Orbit of the Moon around the Sun

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Orbit of the Moon around the Earth 1 The sidereal month of 27.32 days is the

time for the Moon to make one revolution around the Earth with respect to the stars

The synodic month of 29.53 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

Orbit of the Moon around the Earth 2

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

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

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

19 September 2009

20 September 2009

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

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

Eclipses 3 There are two “eclipse seasons” each

year

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

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

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 + 23.5 and colatitude – 23.5

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 + 23.5 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 - 23.5 at the time of sunset

The Tilt of the Crescent 5 So if the latitude is 0, the angle changes

from 66.5 to 113.5 (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

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!

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

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!