Overnight, those of you in the Americas and well out into the Pacific Ocean, if graced with clear skies, will be able to observe what is known as “a total eclipse of the Moon” or a “lunar eclipse”. The Moon’s color will turn orange for about 80 minutes, with mid-eclipse occurring simultaneously in all the areas in which the eclipse is visible: 3:00-4:30 am for observers in New York, 12:00- 1:30 am for observers in Los Angeles, and so forth. [As a bonus, Mars will be quite near the Moon, and about as bright as it gets; you can’t miss it, since it is red and much brighter than anything else near the Moon.]
Since the Moon is so bright, you will be able to see this eclipse from even the most light-polluted cities. You can read more details of what to look for, and when to look for it in your time zone, at many websites, such as http://www.space.com/25479-total-lunar-eclipse-2014-skywatching-guide.html However, many of them don’t really explain what’s going on.
One striking thing that’s truly very strange about the term “eclipse of the Moon” is that the Moon is not eclipsed at all. The Moon isn’t blocked by anything; it just becomes less bright than usual. It’s the Sun that is eclipsed, from the Moon’s point of view. See Figure 1. To say this another way, the terms “eclipse of the Sun” and “eclipse of the Moon”, while natural from the human-centric perspective, hide the fact that they really are not analogous. That is, the role of the Sun in a “solar eclipse” is completely different from the role of the Moon in a “lunar eclipse”, and the experience on Earth is completely different. What’s happening is this:
- a “total eclipse of the Sun” is an “eclipse of the Sun by the Moon that leaves a shadow on the Earth.”
- a “total eclipse of the Moon” is an “eclipse of the Sun by the Earth that leaves a shadow on the Moon.”
In a total solar eclipse, lucky humans in the right place at the right time are themselves, in the midst of broad daylight, cast into shadow by the Moon blocking the Sun. In a total lunar eclipse, however, it is the entire Moon that is cast into shadow; we, rather than being participants, are simply observers at a distance, watching in our nighttime as the Moon experiences this shadow. For us, nothing is eclipsed, or blocked; we are simply watching the effect of our own home, the Earth, eclipsing the Sun for Moon-people.
Simple geometry, shown in Figure 1, assures that the first type of eclipse always happens at “new Moon”, i.e., when the Moon would not be visible in the Earth’s sky at night. Meanwhile the second type of eclipse, also because of geometry, only occurs on the night of the “full Moon”, when the entire visible side of the Moon is (except during an eclipse) in sunlight. Only then can the Earth block the Sun, from the Moon’s point of view.
An total solar eclipse — an eclipse of the Sun by the Moon, as seen from the Earth — is one of the nature’s most spectacular phenomena. [I am fortunate to speak from experience; put this on your bucket list.] That is both because we ourselves pass into darkness during broad daylight, creating an amazing light show, and even more so because, due to an accident of geometry, the Moon and Sun appear to be almost the same size in the sky: the Moon, though 400 times closer to the Earth than the Sun, happens to be just about 400 times smaller in radius than the Sun. What this means is that the Sun’s opaque bright disk, which is all we normally see, is almost exactly blocked by the Moon; but this allows the dimmer (but still bright!) silvery corona of the Sun, and the pink prominences that erupt off the Sun’s apparent “surface”, to become visible, in spectacular fashion, against a twilight sky. (See Figure 2.) This geometry also implies, however, that the length of time during which any part of the Earth sees the Sun as completely blocked is very short — not more than a few minutes — and that very little of the Earth’s surface actually goes into the Moon’s shadow (see Figure 1).
No such accident of geometry affects an “eclipse of the Moon”. If you were on the Moon, you would see the Earth in the sky as several times larger than the Sun, because the Earth, though about 400 times closer to the Moon than is the Sun, is only about 100 times smaller in radius than the Sun. Thus, the Earth in the Moon’s sky looks nearly four times as large, from side to side (and 16 times as large in apparent area) as does the Moon in the Earth’s sky. (In short: Huge!) So when the Earth eclipses the Sun, from the Moon’s point of view, the Sun is thoroughly blocked, and remains so for as much as a couple of hours.
But that’s not to say there’s no light show; it’s just a very different one. The Sun’s light refracts through the Earth’s atmosphere, bending around the earth, such that the Earth’s edge appears to glow bright orange or red (depending on the amount of dust and cloud above the Earth.) This ring of orange light amid the darkness of outer space must be quite something to behold! Thus the Moon, instead of being lit white by direct sunlight, is lit by the unmoonly orange glow of this refracted light. The orange light then reflects off the Moon’s surface, and some travels back to Earth — allowing us to see an orange Moon. And we can see this from any point on the Earth for which the Moon is in the sky — which, during a full Moon, is (essentially) anyplace where the Sun is down. That’s why anyone in the Americas and eastern Pacific Ocean can see this eclipse, and why we all see it simultaneously [though, since we’re in different time zones, our clocks don’t show the same hour.]
Since lunar eclipses (i.e. watching the Moon move into the Earth’s shadow) can be seen simultaneously across any part of the Earth where it is dark during the eclipse, they are common. I have seen two lunar eclipses at dawn, one at sunset, and several in the dark of night; I’ve seen the moon orange, copper-colored, and, once, blood red. If you miss one total lunar eclipse due to clouds, don’t worry; there will be more. But a total solar eclipse (i.e. standing in the shadow of the Moon) can only be seen and appreciated if you’re actually in the Moon’s shadow, which affects, in each eclipse, only a tiny fraction of the Earth — and often a rather inaccessible fraction. If you want to see one, you’ll almost certainly have to plan, and travel. My advice: do it. Meanwhile, good luck with the weather tonight!
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Hello. Several years ago, I decided to distinguish between two types of phenomena: one in which an object is in another object’s shadow, and one in which an object physically obscures light from another object. My main motive for doing this was to discourage the use of “Eath’s shadow” and “blocking” as an explanation for lunar phases, but I’ve decided that it has other significant advantages. In my (undergraduate) astronomy classes, I define “eclipse” as “an event in which one object stands in another object’s shadow, and the object in the shadow is the one that is eclipsed and lends its name to the event.” So in a lunar eclipse, Moon is eclipsed because it stands in Earth’s shadow. What is traditionally called a solar eclipse now becomes an Earth eclipse because Earth stands in Moon’s shadow (albeit not completely). I define “occultation” as “an event in which one object physically blocks light from another object and the object doing the blocking lends its name to the event.” Thus what is traditionally called a solar eclipse becomes a lunar occultation of Sun. This is consistent with terminology used when Moon occults a star, planet, or asteroid. If the occulting object’s angular size is very small compared to the other object’s angular size, we have a “transit of whatever the first object’s name is.”
Of course I’ve been negatively criticized for introducing these distinctions, but I feel very strongly that for the benefit of students, different physical phenomena should have distinct names. There’s no reason to have the same name for two different events.
sorry for my grammar.
I have an unrelated question concerning the masses of particles. I have heard that the reason that the masses of particles are fixed and not a mushy mix of energy is due to the Schrödinger equation, for example it takes 0.511 MeV to make one electron and only one because 0.511 MeV is the electrons rest mass. But does this apply to photons? or gluons? I mean the electromagnetic spectrum suggests that photons have absolutely no quantization in terms of how much energy a photon can have.(what i mean is there is no specific amount of energy that you require to make a photon eny amount of energy seems to do something to the electromagnetic field unlike the electron field. The main question is that does this have something to do with the higgs field. What i mean is that if the electron interacted with the higgs field more than it does now (therefore having more mass) then it must take more energy to create an electron from the electron field. The idea that I have basically fabricated is that the higgs field is responsible for the energy in particles when there at rest, and that the amount of energy it takes to make a particle from its underlying field is the energy that it takes to have a wave in that field that can exist while it interacts with the non-zero higgs field. And the reason it can take an arbitrary amount of energy to make a photon is that the photon particle does not interact with the higgs field. Please correct me if I am wrong because the whole quantization of electron quarks ect.. and the seemingly unquantization of photons (in terms of energy) has bean very confusing.
The PEDAGOGIC aspect of your blog is particurarly useful .
Beautiful , interesting & such useful blog of yours …
What did Shakespeare know about science?
http://www.cbc.ca/ideas/episodes/2014/04/14/the-science-of-shakespeare/
I would rather take on a complete understanding than one i have to look everywhere for.
And much power to you on your quest for knowledge. But it always pays to look a little more than you have to; the first ‘complete’ answer is quite often wrong.
Yes agreed.
Thank you I understand
Thank you for your time and I hope to become more educated on the subject.
@ Derek and Kudzu: Let me add some hopefully clarifying remarks to Kudzu’s replies to Derek’s question. In the standard model, sometime during the first second, there was a unified electroweak field with four carriers, 3 Ws and one hypercharge field, with zero mass (in the equations). Perhaps it is not necessary and may be even confusing to call them zero mass particles. Then a complex doublet containing 4 components of some primitive Higgs field was turned on. The 3 Ws acquired masses as a result of interaction with this field. They ate the three components of the Higgs field as they say in a joke!! 4th component of the electroweak field became mass less photon of the current electromagnetic field. Thus electromagnetic and weak interactions got separated. The remaining component (not eaten!) of the primitive Higgs field has a non-zero average value today and was manifested as a standard model Higgs Boson particle at 125 GeV by whacking the field! Thus I would not say that there were four Higgs particles and only one remains now. Apparently, Higgs field gave masses to quarks and leptons at the same time by interactions.If there are more Higgs field components or different types of Higgs fields beyond the standard model (say Super symmetric), that is altogether a separate question. As of today there is no information on that.As to what happened before the standard model Higgs field was turned on, nobody really knows. Everybody and his brother (and sister) may have a model! Hopefully this clarifies the stuff on which Matt has written extensively. Of course any correction is welcome.
You are correct on a number of points. Notably about how many Higgs particles there are. But I try to stick to simple explanations unless I know that the person I am talking to can understand more. And things like ;’there were four particles but only one remains’ usually suffice. Better to leave someone with an incomplete understanding than a completely confusing one.
The basic question is are the w and x particles really just mixtures of different chirality’s and what are the most basic (absolute fundamental) particles of nature?
Just to make it clear, when i say a particle with its own field, I mean a particle that is not experiencing “quantum mixing” and is rather a single field that has one specific kind of particle.
Ok i understand the four higgs part. But the one thing i’m still having trouble understanding is the three w particles and 1 x particle. Are these particles just theoretical? And is there no such thing as the electromagnetic (photon) field because a photon is just a non-composite mixture of an x and w particle? I understand that we should treat the standard model the way it is because for example if you excite the x particles field it will act as a photon because the non-zero higgs field will “mix” these particles together but it really bugs me to think that all this time there was a whole new set of massless particles. Also Doesn’t the higgs field only mix the two chirality’s of one kind of excitation in a field which means that the mixture of the higgs and the other w and x particles is a different system?
The particles you mention are not theoretical;we have good evidence that they exist even if we cannot isolate and observe them. Their remoteness stems solely from the fact that we have little need to invoke them in any physics we explore at current energy levels.
When it comes to whether the electromagnetic field is a ‘thing’ we come across a number of subtle problems. How do we know for example that the isospin or Higgs fields are fundamental, ‘real’? What if they arise from the combination of some other, currently unseen, fields? And what if fields themselves aren’t the best way to look at things? In that case all that we consider as real things now would just be a way of looking at the world. (String theory would likely supplant fields.)
So when we say ‘there’s no such thing as the electromagnetic field’ we’re only saying that it can be constructed from other things. And that is true of nearly everything in the universe, electrons, protons, atoms; there are layers to the world. A photon IS a particle by nearly all definitions of the term and its field behaves exactly as you would expect for such a particle. It just arises from a more fundamental layer of physics. This discomfort you feel is exactly that which faced physicists when quarks were discovered, and before that protons and electrons.
Your confusion over the Higgs field is because there are *two* distinct phenomena involving the field with a common cause. When the Higgs field becomes nonzero various massless particles interact with it and are mixed, giving them mass. This is the chirality issue you mention and it is called ‘The Higgs Mechanism’ It involves only the massive Higgs component of the Higgs field and can be considered the Higgs-mediated combination of two particles with the Higgs particle involved being merely an onlooker or catalyst.
The second phenomena involves the other 3 Higgs particles and is called ‘Electroweak Symmetry Breaking’ It can be considered the direct combination of various Higgs particles with other particles with the interacting particles being converted to something new.
One phenomena affects fermions, the other bosons.
Matt my man. I have some unrelated burning questions about the article concerning the hypercharge force and iospin force that supposedly existed befor the higgs system came into existence.
Are the 3 w particles for the iospin and the x particle for hypercharge really new particles with there own quantum fields? Or are they just a different chirality of another particle. And if these force carriers are completely new particles then why are they not on the standard model? Also why are there four higgs? Are the four just a different chirality of two more fundamental higgs?Or are they all completely fundamental? And one more simple question. If the four higgs are really all four different particles with there own quantum fields then is it only the one higgs field that is non-zero? I would very much appreciate it if you would reply.
The ‘standard’ standard model describes the universe as it works now, all the particle properties are those that are expected in the everyday world we live in. While things like hypercharge and isospin are part of the standard model they’re typically hidden away from the public in the same way the ‘periodic tables’ of baryons and mesons are.
The particles are ‘new’ particles with their own fields but phrasing it this way is slightly misleading. Protons are not fundamental particles, being composed of quarks and gluons, but they too can be considered as ‘new’ particles with their own field. It is possible to ‘break down’ many fields into two (or more) more fundamental fields. This is the equivalent of treating a composite object (e.g. proton, electron) not as a single object with a single field but as a collection of objects (quarks\gluons, elecctron-lefts\positron-rights).
The four Higgs aprticles actually arise in a very neat way from a single Higgs field. ‘Consider the potential of a field in 3 dimensions. ‘Normal’ fields are a symmetrical well where particles try to sit at the bottom. There is only one possible way to excite this kind of field since the well is symmetrical.
The Higgs potential however is different, it’s a ‘sombrero’; a well where the bottom has been pushed up a bit. Here there is not one but four ways to excite the field. (These are hidden when the field is zero but appear when the field becomes nonzero.) The first three involve particles ‘moving around the ‘brim’ of the sombrero and give us massless Higgs bosons. The fourth involves a particle moving up and down the walls of the well, giving us a massive boson. Only the massless bosons can mix with other particles, leaving us with ‘the’ Higgs particle we look for today.
This answer is oversimplified but I hope it helps.
Algebra is from Arabic al-jebr meaning “reunion of broken parts”.
In QED, the notion of global (electric) charge is easy to understand. This is due to the fact, that in this theory we have a local Gauss law, which is built from gauge invariant operators and which is linear. Thus, one can “sum up (al-jebr)” the local Gauss laws over all points of a given (spacelike) hyperplane in space time yielding the following gauge invariant conservation law.
Conservation laws most often express themselves as pairs of properties that cancel each other out.
But in Lorentz force, this symmetry is broken by combination of electric and magnetic force on a point charge. For any produced force there will be an opposite reactive force. These forces not cancel each other, but make dipole due to angular momentum (spin or polarization) – and charged particle which might be traveling near the speed of light (relativistic form of the Lorentz force).
The mathematical formulations of quantum mechanics provides information about the probability amplitude of position, momentum, and other physical properties of a particle. But we got it only “where we measure” – It always cancels out everywhere and appear everywhere. There is no GAP inbetween. But mathematics need a gap to fill in as virtual particle – making the incomplete as complete.
The particles that make up ordinary matter are subject to some additional more subtle conservation rules that describe the mathematical structure of the particles. These rules are covered by the Standard Model of particles physics, but unfortunately are not expressed in a way that is easy to understand.
Making the incomplete as complete:
Anyone living in California has seen a blood red mood every time there have been nearby forest fires. Having lived through many of them, and been an avid watcher of the night sky, I can imagine that in ancient times of war when many things were set on fire, they would have seen similar unusually blood red moons.
First it was black and white, redness appeared later. I could not figure exactly the details of the “blood moon” (although I know of red sunsets and the Poisson dot, that bright spot behind a sphere from wave theory of light…).
Also the phenomenon was long, as the shadow seemed to chase the moon over well over ten moon diameters. OK, the Moon moves at 3,000 km/h or so, and the Sun (appears to move) at 2,000 km/h..
http://www.cnn.com/video/data/2.0/video/weather/2014/04/15/vos-nasa-lunar-eclipse.nasa-tv.html
The Moon is actually eclipsed – from the Sun’s point of view. 🙂
By the way, the kind of eclipse that we all experience most often is when the Sun is eclipsed by the Earth from our own point of view. We call it “night”.
True on both counts. Thanks for the wry wisdom!
“The Moon’s color will turn orange”
In reality, the eclipsed moon *visually* looks REALLY DARK (no sign of color)..it almost “disappears”.
http://3.bp.blogspot.com/_0PmNhVV6q6g/R70WVgoFwwI/AAAAAAAAAR4/IspdiTgeTPo/s1600/IMG_1679.jpg
Only long-exposure photos pick up the reddish-orange tint (which varies due to amount of particulates in earth’s atmosphere, as scattered sunlight “bends thru it”). I.e., those red-orange photos are OVER-EXPOSED..to make “shadow detail” (dark) come out as if it was highlight detail. Another example to be skeptical of “pretty pictures” (not Science)
Here are some bracketed shots from 2007 lunar eclipse:
http://track.eclipse-chaser.com/search/label/Lunar%20Eclipse%202%2F20%2F08
More lunar eclipse photos at:
http://track.eclipse-chaser.com
This is simply not true. As I wrote, I have personally seen orange, copper and red moons with my own eyes, no optical aids, no cameras. The color and brightness is not always the same (because it depends on the clouds and dust in the Earth’s atmosphere that can block some of the refracted sunlight.) But your statement that only long-exposure photographs pick up the color is just wrong. Maybe it’s true in cities where there’s lots of light pollution.
Hi, I meant that the *really bright* orangish long exposure photos were not close to visual (human eye exposure time is fraction of a second). I was able to get some photos:
http://track.eclipse-chaser.com/2014/04/1-min-into-totality-lunar-eclipse-414.html
The top 2 photos are close to “visual reality”. You could barely discern some red, the eclipsed moon looks dark red-brown.
Last night the moon was *bright* orange to the naked eye. It was equally orange as Mars, though with a good deal less surface brightness. It wasn’t even remotely close to “disappearing”. I could see all the surface details that I normally can with the naked eye. There was absolutely no “barely discerning” the color, it was very clear and very impressive.
In terms of your gallery, it was like the bottom photograph, even when far into totality and the entire moon was orange.
Through my 11″, the orange was relatively muted but still quite apparent. Saw *lots* of interesting surface detail that I normally can’t during a full moon.
The best view imo was through binoculars.
“due to an accident of geometry, the Moon and Sun appear to be almost the same size in the sky”. Since moon is receding from earth gradually, our future descendents will not see this complete blocking! It is a great anthropic coincidence that we are alive to watch this phenomenon and understand it!
Hold on there kashyap…I think you are mixing up the nature of a lunar eclipse and a solar eclipse. It is a TOTAL solar eclipse that specifically depends on the amazing coincidence that the Moon and Sun appear to be almost the same size in our (Earth’s) sky. In fact it is possible that the Earth, and Earth alone, in all the galaxy, has this very, very rare condition. And, as you note, due to the recession of the moon, it won’t even be the case here on Earth further down the road.
It truly is an amazing coincidence, and makes me wonder if there are other amazing coincidences in science that we don’t currently recognize as such. Anybody ever hear of ‘Bodes Law’? How about Einstein’s ‘Principle of Equivalence’ – oops, sorry – jumped the gun on that last one…
@S. Dino: Well. So we agree that total solar eclipse will not be visible to our descendents. I have not seen actual numbers on lunar recession. But if it is sufficiently far, it may not be covered by earth’s shadow.
Good point, I had not even considered that, nor have I ever heard it discussed. Would be an interesting calculation…
Interesting discussion.Thanks to both kashyap and Dino. Particularly, How about Einstein’s ‘Principle of Equivalence’ ? – by Dino.
/Scientists suspect extra dimensions exist in space and time; these dimensions are microscopic, proponents say, making them tricky for detectors to pick up. “But as we go to very high energies with the LHC, maybe we’ll start to see evidence of extra dimensions,”. Such evidence would come in the form new particles, or perhaps missing energy as some particles move off in dimensions other than the ones people can see./– News.
I think this may be the violation of ‘Principle of Equivalence’ due to the change in timeline “now” ?
…and the answer is – Never! The Moon will never recede past the distance of the Earth’s shadow. Even if you assume that the Sun will remain as is forever (which it won’t of course, but let’s just assume) then the Earth and Moon will become tidally locked in ~15 billion years with an eternally stable orbit ~1.6 times its present size. That is still well within the radius of the Earth’s shadow, which will shrink from the current ~4600 km to ~3600 km; more than enough to cover the Moon (r = ~1700 km).
As to my comparison of Einstein’s Principle of Equivalence to Bodes’ Law; let’s just say it is a reflection of my own belief in a truly symmetric universe and best suited for discussion in the future. However, it has nothing to do with string theory or other dimensions. Suffice to say that it is nice to see mankind is finally getting around to seeing how things, other than protons, neutrons and electrons, fall in the Earth’s gravitational field. Such experiments are long overdue.
@S. Dino: Interesting calculation. I have not seen any technical article about moon’s recession except wikipedia(!) based on high school physics. But I am fairly certain, someone must have done detailed calculation. Do you have a reference about orbit-tidal lock in? Of course 15 B years is a long time. Solar system will be gone by that time. How about the other question of our descendents not seeing total solar eclipse before that time? Earth-moon distance of 1.6 times the present distance is too little to make a significant change in viewing solar eclipse. So now I am optimist about our future generations being able to see solar eclipse!!!
Ok kashyap, lost my original source, but found another that says the same thing: “Curious About Astronomy: Will we ever stop having solar eclipses because of the moon’s motion away from Earth?” (Talks about both solar & lunar eclipses).
Looks like we can only look forward to ~500 million years of TOTAL solar eclipses, a mere drop in the bucket cosmically speaking!
I argue the coincidences are not entirely remarkable. The Moon probably started off somewhere near the Roche limit, and has moved out due to tidal interactions. That we happen to be around when it is there now is a coincidence I suppose, but it had to be somewhere. Had we been in the PreCambrian, we would have bigger solar eclipses. I personally disagree with the comment on Bode’s Law. The standard theory of planetary accretion starts by ASSUMING a distribution of planetesimals that then accrete stochastically, but there is no plausible mechanism proposed so far to form them, and that is after nearly 70 years of trying. My view, and admittedly a somewhat biased one (I am actually a chemist by training) is that the initial accretion is of chemical (including physical chemical) origin, and different things happen at discrete parts of the accretion disk due to temperature differences. What you end up with is regions of different probability of accreting something, and the most probable regions are reasonably in accord with the distribution of planets in this system. So I argue it is not a coincidence, but rather it is causal.
The Japanese space agency’s lunar orbiter Kayuga captured pictures of a lunar eclipse, as seen from lunar orbit, in 2009. There are photos and video at http://www.jaxa.jp/press/2009/02/20090218_kaguya_e.html.
A small correction to Edwin. For Aristarchus of Samos, this was not a puzzle, but rather an opportunity, because it gave him an opportunity to be the first person to get the concept of the size of the solar system. Because the eclipse occurs at exactly the same time for all observers, with help he measured the angles the Moon was at from two points that were at as large a distance from each other as he could manage. With two angles and a length, simple geometry gave him a distance, and with the distance the solid angle gave him the size. Experimental error was a bit significant, but he had the idea. Later, he used that to measure the distance to the sun, by measuring the angle moon/observer/sun at half moon, and then used Pythagoras’ theorem. That last angle was a bit beyond his measurement skills, and from memory, he was out on distance by a factor of ten, partly compensated for by the opposite moon distance error. But while the measurements were faulty, it would be wrong to say he did not understand what was going on. Needless to say his heliocentric theory was rejected as nonsense!
Yes, some people had the right ideas amazingly early. I can only express the utmost admiration for these scholars. What a feat it is for someone experiencing the world with the limited means of the times of, for example, Aristarchus to even imagine that there are distances of these orders of magnitude! On the other end of the scale you have people fighting for geocentrism today in our age of images sent back by spacecraft. It seems you can be “crazy” enough to see the truth or crazy enough to be blind to it. Between these extremes the mass of humankind is moving slowly. (How many people today appreciate the profound revelations of quantum mechanics, for example?)
Also eclipses allow us to detect exoplanets.
Yes, eclipses of various sorts might deserve an article all their own…
I’ve been waiting for this. It should be magnificent. I have a excellent pair of Nikon binoculars to boot. Unfortunately, Louisville KY is guaranteed to be overcast and raining all night. Sigh.
I hope everyone with good weather really enjoys this one.
Not looking good east of the Mississippi in the U.S.
Reading this, it struck me how amazing it is that today we can read such a crystal clear explanation of things that must have been totally incomprehensible and frightening to humans in the past. And the funny thing is: The key is simple geometry – geometry which a person from the stone ages would have understood without difficulty. But it took a long journey for humankind to realize in this case how geometry applies.
Typo: “The orange light then reflects off the Earth’s surface,” should be Moon
Thanks! Fixed.