Why is the completely dark disk of the Moon visible on a new moon if the lunar orbit is at an angle to the Earth’s?

Question

As is known, the lunar orbit is inclined to the ecliptic plane at an angle of about 5 degrees. For this reason, the terminator lines of the Earth and the Moon also appear at the same angle, and some of the solar rays reflected from the lunar surface should hit the Earth, allowing even on a new moon to see a small fragment of the Moon, in the form of a narrow luminous strip.

It is possible to see a completely dark disk only if the Earth, Moon and Sun are on the same line, as during an eclipse. Obviously, with an inclined orbit this condition is not satisfied. Why do we see it?

Answer 1

Your diagram is not quite correct. Because the Sun is way in the distance to the right of your picture (about 400 times the Earth-Moon separation), the terminator lines are almost parallel. A rough calculation suggests within 0.15 degrees of parallel. Further, the Earth and Moon are separated by about 70 times the radius of the Earth.

For these reasons, the illuminated strip we might see is very, very narrow indeed and would be hard to pick out in a daylight sky (which is when the new moon is above the horizon), since the illuminated lunar surface isn't much brighter than the daylight sky.

In fact it is just possible (see the picture here) using appropriate photographic equipment to see a very thin illuminated sliver, even when the ecliptic longitude of the Sun and Moon coincide (the definition of new moon), if the elongation (angular separation between Sun and Moon) is large enough at that time.

Answer 2

^{I am confused. Both the title of the question and the last sentence of the question (the one that ends with the question mark) are asking why we do see the dark disk of the moon, and yet both previous answers are responding with why we do not see the bright crescent of the moon. Maybe I am missing something, but here is my attempt to answer what I perceive to be the actual question.}

---

The dark disk of the moon is visible, so obviously, it is not completely dark.

(That is, not as dark as space.)

This means that the dark disk of the moon is illuminated by some light.

Where does this light come from?

It comes from the earth.

So, here is what happens: light travels from the sun to the Earth, gets reflected from the Earth back to the moon, then it gets reflected once more from the moon back to the earth, and then it finally reaches our eyes.

Edit: Thanks to Greg Miller for pointing out in a comment that this is called "Earthshine".

Remember that during new moon the sun is roughly behind the moon from our point of view, which means that from the moon, the earth appears as an almost full disk, so reflection from the earth back to the moon is at its maximum.

Answer 3

Due to shadow hiding effects, the thinner the crescent, the dimmer it is; meanwhile, the glare from the sun makes it even harder to distinguish a faint, small object such as the thin crescent found on the new moon. In conclusion, these factors prevent the naked eye observation of the new moon

Answer 4

A little trigonometry is in order here.

If the Moon has an angular radius of $R$ and it is at an angpe $\theta$ from direct alignment between thecEarth and Sun, then the angular width of the lighted crescent is given by

$R(1-\cos\theta).$

Here we may take $R$ as about $16'$ and $\theta=5.1°$ as its maximium. Then the above formula gives $3.8''$ (3.8 seconds, not minutes).

Wikipedia reports that the resolution of the naked eye us about 1 minute or $60''$, so theproposed crescent width would be under our naked-eye resolution.

As with many other features of the Moon, we can get a better view of this new-Moon crescent with a good pair of binoculars or a small telescope.

Answer 5

I am puzzled by a lot of the other answers, so I may be missing something. But I think the correct answer is that we do not, in fact, see a completely dark disk, except in the case of a solar or lunar eclipse. At the true new moon, which is shown conventionally as a black disk, the moon rises and sets with the sun. That means that it is daytime when the moon is up, and there is no background of stars to be obscured by the moon, and the sky is too bright to see the moon by earthshine.

To be sure, the new moon can be as much as 6° away from the sun in the sky, but it is still civil twilight until the center of the sun is 6° below the horizon. And, as another answer pointed out, in that situation, when the sun has just set (or not yet risen) and the moon is near the horizon, what you see (with the right equipment) is still a crescent.

So, you were right to think it mysterious that you would see a completely dark moon in a non-eclipse situation, because in fact you don't. The geometry never works out.