to the plane of the ecliptic.
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