Jonathan: " OK they [sun and moon] could have been very nearly the same [perceived] size, but exactly the same?

It is misleading to describe our experience of the size of the moon and the sun as "exactly the same". There are two important factors that must be taken into account:

1. There is a very large range of tolerance for a specified visual angle projected on the retina as viewing distance for an object increases. The sun is ~ 93,000,000 miles from earth so there can be wide variation/tolerance for the absolute size of the sun for a given measured retinal projection angle.

2. The least significant difference (LSD) for the discrimination of a difference in the perceived magnitude between visual objects increases linearly as the viewing distance of the objects increases. In the case of celestial objects like the moon and sun, LSD is extremely large. Incidentally, this psychophysical effect is clearly seen in the representational structure of Z-planes in retinoid space.

Jonathan: " OK they [sun and moon] could have been very nearly the same [perceived] size, but exactly the same?

It is misleading to describe our experience of the size of the moon and the sun as "exactly the same". There are two important factors that must be taken into account:

1. There is a very large range of tolerance for a specified visual angle projected on the retina as viewing distance for an object increases. The sun is ~ 93,000,000 miles from earth so there can be wide variation/tolerance for the absolute size of the sun for a given measured retinal projection angle.

2. The least significant difference (LSD) for the discrimination of a difference in the perceived magnitude between visual objects increases linearly as the viewing distance of the objects increases. In the case of celestial objects like the moon and sun, LSD is extremely large. Incidentally, this psychophysical effect is clearly seen in the representational structure of Z-planes in retinoid space.

Correction. In point 2 above, substitute just noticeable difference (jnd) for least significant difference (LSD).

You are right as usual, Arnold. However, in this particular case I am bracketing out all the interesting things we have discovered about perceptual mechanisms. Perhaps I should have asked why is it that the sun and moon subtend exactly the same angle at the surface of the earth such that if you take a high resolution photograph of a total eclipse of the sun all you see is the solar flares dancing around the blackness of the moon.

I realise that the size of the moon and sun seems to change with their place in the sky and that the sun is of course much bigger than the moon. But it still seems that some deity must have made sure that they subtend exactly the same angle so that all things considered we consider them 'the same size'.

I am of course asking this question in a spirit of mischief. But there are times when I do wonder...

I wonder too, Jonathan!

Jonathan,

We are the unwitting victims of our time.

Had you looked up at the sky only a billion years ago, you would not be able to make that comparison - the moon was orbiting at a much closer distance, and would have had an angular diameter between 1.2 to 1.5 times that of the Sun.

Equally, if one were to look up at the sky in a billion years from now (presuming that we have not turned the Earth into a fractal mass of computronium) then the Moon (if we have not mined a hole through it) would seem to be far smaller than the Sun.

I am reminded of a puddle of water, marvelling at how remarkably well it fits into a hole in the ground.

No, that won't do as an answer, James, because there were no people to consider the problem a billion years ago and there will probably be no people in a billion years time. The only cosmic situation we are aware of is that of our species' time on earth. If God wanted to make us a sun and moon the same size he would have done it now - the angles subtended a billion years ago would be irrelevant. Of course the precise agreement of angle subtended by sun and moon may be coincidence. Coincidences are very common. But this one is just a bit hard to swallow. I do swallow it most days. But for the days when I wonder I would not wonder less because of what had to arrange a billion years ago in order to make things like this for us.

Jonathon,

>James, because there were no people to consider the problem a billion years ago

And I wasn't able to witness the 19th Century, so perhaps you might suggest that I cannot speak about events then.

We have good empirical data about the rate of recession of the moon in the present epoch.

We have robust models that explain that rate of recession, and if extrapolated backwards (as one might do with Hubble's law, or tectonic plate motion, etc.) they show that the Moon was, in all likelihood, closer to the Earth.

>The only cosmic situation we are aware of is that of our species' time on earth

And if we could only speak about our direct experiences then we would be able to say very little.

I think you have misunderstood my point James. I am a scientist and well aware of the recession of the moon. That does not change the argument, as I indicated above. (I also indicated that the question was asked in a spirit of mischief.) If God were to set things up so that we had a moon and sun the same size - perhaps deliberately at that point in human history when our concepts of deity were evolving, he would very likely have started the solar system off the way he seems to have done. It would not matter if trilobites saw the moon as bigger - that would all be part of a much lesser purpose. 

The argument is a variation on Descartes's claim that an evil demon is implausible as an explanation of our experiences. They are too regular and predictable - so they must be due to a benign reason, which he called God and we now just call physics. The human epistemic situation is inherent in the argument. And the identical size of sun and moon is not a dynamic regularity, but simply a regularity of how things appear to human souls. That is the one thing that to my mind hints at the God of the Old Testament, rather than the one that Descartes and physicists have believed in. There is a hint of a God specifically putting on a show for the faithful. 

Dear Jonathan

I am not a natural scientist. I am a layman to this scientific discussion going on. But only as a layman, as I am, would you permit me to say that the moon and the sun do not appear the same size to a naked eye. Usually, the sun appears bigger, particularly seen at sunrise or sunset, than the moon. And the moon appears more beautiful and intimate than the sun.

You, the scientists, tell us that the real sizes are not the same. The samenesses are just the retinal appearances.

As to the role of God, everything has been made by the God with a design and a destiny. Because the moon and the sun are also the instruments for assessing the time, and they make a profound impact on earth climate, seasonal variation, day and night, all cyclical movements etc., the present position of these celestial bodies is the most appropriate for the life-planet.  

However, I feel very much amused to see a scientist talking like a poet. That is nice. Maybe, it i.e. the poetic sense is one of the variables for the perceptional equality. But, then, it is the moon that motivates more poetry in comparison to the sun which produces more awe and fear.

I am sorry.

With best regards.

Dear Jonathan,

I was impressed by your rare but good question about the size of sun and moon that we see them everyday.  From millions of the galaxy members, why only sun and moon have more and less the same size to human's eyes? I agree with Dr. Israr Khan's statement that mentioned "everything has been made by the God with a design and a destiny". God wants us to think why it be like that. I can't imagine, if all stars would have the same size to human's eyes, our sky will no longer beautiful. With best regards.

Indeed a special coincidence.

But there is more than only the almost similar angular perception (size) of the sun and moon seen from the earth. By the way, to make this possible the size ratio moon vs. sun jas to be almost equal to the  distance ration "earth-moon" and "earth-sun". Both ratio's are approximately 400.

The other special thing is that the moon's axial rotation is also perfectly in sync with the rotation around the earth (better known as tidal coupling). The moon rotates in 27 days,13 hours, 18 minutes, 37.4 seconds around the earth measusred from one to the other perigee. In the exactly the same time it completes one rotation around its axis. As a result we always see the same side of the moon and never see the other side of the moon. Because the moon's rate of rotation is uniform, but its rate of revolution is not, we can just see around the edge sometimes given 59% visibility of the moon's surface. However at the end of the months the synchronization is perfect.

Although some other celestrial bodies seem to have a smilar type of synchronization it's still quite unique.

Another thing is the maximum depth and shape of craters. The depth of the craters is hardly exceeding 4 miles even for craters almost 200 miles wide. It suggests that the moon's surface must be of an extremely resistant material to prevent deeper impact, much different than on the earth. In addition to this the far side (non visible side) of the moon has the majority (~80%) of the craters and mountains (called geographical assymmetry). 

And with respect to James' answer, we not even know if the moon existed a Billion years ago or was formed or arrived not even that long ago on an astronomical timescale. There are even stories from various ancient civilizations which indicate that the moon was not always there. 

We are only scratching the surface. Still a lot to learn and understand ;-)

https://youtu.be/OZIB_leg75Q

Thanks for the comments, Ronald. However, I would say none of these things need be surprising. Presumably there can be some good reason why an orbiting body might show tidal coupling. Any other arrangement would expend energy of deformation and so there must be a tendency for coupling to be an energy minimum.

The depth of the craters, as you say, presumably reflects the absence of a liquid core, which one would expect in a much smaller body than earth. And I would guess that craters on the far side would be expected since any large body approaching from the earth's side would be likely to hit the earth instead, or be deflected off the track to the moon.

The exact explanations would be of interest to discuss in scientific journals but I do not see any of these things being unexplainable co-incidences. The more or less exact equivalence of the angle subtended by sun and moon seems to me to have no possible mechanistic explanation at all. Hence the mischievous thought that it is the whim of a deity. There may be some rule that says that celestial bodies tend to orbit other bodies that are four orders of magnitude greater in mass - maybe anything closer is unstable. And there is probably a rule that says that orbital radius decreases with mass of orbiting object such that celestial bodies engaged in orbiting tend to look about the same size - whether bigger or smaller than that on which the observer stands. But the sizes of other planets clearly show no precise conformation to a rule. What is odd about the apparent sizes of the sun and moon is that they should be so precisely similar. 

It's the combination of these things that is making it special and important for life on earth. I only took out a few things. There is more which is unique compared to other satellites. For example the relative size of the moon to the earth (it's a rather large satellite), the low density of the moon, slow speed of rotation (10 miles per hour vs. 1000 miles per hour for the earth) etc.

With respect to the tidal coupling of moon and earth it's quite special too. For example Mercury and the sun have also tidal coupling, but not in a 1:1 ratio, but approximately 1.5:1.

The craters and mountains don't have to do with the fact that one side is facing earth. This is only the relative visibility seen from earth. The majority of the space objects potentially being able to hit the moon or the earth are coming from the direction of the sun, which will determine the location of impact on the moon too. By the way, this is also the reason that the meteorite prediction is only limited to about 15% of what is potentially able to hit the earth or moon. Looking in the direction of the sun for tiny dark objects is still problematic (ref. NASA sources).

More likely is that there was an impact with an extremely big object a long time ago.

The moon is moving away from the earth with 3.78 cm per year. So, eventually a full solar eclipse will no longer exist, The current situation therefore suggests that we might live in a special time window on astronomical scale.

A better question from a scientfic point of view would therefore be:

"Where does the moon come from?"

A good Podcast on the topic with an astronomer specialized on this topic is this one:

http://www.astronomycast.com/2007/01/episode-17-where-does-the-moon-come-from/

 Thanks Ronald, but I am not looking for a better question, or any other of these perfectly ordinary scientific questions. I am quite happy that astronomers can work out solutions to other questions. I am only interested in this one question because it seems to have no plausible explanation. In fact I seem to have come up with a very partial possible explanation myself but nobody else seems to have any way of addressing it!