GEK 1506:
Heavenly Mathematics Cultural Astronomy
Moon Homework
Proudly presented by Group 9
Chaw Jia Hui U040988L
Chua Shu Hui U041166E
Chua Yan Ru U042814H
Ng Ling Fong U044640R
Brief Description of this homework
Our group is interested in the moon phases over the course of one lunar month. In this report, we will include pictures of the moon taken on different days of the
Chinese calendar (from the new moon on 4th September to the waning crescent on 24th September), the observations, and the method we used to determine the
altitude-azimuth coordinates. To conclude our report, we will attempt to explain our observations.
Method used to estimate the Azimuth
We used a compass to measure the Azimuth. We first align the compass needle such that it points to the North marking on the compass. Then, we read off the
number of degrees North that we spotted the moon from the degrees calibrated on the compass. The degrees are calibrated such that 0o coincides with North and
increases in a clockwise direction.
Method used to estimate the Altitude
We used the ‘hand method’ to measure the altitude. Stretching out our arm straight and starting from the horizon, we will stack one clenched fist on top of each
other. When we are getting near the moon, we will use our fingers instead. The table below illustrates how the ‘hand method’ is used to estimate angles.
10 degrees
Clenched Fist
2 degrees
Thumb
1 degree
Pinky Finger
Hence, if we have 3 clenched fists, it means that the altitude of the moon is 30 degrees. If on top of the 3 fists, we have to add on a pinky finger or a thumb, it will
be 31 degrees and 32 degrees respectively.
Mon
Tues
Wed
Thurs
1
Fri
2
Sat
3
Sun
4
八月
September
5
初二
6
初三
7
初四
8
初五
9
初六
10
初七
11
初八
12
初九
13
初十
14
十一
15
十二
16
十三
17
十四
18
十五
24
二十一
25
二十二
19
十六
20
十七
21
十八
22
十九
23
二十
26
二十三
27
二十四
28
二十五
29
二十六
30
二十七
LEGEND:
1st 4 Days
1st Quarter
Full Moon
3rd Quarter
Pictures of our moon
Across the dark boundless sky …
1st Observation
Date: 4th Sept
Age: 初一
Time: 7.30pm
Altitude: nil
Azimuth: nil
Location: Outside Central Library
Description:
We can’t see the new moon at all.
Look right there!!
2nd Observation
Date: 5 Sept
Age: 初二
Time: 7.40pm
Altitude: 20˚ (2 fists)
Azimuth: 258˚ SW
Location: outside central library
Description:
The moon is a waxing crescent and is hardly
visible due to the cloud cover. It’s a bottom
right crescent with a very small
percentage of the moon being
illuminated.
.
Azimuth…
3rd Observation
Date: 6 Sept
Age: 初三
Time: 8.05pm
Altitude: 30˚ (3 fists)
Azimuth: 250˚ SW
Location: School of
Computing 6th storey
Description:
This is a bottom right crescent. Compared
to the previous 2 days, a larger percentage
of the moon is illuminated though the
percentage is still quite small. It is also
a waxing crescent.
4th Observation
Date: 7 Sept
Age: 初四
Time: 7.15pm
Altitude: 31˚ (3 fists 1 pinky finger)
Azimuth: 240˚ SW
Location: outside central library
Description:
The moon is a bottom right crescent.
It is a waxing crescent. Compared to the
first 3 days, a greater part of e moon is
illuminated. It is also much more visible
and well defined. We took the
picture of this moon a few
minutes after sunset.
Hmm is the moon covered
by the clouds? Have to
wait for them to move
away I guess
Eh! The moon is
just over there, not
in the clouds!!
Haha
Mine is better!! Use
my photo!!!
You wish! Mine
is good too!!
*Yawn*
What is all that
for? We’ll just take
both.
First Quarter
5th Observation
5th Observation
Date: 10 Sept
Time: 9.35pm
Age: 初七
Date: 11 Sept
Time: 8.30pm
Age: 初八
Altitude: 50˚ (5 fists)
Location: Bukit Panjang
Azimuth: 230˚ SW
Altitude: 60˚ (6 fists)
Location: Choa Chu Kang
Azimuth: 224˚ SW
Description:
This is a right crescent, with slightly less
than 50% of the moon being illuminated.
The moon curves inwards and is expected
to grow bigger. Though there are clouds
around it, the shape of the moon is still well
defined.
Description:
This is a right crescent, with slightly less
than 50% of the moon being
illuminated. The moon curves inwards.
Compared to the previous day observation,
the moon is almost the same
except that it seems to be a
little bigger.
In the mood for the glowing moon…
6th Observation
Date: 18th Sept
Age: 十五
Time: 9.50pm
Altitude: 31˚ (3 fists 1 pinky finger)
Azimuth: 90˚ E
Location: Chinese Garden
Description: Full moon. 100% of the moon illuminated.
7th Observation
*Yawn*
Luckily I
remember!!
Date: 27 Sept
Age: 二十四
Time: 5:45am
Azimuth: 50˚ NE
Altitude: 50˚ (5 fists)
Location: Toh Guan road
Description:
The moon is a waning crescent with only a small
percentage of the moon being illuminated.
We missed the 3rd quarter and took this
picture a few days after the 3rd quarter
time period. Hence, we only managed
to capture the waning crescent.
Moon Cycle
The following section will summarise the observations we have made and illustrate the moon phases that we have
observed in Singapore. Due to the changing relative positions of the Sun and moon in their daily motions during the lunar
month, the moon we observed before the full moon was closer to the western horizon while that after the full moon was
closer to the eastern horizon. Note that the moon in the diagram depicts the view of the moon from earth, and the
diagrams are not drawn to scale.
HORIZON
W
New Moon
Moon is a few
minutes behind
the Sun
HORIZON
E
W
E
Waxing Crescent
Daily motion of the
moon starts to lag behind
the Sun’s daily motion
For the first day of our observation, the new moon is not visible
because the moon is following closely behind the Sun. As such,
the brightness of the Sun has blocked our view of the moon from
Earth.
From the second, third and fourth-day observations, a young
crescent slowly takes form. As the moon gradually falls behind
the Sun, the young crescent is spotted as night falls.
In the context of Singapore where the horizon is very near the
equator, the moon should be observed as a bottom crescent
theoretically. However, due to the tilt of the ecliptic, there would
be an angle between the moon which follows the ecliptic, and the
daily motion of the Sun when both celestial bodies cross the
horizon. As a result, the crescent tilts a little to the right.
HORIZON
W
HORIZON
E
First Quarter
Moon is 6 hours
behind the Sun
During the first quarter of the lunar cycle, half the moon
would be illuminated. The tilt of the moon is greater to the
right compared to the first four days as the angle between
the Sun and the moon is bigger when they cross the
horizon.
W
Full Moon
Moon is 12 hours
behind the Sun
E
HORIZON
W
Third Quarter
Moon is 6 hours
ahead of the Sun
HORIZON
E
W
Waning Crescent
The moon rises less
than 6 hours before
the Sun
Having missed the third quarter (unfortunately), our group
took picture of the waning crescent instead. It is observed
that the moon is getting closer to the Sun which would soon
mark the end of a lunar cycle and the start of the next lunar
month.
E