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It seems to me that the Moon has appeared in many locations - apparent locations - in the 'dome of the sky'. I know that the Sun follows an arc from east to west and that the arc is smaller in winter than in summer. Therefore the Sun cannot appear in every location in the 'dome of the sky'.
My question is: can the moon appear in any (every?) location in the 'dome of the sky'?

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    $\begingroup$ Yes, but only if you don't constrain the time or position on Earth you have to be at in to see the moon at any particular position, and if you only measure the position relative to the surface you are standing on, as opposed to other objects in the sky. $\endgroup$ – Michael Mar 13 '17 at 22:38
  • $\begingroup$ I believe we can assume that the question is meant in the context of being at a fixed position (by mentioning winter vs. summer - there is summer at some place at any time in the year, after all ;) ). $\endgroup$ – AnoE Mar 14 '17 at 13:32
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    $\begingroup$ The moon can lie between a 5.14 degree wide band around the ecliptic. $\endgroup$ – Agile_Eagle Mar 14 '17 at 13:53
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Like the sun, the moon, from our perspective on the surface of the Earth, rises in the East and sets in the West. However, it does not rise exactly due East and set exactly due West. If you were to track the position of the moonrise along the horizon over the course of a year, you would notice that is varies considerably. It cannot, however, be located everywhere in the night sky, even over the course of a year. To understand why, we need to understand some celestial geometry.

Ecliptic Plane

  1. The ecliptic plane is the plane which a hypothetical line between the Earth and the sun sweeps out over the course of a year. In the image above, you can see how the Earth's orbit exists within this plane.

  2. Also notice that the line from the Earth's geographic south pole through its north pole (its rotational axis) is not perpendicular to this ecliptic plane. In fact it is 23.5 degrees off this perpendicular direction.

  3. Notice that the Earth's rotational axis points in the same direction regardless of which side of the Sun the Earth is currently on. This rotational axis always points towards the star Polaris. This means that on different parts of the year, the sun will rise at varying points along the horizon.

  4. The Earth's equatorial plane is a plane defined to extend out from the Earth's equator in all directions. This plane is inclined relative to the ecliptic plane by 23.5 degrees (the same amount as the rotational axis is tilted relative to the perpendicular direction of the ecliptic plane).

Earth Moon System

Now consider the Earth moon system. In order to determine how far North or South the moon can appear to rise from, you need to consider the angle between the Earth's equatorial plane and the moon's orbital plane. Since the Earth's rotational axis is inclined 23.5 degrees relative to the ecliptic, and the Moon's orbit is inclined 5.14 degrees relative to the ecliptic, the highest the Moon's orbit can be relative to the equatorial plane of the Earth is 28.64 degrees.

Thus, the Moon cannot be directly overhead of any point on the surface of the Earth if that point is 28.64 degrees above or (by an symmetric argument) below the equator.

Thus, the Moon cannot appear in every location in the sky for a given location on Earth. There are parts of the sky that the geometry of the Earth moon system simply will not permit the Moon to exist.

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The Moon can appear in only about 48% of the sky* of a stationary Earth observer. The moon must be at least 61.4 degrees away from the celestial poles, such as the one near the North Star.

enter image description here

Compared with the sun, which must always be more than 66.6 degrees from the poles (40% of the sky), the moon has just a little more room to travel in the 'dome' of your sky, a little higher than the summer solar arc, a little lower than winter's.

To visualize what portion of your sky can have a moon in it, start by visualizing the celestial equator. That's the arc the sun appears to travel on the equinoxes. Here's that arc in the sky of someone at middle north latitudes.

enter image description here

The moon must be within about 28.6 degrees north or south of that equatorial arc.

The 28.6 figure adds the Earth's axial tilt - the famous angle between Earth's spin and orbit, 23.437 degrees - to the angle between the Moon and Earth's orbits, 5.145 degrees.

So imagine a 57.2 degree band across your sky (28.6 doubled), along the celestial equator. The sun is confined to a similar 46.9 degree band. Here's a visual for this kind of segment of your celestial sphere.

enter image description here

In this figure which I also just stole off the interwebs, the sphere does not represent Earth, it represents your sky, without the Earth in the way. O is you, call it the Observer, and the angle between the red lines is 57.2 degrees. And you need to imagine this tilted to the same extent as the equator in your sky.

This shows that at latitudes higher than 61.4 degrees (90 minus 28.6), the moon could appear anywhere on your horizon.

*48% is the sine of 28.6 degrees. That surprisingly simple calculation is the portion of the sky taken up by an equatorial band, based on the area of a spherical segment, $2\pi R h$ divided by the area of a hemisphere $2 \pi R^2$, which is $h / R$ or the sine of the angle. That's for a pole observer, but whether at the pole, the equator, or anywhere in between, you can see about half the band and half the sky.

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  • $\begingroup$ I haven't accepted an answer yet. I only joined Astronomy yesterday and I am amazed at the interest in my question. While Unique Worldine answered incredibly quickly and is informative and is getting the most upvotes, this answer is giving me a better understanding because it shows the 'bands' that the Sun and Moon are limited to. $\endgroup$ – Donagh McCarthy Mar 14 '17 at 21:54
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    $\begingroup$ Welcome, @DonaghMcCarthy! Your question struck a chord. (Hey that's almost a pun.) I'd been thinking about this band-across-the-sky thing for years, so when I saw your question under Hot Network Questions I jumped at the chance to write it up. Of course the Earth is no longer fashionably at the center of the universe, but for living on Earth and looking up at the sky it can help to go back to thinking that way. $\endgroup$ – Bob Stein Mar 14 '17 at 23:42
  • $\begingroup$ Thank you @BobStein - I don't get the impression that you view me as some kind of naive "watcher of the skies" but rather as a keen observer from the Earth-bound view. Sure, I follow the developments in the discovery of exoplanets an' all but my question was inspired, I think, by the mindset of Eratosthenes and the wonderful thinking he was capable of. Geometry at an astronomical level is extremely pleasing, is it not? $\endgroup$ – Donagh McCarthy Mar 16 '17 at 21:33
  • $\begingroup$ Heartily agreed, @DonaghMcCarthy. We need a fake news article that Saint Patrick was really Eratosthenes, so that on this day when I am wearing a green hat with a red beard, we would also discuss Green's Spherical Astronomy and red moons. $\endgroup$ – Bob Stein Mar 17 '17 at 14:33
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No, it cannot.

Let me elaborate. If the Moon was orbiting around the Earth in the plane of the ecliptic (the plane containing the orbit of the Earth around the Sun), then it would be obvious that the Sun and Moon would follow the same path. However, both planes are tilted by approximately 5°. This means that the Moon's location is constrained to a small band on both sides of the ecliptic.

Note that due to a phenomenon called the diurnal parallax (the Sun and Moon are not at infinity), their location on the sky depends slightly on the location of the observer on Earth.

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  • $\begingroup$ But how do you know for someone on the Equator, over the course of the year, the Moon doesn't pass through every point of the sky? The natural variations of the direction of the tilt and the orbit of the Moon allow it for being over a pretty wide range of locations. Note I'm not saying you're wrong, just remarking that more explanation is necessary to really show it can't be at all possible locations for some observers on Earth. $\endgroup$ – zephyr Mar 13 '17 at 18:21
  • $\begingroup$ If you consider the example you suggested, a person on the equator, they can only see the moon go as far North as about 28 degrees relative to a point directly overhead. This, there is a wide tangle of angles further North that cannot contain the Moon, ever. $\endgroup$ – Unique Worldline Mar 13 '17 at 19:16
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A lot of the debate in the answers and comments arises from the ambiguity in the OP's phrase the Dome of the Sky. It depends whether you think this means the Sky Above Your Head or the Celestial Dome That is Fixed to the Stars.

The Sky Above Your Head depends on where you are in the world. If you go to the equator, you will, on occasion, see the Moon directly overhead, at the zenith. If you go the North Pole, you will never see it there. If you follow this interpretation, the answer is certainly yes since you are taking the Moon's possible track over time and painting it over the whole sky as you move about. This seems to me a peculiarly pedantic position.

The Celestial Dome doesn't care where you are and the question becomes can the Moon occlude every star in the sky? Here the answer is obviously no. There are broad circumpolar regions of the Northern and Southern sky where the Moon cannot go. The Moon can never appear in Ursa Major, for example.

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    $\begingroup$ Point well made. My knowledge of astronomical terms is clearly deficient. My term 'dome of the sky' should read Celestial Dome. $\endgroup$ – Donagh McCarthy Mar 14 '17 at 11:53

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