What Does the Waxing or Waning Moon Look Like in Different Parts of the World?

The Singapore Flag The Singapore Flag The Singapore Coat of Arms
The Singapore Flag The Reverse Side of the Singapore Flag The Singapore Coat of Arms

Suppose you see a crescent Moon near the horizon. How can you tell if it is a waxing or a waning Moon? In some languages there are mnemonics to help you remember this, but it is important to realize that they all depend on your latitude.

The Singapore flag was adopted in 1959. The crescent Moon is supposed to represents a young nation on
the ascendant, and also the close relationship at the time between Singapore with its ethnic Chinese majority and Malaya with its
Muslim majority. On the front we see a left crescent, while on the back we see a right crescent. So what will a waxing crescent
look like in Singapore, a left or a right crescent? The answer is neither! Near the equator, a waxing crescent will not look like the
crescent on the flag. It will look like the crescent on the coat of arms!

In the northern hemisphere, a waxing crescent will be a right crescent while an waning crescent will be left crescent. In the
southern hemisphere a waxing crescent will be a left crescent while a waning crescent will be a right crescent. In the northern hemisphere the Moon moves clockwise across the sky, while in the southern hemisphere it moves counterclockwise across the sky. So what happens near the equator? The Moon will move in a straight line when seen from above, or straight up and down along an east to west line when seen from the ground. So both the waning and the waxing crescent will be a bottom crescent! In order to tell them apart, you have to think about whether the Moon is in the east or the west and what time it is. Notice that the crescent faces the Sun, so there can never be a top crescent. Notice that this only applies to crescents near the horizon. If the crescent is higher in the sky, there is no natural way to define left or right.

If you look at a young Moon in Singapore, you will see that it is not always straight down. There are two reasons for this. The Moon is on the ecliptic, and when it crosses the horizon, the angle between it and the daily path of the Sun, which is a small circle parallel to the celestial equator, can be up to 23.5 degrees. The angle will be maximal at the time of the equinoxes, while at the time of the solstices, the ecliptic and the celestial equator will be parallel in the sense that their tangent lines will be parallel. In addition the latitude of the Moon can be up to five degrees. (Notice that on the celestial sphere, latitude measures angular separation from the ecliptic, and not from the celestial equator.) I will put up a more detailed explanation of this on the page for my course Heavenly Mathematics & Cultural Astronomy.

Together with Tey Meng Khoon and Frederick H. Willeboordse of CITA (Centre for Information Technology and Applications), I have developed interactive Java applets that I hope will help you understand what the waxing or waning crescent looks like in different parts of the world in the course of the year.

What does the waxing or waning Moon look like in different parts of the world in the course of the year?

A simplified model of the tilt of the waxing or waning Moon in different parts of the world ignores the tilt of the ecliptic, and assumes that the Sun and the Moon both move along the celestial equator. You may want to start out with this applet.

If you prefer to view the applets off-line, you can download them. Just unzip astro-applets.zip, and open astro-applets.html in your browser.

For a simple animation, you can look at A simplified animation of the tilt of the waxing or waning Moon in different parts of the world.

In 2005 I bought a condo called the Spectrum. In their brochure they had the following picture.

As you can tell from the shape of the Moon, they artist is somewhat astronomically-challenged. After I pointed that out to the developer, I got a $4,000 discount. To be honest, it was maybe not just because they felt bad about the bad astronomy. It might have helped that I was standing in the doorway with the check book in my hand and one foot out the door. However, I still believe that it pays to understand the Sun and the Moon when buying real estate!

CrescentWatch Australia is a nice site, but they have a bad moon rising on the top. Can you tell what's wrong with the pictures?

Helmer Aslaksen
Department of Mathematics
National University of Singapore

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