Hello, my question may seem stupid but I was thinking of this: On the Moon (or on Earth ignoring the refraction of light by the atmosphere), I doubt that the sunlight arrives perfectly horizontally like here
https://en.wikipedia.org/wiki/Daytime#/media/File:Earth-lighting-winter-solstice_EN.png, if we consider the apparent size of the sun from the moon, then sunlight hits the moon at a certain (very low) angle, and then the illuminated surface on the moon is very slightly lower than the shadowed surface.
Am I right?
Thank you!
Even in the approximation that light traveling from the sun is ray-like, those rays can originate from any visible point on the sun, and can travel in any direction from any of those points. So yes, sunlight will never be perfectly horizontal.
For starters, take a look at the (admittedly small) wikipedia page discussing the various components of a 'classical' shadow:
https://en.wikipedia.org/wiki/Umbra,_penumbra_and_antumbra The main image itself might be quite informative for you.
From there, some quick googling can tell you much more.
I understand the shadows well, which explains the eclipses well, but despite that, I can't answer my questioning even by searching on google. I don't really know what info i'm missing
I understand the shadows well, which explains the eclipses well, but despite that, I can't answer my questioning even by searching on google. I don't really know what info i'm missing
I do not understand your question, even after looking at that article. Sunlight for all intents an purposes comes in a straight line from all visible parts of the sun to any daytime point on earth (or Moon). So what do you mean by "horizontal"? The angle the light hits depends on the location on the Earth or Moon you are considering. It could be horizontal if the Sun is on the horizon or vertical if the Sun is directly overhead. The angle the light "rays" come in at for that given point can differ by the angular size of the Sun in the sky. That is, the light from one side of the Sun will arrive at an angle different to the light from the other side of the visible disk of the Sun, by the angular size of that disk. Ignoring refraction, this is what gives rise to partial eclipses - the angle of light from one side of the sun is not blocked by the Moon and it is for the other side, (For that given point on Earth.)
Deriving a maximum angle is straightforward trig:
l = 150,000,000 km
d = 1,392,700 km
arc of sky at l = pi * l * 2 = 942.5 m km
So sun occupies = 0.0021 of a 360 degree field of view
Splitting this in 2 as incident angle at most 50% of this = .001 of circular field of view
So at most incident angle of light from sun's outer edge (the smallest part of the radiative field too) occupies 0.37 degrees. Minimal at best, the eye won't see this.
More advanced answer: After you re-calc for the portion of radiation coming in from each fraction of the sun (brightest to centre) you can basically ignore this effect; for solar panels etc the impact is a fraction of the "whoops I forgot to clean them today".
My question relates to the size of the surface of the Moon which is illuminated and which I think but I am not sure depends on the size of the star of its distance and then of the "angle" under which certain ray strikes the Moon. I made a drawing to illustrate my point: the yellow circle is the sun, the gray the moon, everything that is between black lines represents the light which touches the surface of the moon and we can see that if the he star is bigger than the planet/moon the surface on it which is illuminated will be larger than the surface in the shadow.
I can summarize my question to: is the surface of the Moon illuminated by the sun greater, smaller or equal to the surface area of the Moon in the shadow and why ?
I can summarize my question to: is the surface of the Moon illuminated by the sun greater, smaller or equal to the surface area of the Moon in the shadow and why ?
Okay, that makes your question clearer.
The surface of the moon illuminated by the sun is greater than the shadowed area.
Approximating both sun and moon as spherical, then the "last" place a ray of sunlight can contact the moon is where the ray forms a tangent to the surface of the moon. Since the angle of your black lines is tilted rear-ward, that necessarily places that point beyond the central axis of the moon; and therefore more the moon is in sunlight than shade.
The image blow shows a very exaggerated version of this effect. For our own sun and moon, the effect is almost negligible because the much greater size of the sun is offset by the great distance between sun and moon.
The thing to google now is some variation of 'how much of the Earth is visible from the top of a mountain', which is essentially a much more common version of your question; and relies on nearly identical math for the answer.