1. Orbit of the Moon around the SunC

2. Orbit of the Moon around the Earth 1
The sidereal month of days is the time for the Moon to make one revolution around the Earth with respect to the stars
The synodic month of days is the time for the Moon to make one revolution around the Earth with respect to the sun
The synodic month corresponds to the phases of the Moon
The period of rotation of the Moon equals the period of revolution, which is the sidereal month

3. Orbit of the Moon around the Earth 2

4. Orbit of the Moon around the Earth 3
The Moon-Earth plane is tilted 5° with respect to the ecliptic plane, so the latitude of the Moon will always be between -5 and 5
Just like the Sun, the Moon moves backwards with respect to the stars, but much faster, since it makes a complete revolution in a month, instead of a year
So the Moon also moves backwards with respect to the Sun

5. When will the Moon Rise and Set?
The new Moon rises and sets at the same time as the Sun, but is not visible
The first quarter Moon will rise around noon and set around midnight
The full Moon will rise at sunset and set at sunrise
The third quarter Moon will rise at midnight and set at noon
At the quarters, the Moon looks half

6. First Visibility of the Lunar Crescent
Around the time of the new Moon, the small crescent will be washed out by the Sun
When the Sun sets the sky gets darker, but the Moon will set soon after the Sun
If the Moon is at least 24 hours old at the time of sunset, you can realistically hope to see the young crescent

7. 19 September 2009

8. 20 September 2009

9. Eclipses
You will only get an eclipse if the latitude of the Moon is close to zero at the time of the new Moon or full Moon
There are about as many solar eclipses as lunar eclipses, but a total solar eclipse will only be seen in a small area for at most 7 minutes, while a total lunar eclipse will be seen from more than half the Earth for up to more than an hour

10. Eclipses 2
From a given location, you are likely to see a total solar eclipse about once every 400 years, while you will see a total lunar eclipse every couple of years
Another reason why lunar eclipses are more noticeable, is because even a partial lunar eclipse is easily detected, while a partial solar eclipse is easy to miss if you don’t know about it
Mercury and Venus will sometimes transit in front of the Sun, but they are small

11. Eclipses 3
There are two “eclipse seasons” each year

12. The Tilt of the Crescent
When a crescent is near the horizon, it makes sense to talk about the tilt of the crescent
The following discussion makes no sense when the Moon is high in the sky
If we first ignore the obliquity, we can pretend that the monthly motion of the Moon is backwards along the celestial equator
We measure latitude from -90 to +90, which means that the colatitude can range from 0 to 180

13. The Tilt of the Crescent 2
The angle between the celestial equator and the south part of the western horizon equals the colatitude
The celestial equator tilts left in the northern hemisphere and right in the southern hemisphere
On the equator, a waxing crescent will point straight down, in the northern hemisphere, it will be a right crescent and in the southern hemisphere a left crescent

14. The Tilt of the Crescent 3
We will now also consider the obliquity and the fact that the monthly motion of the Moon is backwards along the ecliptic, and not the celestial equator
If we trace the position of the crescent at sunset every day, we will see that it moves backwards along the ecliptic
The angle between the celestial equator and the horizon does not change with time, but the angle between the ecliptic and the left part of the western horizon varies between colatitude and colatitude – 23.5

15. The Tilt of the Crescent 4
When the Sun is at a solstice, the ecliptic is parallel to the celestial equator at the time of moonset, so the tilt of the Moon is the same as discussed above
When the Sun is at the vernal equinox, the angle between the ecliptic and the left part of the western horizon is equal to colatitude at the time of sunset
When the Sun is at the autumnal equinox, the angle between the ecliptic and the left part of the western horizon is equal to colatitude at the time of sunset

16. The Tilt of the Crescent 5
So if the latitude is 0, the angle changes from 66.5 to (which is the same as an angel of 66.5 with the right part of the horizon)
In Singapore, a waxing crescent near the solstices will look like a bottom crescent, a waxing crescent near the vernal equinox will be a slight left crescent while a waxing crescent near the autumnal equinox will be a slight right crescent
The latitude of the Moon complicates it further, but I’m ignoring that for simplicity

17. The Tilt of the Crescent 6
What about a waning crescent?
It is actually quite tricky, and I will only outline it. This last section is only for people who want the whole truth!
Remember that the angle between the left part of the western horizon and the celestial equator is equal to the colatitude
However, in the east, the colatitude is the angle between the celestial equator and the RIGHT part of the horizon!

18. The Tilt of the Crescent 7
So the angle between the left part of the eastern horizon and the celestial equator is 90 + latitude
The vernal equinox will push the ecliptic towards the right in both the east and the west
At the equator, the waning crescent will look just like the waxing crescent

19. The Tilt of the Crescent 8
Off the equator, it will be a bit more complex, since the latitude effect is different, while the ecliptic effect is the same
I challenge you to sort it out for yourself!