This blog is managed by Song Hock Chye, author of Improve Your Thinking Skills in Maths (P1-P3 series), which is published and distributed by EPH.

Wednesday, January 23, 2008

Calculating the Phases of the Moon

The first Science topic taught in P5 in most schools is the Solar System. Of all sub-topics within this topic, Phases of the Moon gives students the most headache. Most students find difficulty in calculating the dates of the phases of the moon.

Here is a quick and simple method to make sure you get your dates right.

The moon revolves round the earth in 28-day cycles. In order to calculate the phases of the moon, we must therefore use a 28-day chart.

Note that in Figure 1 below, the beginning of the cycle is “Day 0” and ends at “Day 28”. It does not start at “Day 1” because if you were to start at Day 1 and end at Day 28, you will be creating a 27-day cycle instead of 28.

Days 0 represents the beginning of the cycle, while Day 28 represents the end of the cycle. It also must be noted that Day 0 of the current month is also Day 28 of the previous month. Likewise, Day 28 of the current month, is Day 0 of the next month.

Since Day 28 is the last day of the cycle, Day 14 is considered mid-cycle. Day 7 is hence right in middle of the beginning and mid-cycle, while Day 21 is the middle of the mid-cycle and the end of cycle.

Let us look at Figure 1 again. We start with a full moon at Day 0. At the end of the cycle, Day 28 will also have a full moon. Since Day 14 is mid-cycle, we will experience a new moon. Day 7 is between full moon and new moon, which means, we will experience half moon. Day 21 is between new moon and full moon, which also means we will experience half moon. Note that the half moon on Day 21 is a mirror image of Day 7’s half moon.

Figure 1

We can use actual dates to calculate. Let us suppose that a full moon was spotted on 26 July.

The next full moon will be 28 days from 26 July.

26 days + 28 days = 54 days.

But we know that there is no such thing as 54 days in a month. The last month was July, which has 31 days. We need to subtract 31 days from 54.

54 – 31 = 23

Therefore, the next full moon will be 23 August.

We can also calculate when the new moon will occur. A new moon occurs 14 days after a full moon. Hence,

26 days + 14 days = 40 days

40 – 31 = 9

Therefore, the new moon will occur on 9 Aug.

The half moons are 7 days from 26 July and 9 Aug.

Your turn now. Study Figure 2 below. Can you calculate the various dates? Try to make an attempt before checking the answers.

Figure 2

Day 28 (next new moon) – 17 Dec.
Day 21 (half moon) - 10 Dec
Day 14 (full moon) – 3 Dec
Day 7 (half moon) - 26 Nov

Now try this one. No answers are given this time.

In tomorrow's post, we will take a look at an actual Science question on phases of the moon, and apply what we have learnt today, to answer that question.

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Update: Related post