# The moon in the first phase visible in the sky is tilted

I never noticed it before that moon I see in the sky is tilted. Does the tilt of the moon in the sky indicate the direction of the Earth's axis and direction of Earth's rotation around the sun?

• This is called the Parallactic angle: en.m.wikipedia.org/wiki/Parallactic_angle Apr 4, 2022 at 14:45
• @GregMiller: Are you sure about that? Parallactic angle seems to describe the orientation of the features of the moon (say, the Sea of Tranquillity), not which part of it is illuminated by the sun. The angle described by OP indeed seems to be related to the parallactic angle, but I don't think they're the same. Apr 4, 2022 at 18:21
• Try this; Look at the tilt of the moon when it rises, then look at it's tilt when it sets. At most latitudes at most times of the year, these will be significantly different. Apr 5, 2022 at 14:19
• @EricDuminil, yes I'm sure. The parallactic angle affects everything, the entire moon appears to rotate based on the angle from due south. Apr 5, 2022 at 14:39
• @GregMiller: We agree that the parallactic angle affects the angle of the crescent, because it affects the entire moon. I don't think the angle of the crescent is the parallactic angle, though. Apr 5, 2022 at 15:08

The moon is lit by the sun, so when the sun is below the horizon, the tips of the crescent moon will point "up" and away from the sun, while the outer bowl will point towards the sun.

This is sometimes hard to recognise because of an optical illusion created by the horizon. We tend to see curves that are parallel to the horizon as "straight", but when I write "point towards the sun" I mean "along a great circle".

The axis of the Earth is consistently pointing towards the North. As I mention in an answer to Tips of Crescent, the tips are not exactly aligned with North or East. The Earth's orbit means it is moving in a direction towards a point that is about 90 degrees behind the sun (in April that means roughly towards Saggitarius). Again, that's not really related to the angle of the moon.

• There's nothing unusual about the angle of the moon in the picture. It does vary from month to month, but not by a lot. Take a look at a simulation in stellarium of similar. That is just how the moon looks when it is a crescent and the sun is below and to the right. Apr 4, 2022 at 20:33
• +1 although if I say it David Hammen downvotes :-)
– uhoh
Apr 4, 2022 at 20:56
• "because of an optical illusion created by the horizon" — not only by the horizon. There's a specific configuration when the Sun may be at (or a bit under) the horizon, while the Moon high in the sky, and in this case the lit part of the Moon will seem to point up instead of down or back. This is explained in my answer here Apr 4, 2022 at 22:21
• "not by a lot". I wrote a script, and was surprised to see the moon tilt vary between -10° and -70° at my location (49°N), for conditions similar to OP's picture. Apr 5, 2022 at 21:10
• @uhoh that's the question I was looking for lmao Apr 5, 2022 at 21:35

I took these cellphone snapshots on the previous two evenings, living nearer the equator than I used to I see slightly unfamiliar things from time to time, like the crescent Moon as a horizontal smiley face and my shadow completely disappearing at local noon in June.

In this answer I link to @DavidHammen's recommended source The Moon Tilt Illusion by Andrea K. Myers-Beaghton and Alan L. Myers which goes into great detail about how the orientation of the Moon's lit side varies.

See also (though they may confuse more than help)

Snapshots of the crescent Moon almost a horizontal smiley face from about 25° N

## The moon tilt was indeed steeper than usual, and the steepest for 2022

I wrote a small script to calculate the moon tilt $$\alpha$$ for every minute of 2022, when those conditions are fulfilled:

• after sunset, during nautical and astronomical twilights, i.e. when the sky is dark enough to clearly see the moon.
• the moon is above the horizon
• its phase angle is between 120° and 140°. This corresponds to a thin crescent, just like in your picture.

I was surprised to see the moon tilt vary between -10° (almost flat) and -60° (clearly pointing towards the ground), even at my latitude (49°N).

The steepest angle in 2022 was indeed a few days ago and a month ago, at -59°:

The flattest angle will be in September, at -12°:

## Variations over the years

I modified the script and let it run for every sunsets between 2000 and 2030, at my location:

The steepest moon tilt happened on 2010-02-17 (at -70°):

The flattest moon tilt happened on 2009-08-23 (at -9°):

## Code

If you're interested, here's the "code" I used to calculate the moon tilt. The program was written in INSEL, which is similar to Simulink:

Another, possibly easier way would be to use Astropy or PyEphem.

• Would you share the script, or at least the library you used for it? I've been wanting to write similar scripts and am looking for a nice API for it (even posted this question on reddit a couple months ago: reddit.com/szsirc ) Apr 6, 2022 at 2:04
• Excellent answer, it's great to know that my feeling that the Moon "looked funny" and taking snapshots of it was somehow warranted. :-)
– uhoh
Apr 6, 2022 at 4:02
• @ChristopherShroba: I've edited the answer. I've used INSEL, a graphical programming language, which only knows the position of the moon and the sun. For your reddit question, I'm pretty sure both astropy and pyephem would work fine, and they can give you the position of millions of objects. Apr 6, 2022 at 7:56
• (1/2) Nice answer. some interesting point: one can literally see the asymmetry of the contribution of the Moon 5 degrees inclination with respect to the ecliptic, to the tilt angle: it is stronger in increasing the tilt than flattening it. It makes sense: if, following the other answer of James K, the tilt is always parallel to the ecliptic than to have no tilt, the Moon most be on the nonagesimal: the highest point on the ecliptic to have no tilt.
– d_e
Apr 6, 2022 at 10:50
• (2/2) even if the Moon has some latitude, it is not going to change because, again, at the nonagesimal the ecliptic is parallel to the horizon, so the Moon earns no bonus from his 5 degrees latitude. It follows that in the night sky (after the Sun already set), in order to see the Moon without tilt, it must be 90 degrees from the Sun at least: for it if is less than 90 degress it means the Moon has already passed the nonagesimal point. All this means that we can't see the Moon less than half full after sunset without tilt.
– d_e
Apr 6, 2022 at 10:52